diff --git a/CHANGELOG.md b/CHANGELOG.md --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -8,6 +8,67 @@ ## Unreleased +## 7.1.0 - 2026-08-21 + +Track the **finished** FSRS-7. Release 7.0.0 implemented the 35-weight, +single-trace draft still published as `models/fsrs_v7.py` in `srs-benchmark`; +the algorithm was subsequently finalised with 34 weights and a dual-trace +memory model, and that is what "FSRS-7" now means. The reference is +[`Expertium/fsrs-rs-speed-autoresearch`](https://github.com/Expertium/fsrs-rs-speed-autoresearch), +upstreamed into `fsrs-rs` in +[PR #426](https://github.com/open-spaced-repetition/fsrs-rs/pull/426). + +This is a breaking change to the model's numbers and to several signatures. +Stored parameter vectors and stored memory states from 7.0.0 are **not** +compatible. + +### Changed + +- `parameterCount` is now `34`, and `defaultParameters`, `parameterBounds` and + `orderingConstraints` are the finished model's. The layout is: `w0..w3` + initial stability, `w4..w6` difficulty, `w7..w14` slow-trace stability, + `w15..w22` fast-trace stability, `w23..w30` forgetting curve, `w31..w33` the + curve's modulation by difficulty and stability. +- `MemoryState` gained a third field, `memoryStabilityFast`: FSRS-7 tracks two + memory traces. A new card's fast trace starts at `fastTraceRatio` (0.8) of + its slow one. +- `retrievability`, `retrievabilityDerivative` and `nextIntervalDays` take a + whole `MemoryState` instead of a `Stability` — the curve mixes both traces + and is shaped by the difficulty too. So does `nextReviewInterval`. +- `retrievability` is rescaled into `[1e-5, 1 - 1e-5]`, so `retrievability p 0` + is now just short of `1` rather than exactly `1`. +- `nextDifficulty` takes the retrievability at review time: a lapse's step is + weighted by how surprising the lapse was. +- `stabilityAfterReview` takes a stability and a difficulty rather than a + `MemoryState`, since it now applies to whichever trace is being updated, and + its post-lapse branch no longer depends on difficulty. +- `nextStability` returns both traces as a `(slow, fast)` pair. +- `longTermWeights` / `shortTermWeights` are now `slowTraceWeights` / + `fastTraceWeights`, and `StabilityWeights` lost + `swFailureDifficultyExponent` — the weight it read was ablated from both + blocks. +- `CurveWeights` was reshaped: `cwDecay1` became `cwDecayBase1` (the fast + component's decay is now scaled by the fast stability, so it is not a + constant), `cwDecay2` holds a magnitude rather than a negated value, and + `cwDifficultyWeight`, `cwDifficultyDecay` and `cwStabilityDecay1` are new. + +### Added + +- `fastTraceRetrievability` — the fast trace's own recall probability, which is + what drives its stability update. +- `initialMemoryState` — the state a card is born with. +- `retrievabilityFloor` and `fastTraceRatio`. +- `orderingConstraints` is now exported from `FSRS.Parameters`. +- The two numeric assertions the reference implementation makes about FSRS-7 in + its own test suite are now reproduced in ours, in Haskell and in Python, so + the port is pinned to upstream and not only to our own transcription. + +### Removed + +- `transitionCoefficient`, `transitionRate` and `transitionAmplitude`, along + with the two weights behind them. The elapsed-time blend between a long- and + a short-term stability update is gone; the fast memory trace replaces it. + ## 7.0.0 - 2026-08-20 Initial release: FSRS-7. @@ -16,7 +77,8 @@ - `FSRS.Types` — `Rating`, `MemoryState` and the `Stability` / `Difficulty` / `Retrievability` / `Days` synonyms. -- `FSRS.Parameters` — the 35 FSRS-7 weights, the default set, bounds taken from +- `FSRS.Parameters` — the 35 FSRS-7 weights (of the draft model, see 7.1.0), + the default set, bounds taken from the upstream optimiser's clipper, validation with per-weight errors, clamping, and typed views onto the weight blocks (`StabilityWeights`, `CurveWeights`). - `FSRS.Algorithm` — the model: the two-component `retrievability` curve and its diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -7,10 +7,12 @@ model behind Anki's scheduler. FSRS predicts when you are about to forget a flashcard so it can be shown to -you just before that happens. It tracks two numbers per card: +you just before that happens. It tracks three numbers per card: - **stability** — the memory's half-life, in days; - **difficulty** — how hard this particular card is for you, on a 1–10 scale; +- a second, faster-decaying **stability** — FSRS-7 tracks two memory traces, + which is how it tells a review minutes later apart from one weeks later; and derives **retrievability**, the probability that you can recall the card right now. @@ -20,21 +22,34 @@ ## What is new in FSRS-7 -FSRS-7 has **35 parameters**, up from FSRS-6's 21. Three things changed: +FSRS-7 has **34 parameters**, up from FSRS-6's 21. What changed: -- **The forgetting curve is a mixture of two power laws** rather than one, with - the mixing weights themselves depending on stability. That is where six of - the new parameters go, and it means the curve has no closed-form inverse — so - computing an interval is a root-find, not a formula. -- **The stability update runs twice**, once with a long-term weight block and - once with a short-term one, and the two are blended by a smooth transition - function of the elapsed time. FSRS-6 instead switched between two separate - formulas on a same-day / not-same-day flag. +- **A card has two memory traces, not one.** Alongside the familiar stability + there is a second, faster-decaying one, and each is updated by its own block + of eight weights — the slow trace from the mixed retrievability, the fast + trace from its own. This is what makes same-day reviews behave differently + from spaced ones, where FSRS-6 switched between two formulas on a same-day / + not-same-day flag. +- **The forgetting curve is a mixture of two power laws** rather than one, one + per trace, with the mixing weights depending on the traces' own stabilities. + The curve has no closed-form inverse, so computing an interval is a + root-find, not a formula. +- **The forgetting curve depends on difficulty**, which it never did in any + earlier version: a hard card experiences time faster, and leans more on its + slow trace. +- **Post-lapse stability no longer depends on difficulty**, and a lapse's + difficulty step is weighted by how *surprising* the lapse was — forgetting a + card you were expected to recall says more about it than forgetting one that + was long overdue. - **Intervals are genuinely continuous.** Every earlier version was designed around whole-day intervals; FSRS-7 is the first that gives realistic predictions for same-day reviews. Ten minutes is `10 / 1440` days and the model means it. +One consequence worth knowing: retrievability is rescaled into +`[1e-5, 1 - 1e-5]`, so a card reviewed a moment ago has a retrievability just +short of `1` rather than exactly `1`. + ## Getting started ```console @@ -55,13 +70,16 @@ -- When should it come back, if we want a 90% chance of recall? whenDue :: Days -whenDue = nextIntervalDays defaultParameters 0.9 (memoryStability secondReview) +whenDue = nextIntervalDays defaultParameters 0.9 secondReview -- How likely are we to recall it three days from now? odds :: Retrievability -odds = retrievability defaultParameters 3 (memoryStability secondReview) +odds = retrievability defaultParameters 3 secondReview ``` +Both take the whole `MemoryState`, not just a stability: the FSRS-7 curve mixes +the two traces and is shaped by the difficulty too. + Whole-card scheduling — learning steps, due dates, lapses, fuzz — lives in `FSRS.Scheduler`: @@ -76,7 +94,7 @@ `reviewCardFuzzed` and hand it the random sample yourself, so scheduling stays a pure function of its inputs. -Optimising the 35 weights against a user's own review history is *not* part of +Optimising the 34 weights against a user's own review history is *not* part of this package. Use the upstream optimiser and feed the result to `mkParameters`. ### Modules @@ -85,25 +103,25 @@ | --- | --- | | `FSRS` | Re-exports everything below. | | `FSRS.Types` | `Rating`, `MemoryState`, the type synonyms. | -| `FSRS.Parameters` | The 35 weights, their bounds, validation, typed views onto the blocks. | +| `FSRS.Parameters` | The 34 weights, their bounds, validation, typed views onto the blocks. | | `FSRS.Algorithm` | The model: forgetting curve, difficulty, stability, interval inversion. | | `FSRS.Scheduler` | Cards, due dates, learning steps, fuzz. | ## Provenance -`FSRS.Algorithm` is a transcription of the reference implementation the -upstream authors benchmark against: -[`srs-benchmark`](https://github.com/open-spaced-repetition/srs-benchmark), -`models/fsrs_v7.py` and `models/fsrs_v7_interval_penalty.py` (revision -`8c11619`). +`FSRS.Algorithm` is a transcription of the **finished** FSRS-7, whose reference +implementation is the Rust model the algorithm's author signed off on: +[`Expertium/fsrs-rs-speed-autoresearch`](https://github.com/Expertium/fsrs-rs-speed-autoresearch) +(`fsrs-rs/src/model.rs`, `PARAM_LEN = 34`), upstreamed into `fsrs-rs` in +[PR #426](https://github.com/open-spaced-repetition/fsrs-rs/pull/426). -Two things are worth knowing about the default weights: +Two things are worth knowing about the weights: -- The published defaults use **1.3** for `w15` and `w24`, the easy bonus of the - two stability blocks. The `Default Parameters` section of the `srs-benchmark` - README still lists `1.15`; that block has not been touched since 2026-03-18, - while the model itself was changed to `1.3` three days later (commit - `e274ac3`). This package follows the model. +- Indices 31–33 follow the reference's all-positive storage convention: they + are stored shifted so that their range starts at zero, and the formulas + offset them back (`w - 0.5` for the difficulty weight, `w - 0.3` for the two + decay modulators). `parametersToList` gives you the stored values, which is + what an upstream optimiser produces and consumes. - The parameter bounds in `parameterBounds` come from the clipper the upstream optimiser applies after every gradient step, so any weights a real optimiser produces will satisfy them. @@ -115,24 +133,36 @@ ## Tests -Two complementary suites, 113 test cases in all: +Three complementary suites, 126 test cases in all: -- **Golden vectors** — 2,589 of them, covering every function of the model +- **Golden vectors** — 5,586 of them, covering every function of the model across three parameter sets, generated by `reference/fsrs7_reference.py`, a pure-Python transcription of the same upstream source. Both implementations perform the same floating-point operations in the same order, so they are checked to a relative tolerance of `1e-12`. +- **Upstream fixtures** — the two numeric assertions the reference + implementation makes about FSRS-7 in its own test suite + (`test_memory_state_fsrs7` and `test_next_interval_fsrs7`), reproduced + verbatim. These are the only fixtures in the package that did not come out of + our own transcription, so they are what pins the port to upstream rather than + to itself. - **Properties** — invariants that should hold for *every* parameter vector inside the valid box: retrievability is a probability and decreases with - time, a better rating never means less stability, difficulty stays in range - however long the history, the interval solver really does land on the desired - retention, and so on. + time, a better rating never means less stability, post-lapse stability + ignores difficulty, difficulty stays in range however long the history, the + interval solver really does land on the desired retention, and so on. -A few properties hold only for well-behaved weights and say so. Because -FSRS-7 re-weights its two power laws by stability, adversarial-but-in-bounds -weights can make retrievability *fall* as stability grows; the properties about -how the model responds to stability are therefore stated for -`defaultParameters`. +A few properties hold only for well-behaved weights and say so. Two kinds of +caveat show up: + +- Because FSRS-7 re-weights its two power laws by stability, + adversarial-but-in-bounds weights can make retrievability *fall* as stability + grows. Those properties are stated for `defaultParameters`. +- Difficulty pulls the curve two ways — it speeds the slow component up, but + also shifts mixing weight onto the fast one. At the trace ratio the model + itself maintains the first effect wins; for an arbitrarily lopsided pair of + traces neither does. Properties about difficulty and about stability are + therefore stated over states at that ratio. To regenerate the golden vectors after touching the reference: diff --git a/haskell-fsrs.cabal b/haskell-fsrs.cabal --- a/haskell-fsrs.cabal +++ b/haskell-fsrs.cabal @@ -3,7 +3,7 @@ name: haskell-fsrs -- The major version tracks the algorithm version, as py-fsrs and fsrs-rs do: -- 7.x.y implements FSRS-7. -version: 7.0.0 +version: 7.1.0 synopsis: FSRS-7, the Free Spaced Repetition Scheduler description: A Haskell implementation of FSRS-7, the seventh version of the Free Spaced @@ -11,9 +11,13 @@ forget a flashcard, so it can be shown to you just before that happens. . The model itself lives in "FSRS.Algorithm" and is a direct transcription of - the reference implementation used by the upstream benchmark. A card - scheduler built on top of it — learning steps, due dates, lapses, fuzz — - lives in "FSRS.Scheduler". Import "FSRS" for everything at once. + the finished FSRS-7 reference implementation. A card scheduler built on top + of it — learning steps, due dates, lapses, fuzz — lives in + "FSRS.Scheduler". Import "FSRS" for everything at once. + . + FSRS-7 has 34 weights and tracks two memory traces per card; see the + changelog if you are upgrading from 7.0.0, which implemented an earlier + 35-weight draft. homepage: https://github.com/kutyel/haskell-fsrs#readme bug-reports: https://github.com/kutyel/haskell-fsrs/issues diff --git a/reference/fsrs7_reference.py b/reference/fsrs7_reference.py --- a/reference/fsrs7_reference.py +++ b/reference/fsrs7_reference.py @@ -1,138 +1,203 @@ """Pure-Python transcription of the FSRS-7 memory model. -Transcribed line-by-line from the reference implementation used by the official -benchmark: +Transcribed line-by-line from the *finished* FSRS-7, whose reference +implementation is the Rust model the algorithm's author signed off on: - https://github.com/open-spaced-repetition/srs-benchmark - models/fsrs_v7.py (rev 8c11619, 2026-08-04) - models/fsrs_v7_interval_penalty.py (same rev) + https://github.com/Expertium/fsrs-rs-speed-autoresearch + fsrs-rs/src/model.rs (PARAM_LEN = 34, "DUAL-TRACE ... finished FSRS-7") + fsrs-rs/src/inference.rs (DEFAULT_PARAMETERS) -The benchmark implementation is written in PyTorch; this file reproduces the -exact same scalar arithmetic with the standard library only, so that it can be -used to generate golden vectors for the Haskell port without pulling in torch. +and its scalar port in the fsrs-rs pull request that upstreams it: + + https://github.com/open-spaced-repetition/fsrs-rs/pull/426 + src/model_v7.rs, src/parameter_clipper_v7.rs + +The reference is written with tensors; this file reproduces the exact same +scalar arithmetic with the standard library only, so that it can be used to +generate golden vectors for the Haskell port without pulling in torch. + +What the finished model changed relative to the 35-parameter draft: + +* The single memory trace became *two*. A card carries a slow stability and a + fast one, and the forgetting curve is a mixture of a fast and a slow recall + component. This replaces the draft's `transition_function`, which blended a + long- and a short-term stability update by elapsed time; the two weights that + parameterised it are gone. +* Post-lapse stability lost its `d ** -fail_d_exp` factor in both stability + blocks — it is now difficulty-independent — so each block has eight weights + instead of nine. +* The forgetting curve gained three weights that modulate it by difficulty and + stability, and it now depends on difficulty at all, which it never did before. +* A lapse's difficulty step is weighted by how surprising the lapse was. +* Retrievability is rescaled into `[1e-5, 1 - 1e-5]`, so a card reviewed at + `t == 0` has recall probability `1 - 1e-5` rather than exactly `1`. """ import math -# w[15] / w[24] (the "easy bonus" of the long-/short-term blocks) are 1.3 here. -# The srs-benchmark README still lists 1.15 for those two weights, but that -# block of the README has not been touched since 2026-03-18 while the code was -# updated to 1.3 on 2026-03-21 (commit e274ac3, "Update FSRS-7"). The code wins. +# Indices 31..33 follow the reference's all-positive storage convention: they +# are stored shifted so that their range starts at zero, and the formulas below +# offset them back (`w - 0.5` for the difficulty weight, `w - 0.3` for the two +# decay modulators). DEFAULT_PARAMETERS = [ # Initial stability, indexed by rating - 1 - 0.041, 2.4175, 4.1283, 11.9709, + 0.1104, 2.2395, 3.9221, 11.7841, # Difficulty - 5.6385, 0.4468, 3.262, - # Stability, long-term block - 2.3054, 0.1688, 1.3325, 0.3524, 0.0049, 0.7503, 0.0896, 0.6625, 1.3, - # Stability, short-term block - 0.882, 0.3072, 3.5875, 0.303, 0.0107, 0.2279, 2.6413, 0.5594, 1.3, - # Long/short-term transition function - 2.5, 1.0, + 6.1686, 0.6457, 3.6807, + # Stability, slow trace + 1.9795, 0.0, 1.3826, 0.7024, 0.5999, 0.8146, 0.6398, 1.0, + # Stability, fast trace + 1.3207, 0.6707, 3.8668, 0.4416, 0.0934, 1.8631, 0.6162, 1.0869, # Forgetting curve - 0.0723, 0.1634, 0.5, 0.9555, 0.2245, 0.6232, 0.1362, 0.3862, + 0.1567, 0.0801, 0.2421, 0.9464, 0.1433, 0.7145, 0.0, 0.5667, + # Forgetting-curve modulation by difficulty and stability + 0.3734, 0.5333, 0.3048, ] LOWER_BOUNDS = [ 0.0001, 0.0001, 0.0001, 0.0001, 1.0, 0.001, 0.1, - 0.0, 0.0, 0.3, 0.01, 0.001, 0.1, 0.0, 0.0, 1.0, - 0.0, 0.0, 0.5, 0.001, 0.001, 0.001, 0.0, 0.0, 1.0, - 2.5, 0.0, - 0.01, 0.01, 0.5, 0.5, 0.01, 0.1, 0.0, 0.1, + 0.0, 0.0, 0.3, 0.01, 0.1, 0.0, 0.0, 1.0, + 0.0, 0.0, 0.5, 0.001, 0.001, 0.0, 0.0, 1.0, + 0.01, 0.01, 0.2, 0.5, 0.01, 0.1, 0.0, 0.1, + 0.0, 0.0, 0.0, ] UPPER_BOUNDS = [ 50.0, 100.0, 100.0, 100.0, 10.0, 4.0, 4.0, - 4.0, 1.2, 3.0, 1.5, 0.9, 1.0, 3.5, 1.0, 7.0, - 4.0, 2.0, 6.0, 1.5, 2.0, 1.0, 5.0, 1.0, 7.0, - 15.0, 1.0, + 4.0, 1.2, 3.0, 1.5, 1.0, 3.5, 1.0, 7.0, + 4.0, 2.0, 6.0, 1.5, 1.0, 5.0, 1.0, 7.0, 0.25, 0.95, 0.85, 0.99, 1.0, 1.0, 0.9, 1.1, + 1.0, 0.6, 0.6, ] -STABILITY_MIN = 0.0001 # config.s_min for FSRS-7 (always run with --secs) -STABILITY_MAX = 36500.0 # config.s_max -MIN_DIFFICULTY = 1.0 -MAX_DIFFICULTY = 10.0 +STABILITY_MIN = 0.0001 # S_MIN +STABILITY_MAX = 36500.0 # S_MAX +MIN_DIFFICULTY = 1.0 # D_MIN +MAX_DIFFICULTY = 10.0 # D_MAX MIN_INTERVAL = 1.0 / 86400.0 # one second, in days MAX_INTERVAL = 36500.0 # one hundred years, in days -LONG_TERM_BASE = 7 -SHORT_TERM_BASE = 16 +# Where each trace's block of eight stability weights starts. +SLOW_TRACE_BASE = 7 +FAST_TRACE_BASE = 15 +# The fast trace starts at, and after a lapse is capped at, this fraction of +# the slow one. +FAST_TRACE_RATIO = 0.8 +# Retrievability is squeezed into [RETENTION_FLOOR, 1 - RETENTION_FLOOR] so +# that neither it nor its logarithm can saturate. +RETENTION_FLOOR = 1e-5 + +# The exponent of `factor1` is built in log space and capped here so that both +# the value and its gradient stay finite. +LOG_FACTOR_CAP = 60.0 + +# The magnitude of either decay is held inside this range. +DECAY_MIN = 0.01 +DECAY_MAX = 0.95 + + def clamp(x, lo, hi): return min(max(x, lo), hi) # -------------------------------------------------------------------------- -# Forgetting curve: a stability-weighted mixture of two power laws. +# Forgetting curve: a mixture of a fast-trace and a slow-trace power law. # -------------------------------------------------------------------------- -def forgetting_curve(w, t, s): - """Probability of recall after `t` days with stability `s` days.""" - decay1 = -w[-8] - decay2 = -w[-7] - base1, base2 = w[-6], w[-5] - base_weight1, base_weight2 = w[-4], w[-3] - swp1, swp2 = w[-2], w[-1] +def fast_component_recall(w, t, s_fast): + """The fast trace's own recall probability after `t` days. - t_over_s = t / s + Shared by the forgetting curve, as its fast component, and by the + fast-trace stability update, which reads this rather than the mixture. + """ + t = max(t, 0.0) + s_fast = clamp(s_fast, STABILITY_MIN, STABILITY_MAX) + decay1 = -clamp(w[23] * s_fast ** (w[33] - 0.3), DECAY_MIN, DECAY_MAX) + factor1 = math.exp(min(math.log(w[25]) / decay1, LOG_FACTOR_CAP)) - 1.0 + return (1.0 + factor1 * (t / s_fast)) ** decay1 - def power_law_retention(base, decay): - factor = base ** (1.0 / decay) - 1.0 - return (1.0 + factor * t_over_s) ** decay - r1 = power_law_retention(base1, decay1) - r2 = power_law_retention(base2, decay2) +def _curve_parts(w, t, state): + """The pieces of the mixture, shared by the curve and its derivative.""" + t = max(t, 0.0) + s = clamp(state[0], STABILITY_MIN, STABILITY_MAX) + d = clamp(state[1], MIN_DIFFICULTY, MAX_DIFFICULTY) + s_fast = clamp(state[2], STABILITY_MIN, STABILITY_MAX) - weight1 = base_weight1 * s ** -swp1 - weight2 = base_weight2 * s ** swp2 + # Fast component: decay modulated by the fast stability itself. + decay1 = -clamp(w[23] * s_fast ** (w[33] - 0.3), DECAY_MIN, DECAY_MAX) + factor1 = math.exp(min(math.log(w[25]) / decay1, LOG_FACTOR_CAP)) - 1.0 + inner1 = 1.0 + factor1 * (t / s_fast) - return (weight1 * r1 + weight2 * r2) / (weight1 + weight2) + # Slow component: difficulty rescales *time* rather than the decay, so a + # hard card experiences time faster but decays with the same slope. + decay2 = -clamp(w[24], DECAY_MIN, DECAY_MAX) + factor2 = w[26] ** (1.0 / decay2) - 1.0 + d_timescale = math.exp((d - 5.0) * (w[32] - 0.3)) + inner2 = 1.0 + factor2 * d_timescale * (t / s) + # Mixture weights, one keyed to each trace; the slow one is also modulated + # by difficulty. + weight1 = w[27] * s_fast ** -w[29] + weight2 = w[28] * s ** w[30] * math.exp((d - 5.0) * (w[31] - 0.5)) -def forgetting_curve_derivative(w, t, s): - """dR/dt of `forgetting_curve`; always <= 0 for in-bounds parameters.""" - decay1 = -w[-8] - decay2 = -w[-7] - base1, base2 = w[-6], w[-5] - base_weight1, base_weight2 = w[-4], w[-3] - swp1, swp2 = w[-2], w[-1] + return ( + decay1, factor1, inner1, s_fast, + decay2, factor2 * d_timescale, inner2, s, + weight1, weight2, + ) - c1 = base1 ** (1.0 / decay1) - 1.0 - c2 = base2 ** (1.0 / decay2) - 1.0 - t_over_s = t / s - i1 = 1.0 + c1 * t_over_s - i2 = 1.0 + c2 * t_over_s - weight1 = base_weight1 * s ** -swp1 - weight2 = base_weight2 * s ** swp2 +def forgetting_curve(w, t, state): + """Probability of recall after `t` days, given a `(S, D, S_fast)` state.""" + ( + decay1, _factor1, inner1, _s_fast, + decay2, _factor2, inner2, _s, + weight1, weight2, + ) = _curve_parts(w, t, state) - d1 = decay1 * i1 ** (decay1 - 1.0) * (c1 / s) - d2 = decay2 * i2 ** (decay2 - 1.0) * (c2 / s) - return (weight1 * d1 + weight2 * d2) / (weight1 + weight2) + r1 = inner1 ** decay1 + r2 = inner2 ** decay2 + retention = (weight1 * r1 + weight2 * r2) / (weight1 + weight2) + return retention * (1.0 - 2.0 * RETENTION_FLOOR) + RETENTION_FLOOR -def next_interval(w, desired_retention, s): - """Invert the forgetting curve: the t with R(t, s) = desired_retention. +def forgetting_curve_derivative(w, t, state): + """dR/dt of `forgetting_curve`; always <= 0 for in-bounds parameters.""" + ( + decay1, factor1, inner1, s_fast, + decay2, factor2, inner2, s, + weight1, weight2, + ) = _curve_parts(w, t, state) + d1 = decay1 * inner1 ** (decay1 - 1.0) * (factor1 / s_fast) + d2 = decay2 * inner2 ** (decay2 - 1.0) * (factor2 / s) + derivative = (weight1 * d1 + weight2 * d2) / (weight1 + weight2) + return derivative * (1.0 - 2.0 * RETENTION_FLOOR) + + +def next_interval(w, desired_retention, state): + """Invert the forgetting curve: the t with R(t, state) = desired_retention. + The mixture has no closed-form inverse. R is strictly decreasing in t, so a bisection on [MIN_INTERVAL, MAX_INTERVAL] converges to full double precision; this is the value the Haskell root-finder is checked against. """ lo, hi = MIN_INTERVAL, MAX_INTERVAL - if forgetting_curve(w, lo, s) <= desired_retention: + if forgetting_curve(w, lo, state) <= desired_retention: return lo - if forgetting_curve(w, hi, s) >= desired_retention: + if forgetting_curve(w, hi, state) >= desired_retention: return hi for _ in range(200): mid = math.sqrt(lo * hi) # bisect in log space if mid <= lo or mid >= hi: break - if forgetting_curve(w, mid, s) > desired_retention: + if forgetting_curve(w, mid, state) > desired_retention: lo = mid else: hi = mid @@ -157,10 +222,19 @@ return 0.01 * init + 0.99 * current -def next_difficulty(w, difficulty, rating): +def next_difficulty(w, difficulty, rating, retrievability): + """Difficulty after a review. + + A lapse's step is weighted by how surprising the lapse was: forgetting a + card the model expected you to recall says more about the card's difficulty + than forgetting one that was long overdue. + """ delta_d = -w[6] * (rating - 3) + if rating == 1: + delta_d *= retrievability + 0.1 new_d = difficulty + linear_damping(delta_d, difficulty) - return mean_reversion(initial_difficulty(w, 4), new_d) + reverted = mean_reversion(initial_difficulty(w, 4), new_d) + return clamp(reverted, MIN_DIFFICULTY, MAX_DIFFICULTY) # -------------------------------------------------------------------------- @@ -169,23 +243,25 @@ def stability_after_review(w, s, d, r, rating, base): - """One half of the stability update; `base` is 7 (long) or 16 (short).""" + """One trace's stability update; `base` is SLOW_TRACE_BASE or FAST_TRACE_BASE. + + Post-lapse stability is difficulty-independent in the finished model: the + `d ** -fail_d_exp` factor of the draft was ablated. + """ w_sinc_base = w[base] w_sinc_s_exp = w[base + 1] w_sinc_r_mult = w[base + 2] w_fail_mult = w[base + 3] - w_fail_d_exp = w[base + 4] - w_fail_s_exp = w[base + 5] - w_fail_r_mult = w[base + 6] - w_hard = w[base + 7] - w_easy = w[base + 8] + w_fail_s_exp = w[base + 4] + w_fail_r_mult = w[base + 5] + w_hard = w[base + 6] + w_easy = w[base + 7] hard_penalty = w_hard if rating == 2 else 1.0 easy_bonus = w_easy if rating == 4 else 1.0 new_s_fail = ( w_fail_mult - * d ** -w_fail_d_exp * ((s + 1.0) ** w_fail_s_exp - 1.0) * math.exp((1.0 - r) * w_fail_r_mult) ) @@ -201,43 +277,77 @@ ) new_s_success = max(pls, s * s_inc) - return new_s_success if rating > 1 else pls + result = new_s_success if rating > 1 else pls + return clamp(result, STABILITY_MIN, STABILITY_MAX) -def transition_function(w, delta_t): - """1 for a fully long-term review, 0 for a same-instant (short-term) one.""" - return 1.0 - w[26] * math.exp(-w[25] * delta_t) +def next_state(w, state, delta_t, rating): + """Both traces and the difficulty, after a review of an existing card. + The slow trace updates from the mixed retrievability; the fast trace + updates from its *own* recall component, and on a lapse is pulled down to + at most `FAST_TRACE_RATIO` of the post-lapse slow stability. + """ + delta_t = max(delta_t, 0.0) + s, d, s_fast = state -def next_stability(w, s, d, delta_t, rating): - r = forgetting_curve(w, delta_t, s) - s_long = stability_after_review(w, s, d, r, rating, LONG_TERM_BASE) - s_short = stability_after_review(w, s, d, r, rating, SHORT_TERM_BASE) - coefficient = transition_function(w, delta_t) - return coefficient * s_long + (1.0 - coefficient) * s_short + r = forgetting_curve(w, delta_t, state) + new_s_long = stability_after_review(w, s, d, r, rating, SLOW_TRACE_BASE) + r_fast = fast_component_recall(w, delta_t, s_fast) + new_s_short = stability_after_review(w, s_fast, d, r_fast, rating, FAST_TRACE_BASE) + if rating == 1: + new_s_short = min(new_s_short, FAST_TRACE_RATIO * new_s_long) + new_d = next_difficulty(w, d, rating, r) + return (new_s_long, new_d, new_s_short) + + # -------------------------------------------------------------------------- # The state transition # -------------------------------------------------------------------------- -def step(w, state, delta_t, rating, s_min=STABILITY_MIN): - """`state` is None for the very first review, else an (S, D) pair.""" +def initial_state(w, rating): + """The state a card is born with, given its first rating.""" + s = clamp(w[rating - 1], STABILITY_MIN, STABILITY_MAX) + d = clamp(initial_difficulty(w, rating), MIN_DIFFICULTY, MAX_DIFFICULTY) + s_fast = clamp(FAST_TRACE_RATIO * s, STABILITY_MIN, STABILITY_MAX) + return (s, d, s_fast) + + +def step(w, state, delta_t, rating): + """`state` is None for the very first review, else an (S, D, S_fast) triple.""" if state is None: - new_s = w[rating - 1] - new_d = clamp(initial_difficulty(w, rating), MIN_DIFFICULTY, MAX_DIFFICULTY) - else: - s, d = state - new_s = next_stability(w, s, d, delta_t, rating) - new_d = clamp(next_difficulty(w, d, rating), MIN_DIFFICULTY, MAX_DIFFICULTY) - new_s = clamp(new_s, s_min, STABILITY_MAX) - return (new_s, new_d) + return initial_state(w, rating) + s, d, s_fast = next_state(w, state, delta_t, rating) + return ( + clamp(s, STABILITY_MIN, STABILITY_MAX), + clamp(d, MIN_DIFFICULTY, MAX_DIFFICULTY), + clamp(s_fast, STABILITY_MIN, STABILITY_MAX), + ) -def replay(w, reviews, s_min=STABILITY_MIN): +def replay(w, reviews): """Fold `step` over a list of (delta_t, rating) pairs.""" state = None for delta_t, rating in reviews: - state = step(w, state, delta_t, rating, s_min) + state = step(w, state, delta_t, rating) return state + + +# -------------------------------------------------------------------------- +# Parameter clipping +# -------------------------------------------------------------------------- + +# Pairs (i, j) for which w[i] <= w[j] must hold. The reference restores these +# *after* the per-parameter box clamps, by pulling the larger index up. +ORDERING_CONSTRAINTS = [(0, 1), (1, 2), (2, 3), (25, 26)] + + +def clip_parameters(w): + """The reference clipper: box clamps first, then monotonicity.""" + out = [clamp(v, lo, hi) for v, lo, hi in zip(w, LOWER_BOUNDS, UPPER_BOUNDS)] + for lower, upper in ORDERING_CONSTRAINTS: + out[upper] = max(out[upper], out[lower]) + return out diff --git a/reference/gen_golden.py b/reference/gen_golden.py --- a/reference/gen_golden.py +++ b/reference/gen_golden.py @@ -12,18 +12,22 @@ from fsrs7_reference import ( # noqa: E402 DEFAULT_PARAMETERS, + FAST_TRACE_BASE, + FAST_TRACE_RATIO, LOWER_BOUNDS, + SLOW_TRACE_BASE, + STABILITY_MAX, + STABILITY_MIN, UPPER_BOUNDS, - LONG_TERM_BASE, - SHORT_TERM_BASE, clamp, + clip_parameters, + fast_component_recall, forgetting_curve, initial_difficulty, next_difficulty, next_interval, stability_after_review, step, - transition_function, ) OUT = os.path.join( @@ -53,6 +57,10 @@ return "[" + ", ".join(xs) + "]" +def hs_triple(t): + return "(" + ", ".join(hs(v) for v in t) + ")" + + # -------------------------------------------------------------------------- # Alternative parameter sets: a deterministic LCG walk over the valid box. # -------------------------------------------------------------------------- @@ -65,12 +73,7 @@ state = (state * 6364136223846793005 + 1442695040888963407) % (2**64) u = (state >> 11) / float(2**53) w.append(lo + u * (hi - lo)) - # Restore the ordering constraints the clipper enforces. - for i in (1, 2, 3): - w[i] = max(w[i], w[i - 1]) - w[28] = max(w[28], w[27]) - w[30] = max(w[30], w[29]) - return [round(v, 6) for v in w] + return [round(v, 6) for v in clip_parameters(w)] PARAMETER_SETS = [ @@ -80,18 +83,48 @@ ] TIMES = [0.0, 1.0 / 86400.0, 1.0 / 1440.0, 10.0 / 1440.0, 0.25, 1.0, 3.0, 7.5, 30.0, 365.0, 3650.0] -STABILITIES = [0.0001, 0.01, 0.5, 1.0, 4.1283, 15.0, 100.0, 1000.0, 36500.0] -DIFFICULTIES = [1.0, 2.5, 4.194588083372719, 7.0, 10.0] -HALF_DIFFICULTIES = [1.0, 4.194588083372719, 10.0] -HALF_STABILITIES = [0.01, 1.0, 4.1283, 1000.0] -HALF_RETRIEVABILITIES = [0.05, 0.5, 1.0] -STEP_STABILITIES = [0.0001, 1.0, 4.1283, 1000.0, 36500.0] -STEP_DIFFICULTIES = [1.0, 4.194588083372719, 10.0] -STEP_DELTAS = [0.0, 10.0 / 1440.0, 0.5, 1.0, 45.0, 400.0] -DELTAS = [0.0, 1.0 / 1440.0, 10.0 / 1440.0, 0.5, 1.0, 6.0, 45.0, 400.0] -RETENTIONS = [0.7, 0.8, 0.85, 0.9, 0.95, 0.97, 0.99] +STABILITIES = [0.0001, 0.01, 0.5, 1.0, 3.9221, 15.0, 100.0, 1000.0, 36500.0] +DIFFICULTIES = [1.0, 2.5, 3.5307239812763354, 7.0, 10.0] RATINGS = [1, 2, 3, 4] +RETRIEVABILITIES = [0.05, 0.5, 0.95] +RETENTIONS = [0.7, 0.8, 0.85, 0.9, 0.95, 0.97, 0.99] +HALF_DIFFICULTIES = [1.0, 3.5307239812763354, 10.0] +HALF_STABILITIES = [0.01, 1.0, 3.9221, 1000.0] + +FAST_STABILITIES = [0.0001, 0.01, 1.0, 3.9221, 100.0, 36500.0] + + +def fast_of(s, ratio): + return clamp(s * ratio, STABILITY_MIN, STABILITY_MAX) + + +# States for the forgetting curve: the whole stability range at three +# difficulties with the natural fast/slow ratio, plus a block that moves the +# fast trace independently of the slow one. +CURVE_STATES = [ + (s, d, fast_of(s, FAST_TRACE_RATIO)) + for s in STABILITIES + for d in (1.0, 5.0, 10.0) +] + [ + (s, d, fast_of(s, ratio)) + for s in (0.5, 3.9221, 100.0) + for d in (2.5, 7.0) + for ratio in (0.05, 1.0, 20.0) +] + +INTERVAL_STATES = [ + (s, d, fast_of(s, FAST_TRACE_RATIO)) for s in STABILITIES for d in (1.0, 5.0, 10.0) +] + [(3.9221, 5.0, fast_of(3.9221, ratio)) for ratio in (0.05, 1.0, 20.0)] + +STEP_STATES = [ + (s, d, fast_of(s, ratio)) + for s in (0.0001, 1.0, 3.9221, 1000.0, 36500.0) + for d in (1.0, 3.5307239812763354, 10.0) + for ratio in (FAST_TRACE_RATIO, 5.0) +] +STEP_DELTAS = [0.0, 10.0 / 1440.0, 0.5, 1.0, 45.0, 400.0] + REVIEW_SEQUENCES = [ [(0.0, 3)], [(0.0, 1)], @@ -99,6 +132,8 @@ [(0.0, 3), (10.0 / 1440.0, 3)], [(0.0, 1), (1.0 / 1440.0, 3), (10.0 / 1440.0, 3), (1.0, 3)], [(0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)], + # The fixture the reference implementation's own test suite asserts on. + [(0.0, 1), (0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)], [(0.0, 2), (1.0, 2), (2.0, 2), (3.0, 2)], [(0.0, 4), (15.0, 4), (90.0, 4), (365.0, 4)], [(0.0, 3), (5.0, 1), (10.0 / 1440.0, 3), (1.0, 3), (4.0, 4)], @@ -124,18 +159,18 @@ add("-- | Golden vectors for the FSRS-7 implementation.") add("--") add("-- Generated by @reference\\/gen_golden.py@ from the pure-Python") - add("-- transcription of the official benchmark model. Do not edit by hand;") + add("-- transcription of the reference model. Do not edit by hand;") add("-- regenerate with @python3 reference\\/gen_golden.py@.") add("module Test.FSRS.GoldenData") add(" ( goldenParameterSets") add(" , CurveVector (..)") add(" , goldenCurveVectors") + add(" , FastRecallVector (..)") + add(" , goldenFastRecallVectors") add(" , DifficultyVector (..)") add(" , goldenDifficultyVectors") add(" , HalfStabilityVector (..)") add(" , goldenHalfStabilityVectors") - add(" , TransitionVector (..)") - add(" , goldenTransitionVectors") add(" , StepVector (..)") add(" , goldenStepVectors") add(" , IntervalVector (..)") @@ -155,11 +190,12 @@ add("") # ---------------------------------------------------------------- curve - add("-- | @R(t, s)@, the probability of recall.") + add("-- | @R(t, state)@, the probability of recall. The state is spelled out") + add("-- as a @(stability, difficulty, fast stability)@ triple.") add("data CurveVector = CurveVector") add(" { cvParams :: !Int") add(" , cvElapsedDays :: !Double") - add(" , cvStability :: !Double") + add(" , cvState :: !(Double, Double, Double)") add(" , cvRetrievability :: !Double") add(" }") add(" deriving stock (Eq, Show)") @@ -167,18 +203,43 @@ rows = [] for pi, w in enumerate(PARAMETER_SETS): for t in TIMES: - for s in STABILITIES: + for st in CURVE_STATES: rows.append( - f"CurveVector {pi} {hs(t)} {hs(s)} {hs(forgetting_curve(w, t, s))}" + f"CurveVector {pi} {hs(t)} {hs_triple(st)} " + f"{hs(forgetting_curve(w, t, st))}" ) emit_list(add, "goldenCurveVectors", rows) + # ----------------------------------------------------------- fast recall + add("-- | The fast trace's own recall probability, which drives its own") + add("-- stability update. This is the piece that replaced the draft's") + add("-- long-\\/short-term transition function.") + add("data FastRecallVector = FastRecallVector") + add(" { frParams :: !Int") + add(" , frElapsedDays :: !Double") + add(" , frStabilityFast :: !Double") + add(" , frRecall :: !Double") + add(" }") + add(" deriving stock (Eq, Show)") + add("") + rows = [] + for pi, w in enumerate(PARAMETER_SETS): + for t in TIMES: + for s in FAST_STABILITIES: + rows.append( + f"FastRecallVector {pi} {hs(t)} {hs(s)} " + f"{hs(fast_component_recall(w, t, s))}" + ) + emit_list(add, "goldenFastRecallVectors", rows) + # ----------------------------------------------------------- difficulty - add("-- | Initial and subsequent difficulty.") + add("-- | Initial and subsequent difficulty. The retrievability only") + add("-- matters on a lapse, where it weights the step.") add("data DifficultyVector = DifficultyVector") add(" { dvParams :: !Int") add(" , dvDifficulty :: !(Maybe Double)") add(" -- ^ 'Nothing' for the initial difficulty of a brand-new card.") + add(" , dvRetrievability :: !Double") add(" , dvRating :: !Int") add(" , dvNextDifficulty :: !Double") add(" }") @@ -188,21 +249,22 @@ for pi, w in enumerate(PARAMETER_SETS): for g in RATINGS: v = clamp(initial_difficulty(w, g), 1.0, 10.0) - rows.append(f"DifficultyVector {pi} Nothing {g} {hs(v)}") + rows.append(f"DifficultyVector {pi} Nothing 1.0 {g} {hs(v)}") for d in DIFFICULTIES: - for g in RATINGS: - v = clamp(next_difficulty(w, d, g), 1.0, 10.0) - rows.append( - f"DifficultyVector {pi} (Just {hs(d)}) {g} {hs(v)}" - ) + for r in RETRIEVABILITIES: + for g in RATINGS: + v = next_difficulty(w, d, g, r) + rows.append( + f"DifficultyVector {pi} (Just {hs(d)}) {hs(r)} {g} {hs(v)}" + ) emit_list(add, "goldenDifficultyVectors", rows) # ------------------------------------------------------- half stability - add("-- | One half of the stability update, before the two are blended.") + add("-- | One trace's stability update, before the lapse cap is applied.") add("data HalfStabilityVector = HalfStabilityVector") add(" { hsParams :: !Int") - add(" , hsLongTerm :: !Bool") - add(" -- ^ 'True' for the long-term block, 'False' for the short-term one.") + add(" , hsSlowTrace :: !Bool") + add(" -- ^ 'True' for the slow trace's block, 'False' for the fast one's.") add(" , hsStability :: !Double") add(" , hsDifficulty :: !Double") add(" , hsRetrievability :: !Double") @@ -215,59 +277,42 @@ for pi, w in enumerate(PARAMETER_SETS): for s in HALF_STABILITIES: for d in HALF_DIFFICULTIES: - for r in HALF_RETRIEVABILITIES: + for r in RETRIEVABILITIES: for g in RATINGS: - for long, base in ((True, LONG_TERM_BASE), (False, SHORT_TERM_BASE)): + for slow, base in ((True, SLOW_TRACE_BASE), (False, FAST_TRACE_BASE)): v = stability_after_review(w, s, d, r, g, base) rows.append( - f"HalfStabilityVector {pi} {long} {hs(s)} {hs(d)} " + f"HalfStabilityVector {pi} {slow} {hs(s)} {hs(d)} " f"{hs(r)} {g} {hs(v)}" ) emit_list(add, "goldenHalfStabilityVectors", rows) - # --------------------------------------------------------- transition - add("-- | The long-\\/short-term blending coefficient.") - add("data TransitionVector = TransitionVector") - add(" { tvParams :: !Int") - add(" , tvElapsedDays :: !Double") - add(" , tvCoefficient :: !Double") - add(" }") - add(" deriving stock (Eq, Show)") - add("") - rows = [] - for pi, w in enumerate(PARAMETER_SETS): - for t in TIMES: - rows.append( - f"TransitionVector {pi} {hs(t)} {hs(transition_function(w, t))}" - ) - emit_list(add, "goldenTransitionVectors", rows) - # --------------------------------------------------------------- step add("-- | A full memory-state transition.") add("data StepVector = StepVector") add(" { svParams :: !Int") - add(" , svState :: !(Maybe (Double, Double))") - add(" -- ^ @(stability, difficulty)@; 'Nothing' for the first review.") + add(" , svState :: !(Maybe (Double, Double, Double))") + add(" -- ^ @(stability, difficulty, fast stability)@; 'Nothing' for the") + add(" -- first review.") add(" , svElapsedDays :: !Double") add(" , svRating :: !Int") - add(" , svNextState :: !(Double, Double)") + add(" , svNextState :: !(Double, Double, Double)") add(" }") add(" deriving stock (Eq, Show)") add("") rows = [] for pi, w in enumerate(PARAMETER_SETS): for g in RATINGS: - s1, d1 = step(w, None, 0.0, g) - rows.append(f"StepVector {pi} Nothing 0.0 {g} ({hs(s1)}, {hs(d1)})") - for s in STEP_STABILITIES: - for d in STEP_DIFFICULTIES: - for dt in STEP_DELTAS: - for g in RATINGS: - s1, d1 = step(w, (s, d), dt, g) - rows.append( - f"StepVector {pi} (Just ({hs(s)}, {hs(d)})) {hs(dt)} {g} " - f"({hs(s1)}, {hs(d1)})" - ) + rows.append( + f"StepVector {pi} Nothing 0.0 {g} {hs_triple(step(w, None, 0.0, g))}" + ) + for st in STEP_STATES: + for dt in STEP_DELTAS: + for g in RATINGS: + rows.append( + f"StepVector {pi} (Just {hs_triple(st)}) {hs(dt)} {g} " + f"{hs_triple(step(w, st, dt, g))}" + ) emit_list(add, "goldenStepVectors", rows) # ----------------------------------------------------------- intervals @@ -275,7 +320,7 @@ add("data IntervalVector = IntervalVector") add(" { ivParams :: !Int") add(" , ivDesiredRetention :: !Double") - add(" , ivStability :: !Double") + add(" , ivState :: !(Double, Double, Double)") add(" , ivInterval :: !Double") add(" }") add(" deriving stock (Eq, Show)") @@ -283,9 +328,10 @@ rows = [] for pi, w in enumerate(PARAMETER_SETS): for dr in RETENTIONS: - for s in STABILITIES: + for st in INTERVAL_STATES: rows.append( - f"IntervalVector {pi} {hs(dr)} {hs(s)} {hs(next_interval(w, dr, s))}" + f"IntervalVector {pi} {hs(dr)} {hs_triple(st)} " + f"{hs(next_interval(w, dr, st))}" ) emit_list(add, "goldenIntervalVectors", rows) @@ -295,7 +341,7 @@ add(" { rvParams :: !Int") add(" , rvReviews :: ![(Double, Int)]") add(" -- ^ @(days since the previous review, rating)@.") - add(" , rvFinalState :: !(Double, Double)") + add(" , rvFinalState :: !(Double, Double, Double)") add(" }") add(" deriving stock (Eq, Show)") add("") @@ -307,9 +353,7 @@ state = step(w, state, dt, g) reviews = hs_list([f"({hs(dt)}, {g})" for dt, g in seq_]) assert state is not None - rows.append( - f"ReplayVector {pi} {reviews} ({hs(state[0])}, {hs(state[1])})" - ) + rows.append(f"ReplayVector {pi} {reviews} {hs_triple(state)}") emit_list(add, "goldenReplayVectors", rows) return "\n".join(lines).rstrip() + "\n" diff --git a/reference/test_reference.py b/reference/test_reference.py --- a/reference/test_reference.py +++ b/reference/test_reference.py @@ -5,6 +5,11 @@ the model's structural invariants, not a second copy of the Haskell suite: enough to catch a transcription typo before it is baked into GoldenData.hs. +`test_upstream_*` are the two numeric assertions the reference implementation +makes about FSRS-7 in its own test suite. They are the only fixtures here that +did not come out of this file, so they are what pins the transcription to +upstream rather than to itself. + No test framework needed. Run from the repository root: python3 reference/test_reference.py @@ -19,22 +24,32 @@ from fsrs7_reference import ( # noqa: E402 DEFAULT_PARAMETERS, + FAST_TRACE_RATIO, LOWER_BOUNDS, MAX_DIFFICULTY, MIN_DIFFICULTY, + ORDERING_CONSTRAINTS, + RETENTION_FLOOR, STABILITY_MAX, STABILITY_MIN, UPPER_BOUNDS, + clamp, + clip_parameters, + fast_component_recall, forgetting_curve, + forgetting_curve_derivative, initial_difficulty, + initial_state, next_difficulty, next_interval, + replay, + stability_after_review, step, - transition_function, ) -ORDERING_CONSTRAINTS = [(0, 1), (1, 2), (2, 3), (27, 28), (29, 30)] +PARAM_LEN = 34 RATINGS = [1, 2, 3, 4] +RETENTION_CEILING = 1.0 - RETENTION_FLOOR def parameter_sets(count, seed): @@ -42,27 +57,46 @@ rng = random.Random(seed) yield DEFAULT_PARAMETERS for _ in range(count): - w = [rng.uniform(lo, hi) for lo, hi in zip(LOWER_BOUNDS, UPPER_BOUNDS)] - for i, j in ORDERING_CONSTRAINTS: - w[j] = max(w[j], w[i]) - yield w + yield clip_parameters( + [rng.uniform(lo, hi) for lo, hi in zip(LOWER_BOUNDS, UPPER_BOUNDS)] + ) def sample_states(seed): + """Random `(state, delta_t)` pairs, mostly at the model's own trace ratio.""" rng = random.Random(seed) for _ in range(40): s = math.exp(rng.uniform(math.log(STABILITY_MIN), math.log(STABILITY_MAX))) d = rng.uniform(MIN_DIFFICULTY, MAX_DIFFICULTY) - dt = 0.0 if rng.random() < 0.2 else math.exp(rng.uniform(math.log(1 / 86400), math.log(3650))) - yield s, d, dt + if rng.random() < 0.6: + s_fast = clamp(s * FAST_TRACE_RATIO, STABILITY_MIN, STABILITY_MAX) + else: + s_fast = math.exp(rng.uniform(math.log(STABILITY_MIN), math.log(STABILITY_MAX))) + dt = ( + 0.0 + if rng.random() < 0.2 + else math.exp(rng.uniform(math.log(1 / 86400), math.log(3650))) + ) + yield (s, d, s_fast), dt +def natural_states(seed): + """States at exactly the fast/slow ratio the model establishes.""" + rng = random.Random(seed) + for _ in range(40): + s = math.exp( + rng.uniform(math.log(STABILITY_MIN / FAST_TRACE_RATIO), math.log(STABILITY_MAX)) + ) + d = rng.uniform(MIN_DIFFICULTY, MAX_DIFFICULTY) + yield (s, d, s * FAST_TRACE_RATIO) + + # --------------------------------------------------------------------------- def test_parameter_vector_is_well_formed(): - assert len(DEFAULT_PARAMETERS) == 35, len(DEFAULT_PARAMETERS) - assert len(LOWER_BOUNDS) == 35 and len(UPPER_BOUNDS) == 35 + assert len(DEFAULT_PARAMETERS) == PARAM_LEN, len(DEFAULT_PARAMETERS) + assert len(LOWER_BOUNDS) == PARAM_LEN and len(UPPER_BOUNDS) == PARAM_LEN for i, (lo, hi) in enumerate(zip(LOWER_BOUNDS, UPPER_BOUNDS)): assert lo <= hi, f"bound {i} is inverted: {lo} > {hi}" for i, w in enumerate(DEFAULT_PARAMETERS): @@ -71,92 +105,202 @@ assert DEFAULT_PARAMETERS[i] <= DEFAULT_PARAMETERS[j], f"w{i} > w{j}" -def test_nothing_is_forgotten_immediately(): +def test_clipping_is_idempotent_and_lands_in_the_box(): + rng = random.Random(13) + for _ in range(200): + w = [rng.uniform(-1000, 1000) for _ in range(PARAM_LEN)] + once = clip_parameters(w) + assert clip_parameters(once) == once + for i, (lo, hi) in enumerate(zip(LOWER_BOUNDS, UPPER_BOUNDS)): + assert lo <= once[i] <= hi, (i, once[i]) + for i, j in ORDERING_CONSTRAINTS: + assert once[i] <= once[j], (i, j) + + +def test_retrievability_is_rescaled_away_from_one(): + # FSRS-7 squeezes R into [1e-5, 1 - 1e-5], so a card reviewed a moment ago + # is *almost* certain rather than certain. for w in parameter_sets(20, seed=1): - for s in (STABILITY_MIN, 1.0, 37.0, STABILITY_MAX): - assert forgetting_curve(w, 0.0, s) == 1.0 + for state, _ in sample_states(seed=2): + assert abs(forgetting_curve(w, 0.0, state) - RETENTION_CEILING) < 1e-12 def test_retrievability_is_a_decreasing_probability(): - for w in parameter_sets(40, seed=2): - for s, _, dt in sample_states(seed=3): - r = forgetting_curve(w, dt, s) - assert 0.0 < r <= 1.0, r - assert forgetting_curve(w, dt + 1e-3, s) <= r + for w in parameter_sets(40, seed=3): + for state, dt in sample_states(seed=4): + r = forgetting_curve(w, dt, state) + assert RETENTION_FLOOR <= r <= RETENTION_CEILING, r + assert forgetting_curve(w, dt + 1e-3, state) <= r +def test_the_fast_component_is_a_bare_power_law(): + # Unlike the mixture, this one is not rescaled: it hits 1 exactly. + for w in parameter_sets(20, seed=5): + for s in (STABILITY_MIN, 0.01, 1.0, 37.0, STABILITY_MAX): + assert fast_component_recall(w, 0.0, s) == 1.0 + previous = 1.0 + for dt in (1 / 86400, 0.01, 0.5, 1.0, 10.0, 3650.0): + r = fast_component_recall(w, dt, s) + assert 0.0 < r <= 1.0, r + assert r <= previous + previous = r + + +def test_the_derivative_matches_a_finite_difference(): + for w in parameter_sets(20, seed=6): + for state, _ in sample_states(seed=7): + for t in (0.5, 5.0, 50.0): + h = 1e-6 * t + numeric = ( + forgetting_curve(w, t + h, state) - forgetting_curve(w, t - h, state) + ) / (2 * h) + exact = forgetting_curve_derivative(w, t, state) + assert exact <= 0.0, exact + assert abs(numeric - exact) <= 1e-7 + 1e-5 * abs(exact), (numeric, exact) + + def test_base_weights_are_the_recall_probability_at_t_equals_s(): - # Give both power laws the same base and the mixture collapses to it. - for base in (0.5, 0.85): + # Give both power laws the same base and, at an average difficulty with the + # two traces level, the mixture collapses to that base at t == s. + for base in (0.5, 0.7, 0.85): w = list(DEFAULT_PARAMETERS) - w[29] = w[30] = base + w[25] = w[26] = base for s in (0.5, 1.0, 37.0, 1000.0): - assert abs(forgetting_curve(w, s, s) - base) < 1e-12 + expected = base * (1.0 - 2.0 * RETENTION_FLOOR) + RETENTION_FLOOR + assert abs(forgetting_curve(w, s, (s, 5.0, s)) - expected) < 1e-12 def test_intervals_land_on_the_desired_retention(): - for w in parameter_sets(20, seed=4): + for w in parameter_sets(20, seed=8): for dr in (0.7, 0.8, 0.9, 0.95, 0.99): - for s in (0.01, 1.0, 37.0, 1000.0): - t = next_interval(w, dr, s) + for state, _ in sample_states(seed=9): + t = next_interval(w, dr, state) if t <= 1 / 86400 or t >= 36500: continue # saturated, cannot hit the target - assert abs(forgetting_curve(w, t, s) - dr) < 1e-9 + assert abs(forgetting_curve(w, t, state) - dr) < 1e-9 def test_a_better_rating_is_never_worse_for_the_card(): - for w in parameter_sets(40, seed=5): - for s, d, dt in sample_states(seed=6): - outcomes = [step(w, (s, d), dt, g) for g in RATINGS] - stabilities = [new_s for new_s, _ in outcomes] - difficulties = [new_d for _, new_d in outcomes] + for w in parameter_sets(40, seed=10): + for state, dt in sample_states(seed=11): + outcomes = [step(w, state, dt, g) for g in RATINGS] + stabilities = [new_s for new_s, _, _ in outcomes] assert stabilities == sorted(stabilities), stabilities - assert difficulties == sorted(difficulties, reverse=True), difficulties +def test_a_lapse_is_the_harshest_answer_when_it_was_surprising(): + # FSRS-7 weights a lapse's difficulty step by `r + 0.1`, so a lapse only + # outweighs a Hard once the model expected the card to be recalled. + for w in parameter_sets(20, seed=12): + for d in (1.0, 3.0, 5.0, 7.5, 10.0): + for r in (0.4, 0.7, 0.95): + difficulties = [next_difficulty(w, d, g, r) for g in RATINGS] + assert difficulties == sorted(difficulties, reverse=True), difficulties + # ... and a gentler lapse really is gentler. + assert next_difficulty(w, d, 1, 0.05) <= next_difficulty(w, d, 1, 0.95) + + def test_remembering_helps_and_forgetting_does_not(): - for w in parameter_sets(40, seed=7): - for s, d, dt in sample_states(seed=8): + for w in parameter_sets(40, seed=13): + for state, dt in sample_states(seed=14): + s = state[0] for g in (2, 3, 4): - assert step(w, (s, d), dt, g)[0] >= s * (1 - 1e-12) - assert step(w, (s, d), dt, 1)[0] <= s * (1 + 1e-12) + assert step(w, state, dt, g)[0] >= s * (1 - 1e-12) + assert step(w, state, dt, 1)[0] <= s * (1 + 1e-12) +def test_post_lapse_stability_ignores_difficulty(): + # The finished model ablated the d ** -fail_d_exp factor from both blocks. + for w in parameter_sets(20, seed=15): + for base in (7, 15): + for s in (0.01, 1.0, 37.0, 1000.0): + for r in (0.05, 0.5, 0.95): + values = { + stability_after_review(w, s, d, r, 1, base) + for d in (1.0, 3.0, 5.0, 7.0, 10.0) + } + assert len(values) == 1, values + + +def test_a_lapse_pulls_the_fast_trace_under_the_slow_one(): + for w in parameter_sets(40, seed=16): + for state, dt in sample_states(seed=17): + new_s, _, new_s_short = step(w, state, dt, 1) + # The cap is applied before the final clamp, so at the very bottom + # of the range the floor wins. + cap = max(STABILITY_MIN, FAST_TRACE_RATIO * new_s) + assert new_s_short <= cap + 1e-12, (new_s_short, cap) + + def test_the_state_stays_in_range(): - for w in parameter_sets(40, seed=9): - for s, d, dt in sample_states(seed=10): + for w in parameter_sets(40, seed=18): + for state, dt in sample_states(seed=19): for g in RATINGS: - new_s, new_d = step(w, (s, d), dt, g) + new_s, new_d, new_s_short = step(w, state, dt, g) assert STABILITY_MIN <= new_s <= STABILITY_MAX, new_s + assert STABILITY_MIN <= new_s_short <= STABILITY_MAX, new_s_short assert MIN_DIFFICULTY <= new_d <= MAX_DIFFICULTY, new_d - first_s, first_d = step(w, None, 0.0, g) - assert first_s == min(max(w[g - 1], STABILITY_MIN), STABILITY_MAX) + for g in RATINGS: + first_s, first_d, first_s_fast = initial_state(w, g) + assert first_s == clamp(w[g - 1], STABILITY_MIN, STABILITY_MAX) + assert first_s_fast == clamp( + FAST_TRACE_RATIO * first_s, STABILITY_MIN, STABILITY_MAX + ) assert MIN_DIFFICULTY <= first_d <= MAX_DIFFICULTY def test_difficulty_reverts_towards_an_easy_first_review(): # A Good review leaves the rating delta at zero, so all that is left is the - # 1% pull towards init_d(4). Iterating it therefore converges on exactly - # that anchor, which pins down which rating the anchor is taken from. - for w in parameter_sets(10, seed=12): - anchor = min(max(initial_difficulty(w, 4), MIN_DIFFICULTY), MAX_DIFFICULTY) - for start in (MIN_DIFFICULTY, 5.0, MAX_DIFFICULTY): - d = start - for _ in range(3000): - d = min(max(next_difficulty(w, d, 3), MIN_DIFFICULTY), MAX_DIFFICULTY) - assert abs(d - anchor) < 1e-9, (d, anchor) + # 1% pull towards the *unclamped* init_d(4). That is what pins down which + # rating the anchor is taken from — with the default weights the anchor sits + # below the difficulty floor, so the iterate itself only reaches the floor. + for w in parameter_sets(10, seed=20): + anchor = initial_difficulty(w, 4) + for d in (1.0, 2.5, 5.0, 7.5, 10.0): + expected = clamp(0.01 * anchor + 0.99 * d, MIN_DIFFICULTY, MAX_DIFFICULTY) + assert abs(next_difficulty(w, d, 3, 0.9) - expected) < 1e-12 + limit = 5.0 + for _ in range(5000): + limit = next_difficulty(w, limit, 3, 0.9) + assert abs(limit - clamp(anchor, MIN_DIFFICULTY, MAX_DIFFICULTY)) < 1e-9, limit -def test_the_transition_function_is_a_weight(): - for w in parameter_sets(40, seed=11): - assert transition_function(w, 0.0) == 1 - w[26] - assert transition_function(w, 3650.0) == 1.0 - previous = -1.0 - for dt in (0.0, 1 / 86400, 0.01, 0.5, 1.0, 10.0, 3650.0): - c = transition_function(w, dt) - assert 0.0 <= c <= 1.0, c - assert c >= previous - previous = c +def test_difficulty_never_helps_recall_at_the_natural_trace_ratio(): + # Difficulty pulls two ways: it speeds the slow component up, but also + # shifts mixture weight onto the fast one. At the ratio the model maintains + # the first wins; for an arbitrarily lopsided pair of traces neither does. + w = DEFAULT_PARAMETERS + for s, _, s_fast in natural_states(seed=21): + for dt in (0.001, 0.5, 7.0, 365.0): + previous = None + for d in range(1, 11): + r = forgetting_curve(w, dt, (s, float(d), s_fast)) + if previous is not None: + assert r <= previous + 1e-15, (s, dt, d, previous, r) + previous = r + + +# -------------------------------------------------------------------------- +# Fixtures taken from the reference implementation's own test suite: +# src/inference.rs of https://github.com/open-spaced-repetition/fsrs-rs/pull/426 +# Upstream computes in single precision, hence the loose tolerances. +# -------------------------------------------------------------------------- + + +def test_upstream_memory_state_fsrs7(): + history = [(0.0, 1), (0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] + s, d, _ = replay(DEFAULT_PARAMETERS, history) + assert abs(s - 25.985723) < 1e-4, s + assert abs(d - 5.877549) < 1e-4, d + + +def test_upstream_next_interval_fsrs7(): + state = (1.0, 5.0, 1.0) + intervals = [ + max(1, round(next_interval(DEFAULT_PARAMETERS, i / 10.0, state))) + for i in range(1, 11) + ] + assert intervals == [36500, 36500, 36500, 12813, 843, 92, 13, 2, 1, 1], intervals # --------------------------------------------------------------------------- diff --git a/src/FSRS.hs b/src/FSRS.hs --- a/src/FSRS.hs +++ b/src/FSRS.hs @@ -1,10 +1,13 @@ -- | FSRS-7 — the Free Spaced Repetition Scheduler, version 7. -- -- FSRS predicts when you are about to forget something and schedules the --- review for just before that happens. It models a card with two numbers: +-- review for just before that happens. It models a card with three numbers: -- --- * /stability/, the memory's half-life in days, and +-- * /stability/, the memory's half-life in days, -- * /difficulty/, how hard this particular card is for you, on a 1–10 scale, +-- and +-- * a second, faster-decaying /stability/ — FSRS-7 tracks two memory traces, +-- which is how it tells a review minutes later apart from one weeks later, -- -- from which it derives /retrievability/, the probability that you can recall -- the card right now. @@ -20,7 +23,7 @@ -- second = 'nextMemoryState' p ('Just' first) 7 'Good' -- -- -- When should it come back, if we want a 90% chance of recall? --- 'nextIntervalDays' p 0.9 ('memoryStability' second) +-- 'nextIntervalDays' p 0.9 second -- @ -- -- For whole-card scheduling — learning steps, due dates, lapses — use @@ -31,7 +34,7 @@ -- @ -- -- The modules underneath are "FSRS.Types" (ratings and memory states), --- "FSRS.Parameters" (the 35 weights), "FSRS.Algorithm" (the model itself) and +-- "FSRS.Parameters" (the 34 weights), "FSRS.Algorithm" (the model itself) and -- "FSRS.Scheduler". module FSRS ( module FSRS.Types diff --git a/src/FSRS/Algorithm.hs b/src/FSRS/Algorithm.hs --- a/src/FSRS/Algorithm.hs +++ b/src/FSRS/Algorithm.hs @@ -2,26 +2,34 @@ -- | The FSRS-7 memory model. -- --- This module is a direct transcription of the reference implementation in --- --- (@models\/fsrs_v7.py@ and @models\/fsrs_v7_interval_penalty.py@). Every --- function here is pure and total. +-- This module is a direct transcription of the finished FSRS-7, whose +-- reference implementation is the Rust model its author signed off on: +-- (see +-- @fsrs-rs\/src\/model.rs@), upstreamed in +-- . +-- Every function here is pure and total. -- -- What changed in FSRS-7 relative to FSRS-6: -- --- * The forgetting curve is a stability-weighted mixture of /two/ power laws --- instead of one, which is why it has eight weights and no closed-form --- inverse (see 'nextIntervalDays'). --- * The stability update is computed twice — once with a long-term weight --- block and once with a short-term one — and the two are blended by --- 'transitionCoefficient', a smooth function of the elapsed time. FSRS-6 --- switched between two separate formulas on a same-day\/not-same-day flag. +-- * A card carries /two/ memory traces instead of one — see t'MemoryState'. +-- The forgetting curve is a mixture of a fast and a slow component, one per +-- trace, and each trace is updated by its own block of weights. This is what +-- makes same-day reviews behave differently from spaced ones; FSRS-6 +-- switched between two formulas on a same-day\/not-same-day flag. +-- * The forgetting curve depends on /difficulty/, which it never did before: +-- a hard card experiences time faster, and counts the slow trace for more. +-- * Post-lapse stability no longer depends on difficulty. +-- * A lapse's difficulty step is weighted by how surprising the lapse was — +-- see 'nextDifficulty'. +-- * Retrievability is squeezed into @[1e-5, 1 - 1e-5]@, so a card reviewed a +-- moment ago has a retrievability just short of @1@. -- * Intervals are genuinely continuous. Ten minutes is @10 \/ 1440@ days and -- the model is meant to be evaluated at such values, not at whole days. module FSRS.Algorithm ( -- * Forgetting curve retrievability , retrievabilityDerivative + , fastTraceRetrievability , nextIntervalDays -- * Difficulty @@ -31,10 +39,10 @@ -- * Stability , initialStability , stabilityAfterReview - , transitionCoefficient , nextStability -- * State transition + , initialMemoryState , nextMemoryState , replayReviews @@ -45,6 +53,8 @@ , difficultyMax , minimumIntervalDays , maximumIntervalDays + , retrievabilityFloor + , fastTraceRatio ) where import FSRS.Parameters @@ -53,13 +63,11 @@ , StabilityWeights (..) , curveWeights , difficultyDelta + , fastTraceWeights , initialDifficultyBase , initialDifficultyRate , initialStabilityWeight - , longTermWeights - , shortTermWeights - , transitionAmplitude - , transitionRate + , slowTraceWeights ) import FSRS.Types ( Days @@ -72,8 +80,7 @@ ) -- | The smallest stability the model will report, @1e-4@ days (about nine --- seconds). This is the @s_min@ the upstream configuration uses for FSRS-7, --- which is always run with second-precision intervals. +-- seconds). FSRS-7 is always run with second-precision intervals. stabilityMin :: Stability stabilityMin = 1.0e-4 @@ -98,73 +105,173 @@ maximumIntervalDays :: Days maximumIntervalDays = 36500.0 +-- | @1e-5@. 'retrievability' is rescaled into +-- @['retrievabilityFloor', 1 - 'retrievabilityFloor']@ so that neither it nor +-- its logarithm can saturate. +retrievabilityFloor :: Retrievability +retrievabilityFloor = 1.0e-5 + +-- | @0.8@. The fast trace starts at this fraction of the slow one, and after a +-- lapse is pulled back down to at most this fraction of it. +fastTraceRatio :: Double +fastTraceRatio = 0.8 + +-- | The magnitude of either decay is held inside @[0.01, 0.95]@. +decayMin, decayMax :: Double +decayMin = 0.01 +decayMax = 0.95 + +-- | The exponent that builds the fast component's shape factor is capped here, +-- in log space, so that both the value and its gradient stay finite. +logFactorCap :: Double +logFactorCap = 60.0 + clampTo :: Double -> Double -> Double -> Double clampTo lo hi x = min hi (max lo x) +clampStability :: Stability -> Stability +clampStability = clampTo stabilityMin stabilityMax + +clampDifficulty :: Difficulty -> Difficulty +clampDifficulty = clampTo difficultyMin difficultyMax + -- --------------------------------------------------------------------------- -- Forgetting curve -- --------------------------------------------------------------------------- --- | The probability of recalling a card @t@ days after the last review, given --- its stability. --- --- FSRS-7 mixes two power laws whose relative weight depends on the stability --- itself, so — unlike every earlier version — the retrievability at @t == s@ --- is not a fixed @0.9@ but drifts with @s@. +-- | The pieces of the two-component mixture, shared by 'retrievability' and +-- 'retrievabilityDerivative' so that the two cannot drift apart. -- --- @t@ must be non-negative and @s@ strictly positive. -retrievability :: Parameters -> Days -> Stability -> Retrievability -retrievability params t s = (weight1 * r1 + weight2 * r2) / (weight1 + weight2) +-- Each component is @inner ** decay@ where @inner = 1 + rate * t@, which makes +-- both the value and its slope one-liners. +data CurveParts = CurveParts + { cpDecay1 :: !Double + , cpRate1 :: !Double + , cpInner1 :: !Double + , cpDecay2 :: !Double + , cpRate2 :: !Double + , cpInner2 :: !Double + , cpWeight1 :: !Double + , cpWeight2 :: !Double + } + +curveParts :: Parameters -> Days -> MemoryState -> CurveParts +curveParts params t0 state = + CurveParts + { cpDecay1 = decay1 + , cpRate1 = rate1 + , cpInner1 = 1 + rate1 * t + , cpDecay2 = decay2 + , cpRate2 = rate2 + , cpInner2 = 1 + rate2 * t + , cpWeight1 = cwWeight1 cw * sFast ** negate (cwStabilityPower1 cw) + , cpWeight2 = + cwWeight2 cw + * s ** cwStabilityPower2 cw + * exp ((d - 5) * (cwDifficultyWeight cw - 0.5)) + } where cw = curveWeights params - tOverS = t / s - powerLaw base decay = (1 + factor * tOverS) ** decay - where - factor = base ** (1 / decay) - 1 - r1 = powerLaw (cwBase1 cw) (cwDecay1 cw) - r2 = powerLaw (cwBase2 cw) (cwDecay2 cw) - weight1 = cwWeight1 cw * s ** negate (cwStabilityPower1 cw) - weight2 = cwWeight2 cw * s ** cwStabilityPower2 cw + t = max 0 t0 + s = clampStability (memoryStability state) + d = clampDifficulty (memoryDifficulty state) + sFast = clampStability (memoryStabilityFast state) + -- Fast component: the decay is scaled by the fast stability itself. + decay1 = fastDecay cw sFast + rate1 = shapeFactor1 cw decay1 / sFast + + -- Slow component: difficulty rescales *time* rather than the decay, so a + -- hard card experiences time faster but decays with the same slope. + decay2 = negate (clampTo decayMin decayMax (cwDecay2 cw)) + factor2 = cwBase2 cw ** (1 / decay2) - 1 + timescale = exp ((d - 5) * (cwDifficultyDecay cw - 0.3)) + rate2 = factor2 * timescale / s + +fastDecay :: CurveWeights -> Stability -> Double +fastDecay cw sFast = + negate . clampTo decayMin decayMax $ + cwDecayBase1 cw * sFast ** (cwStabilityDecay1 cw - 0.3) + +-- | @base1 ** (1 \/ decay1) - 1@, built in log space and capped so that a +-- decay near zero cannot overflow it. +shapeFactor1 :: CurveWeights -> Double -> Double +shapeFactor1 cw decay1 = exp (min logFactorCap (log (cwBase1 cw) / decay1)) - 1 + +-- | Rescale a raw mixture value into +-- @['retrievabilityFloor', 1 - 'retrievabilityFloor']@. +rescale :: Double -> Double +rescale x = x * (1 - 2 * retrievabilityFloor) + retrievabilityFloor + +-- | The probability of recalling a card @t@ days after the last review. +-- +-- FSRS-7 mixes a fast-trace and a slow-trace power law, so this needs the +-- whole memory state — both stabilities /and/ the difficulty. The weight of +-- each component depends on its own stability, so — unlike every earlier +-- version — the retrievability at @t == s@ is not a fixed @0.9@. +-- +-- @t@ is treated as @0@ if negative; the state is clamped into range, so any +-- finite state is safe. +retrievability :: Parameters -> Days -> MemoryState -> Retrievability +retrievability params t state = rescale ((w1 * r1 + w2 * r2) / (w1 + w2)) + where + cp = curveParts params t state + r1 = cpInner1 cp ** cpDecay1 cp + r2 = cpInner2 cp ** cpDecay2 cp + w1 = cpWeight1 cp + w2 = cpWeight2 cp + -- | @d\/dt@ of 'retrievability'. Never positive for in-bounds parameters. -retrievabilityDerivative :: Parameters -> Days -> Stability -> Double -retrievabilityDerivative params t s = - (weight1 * d1 + weight2 * d2) / (weight1 + weight2) +retrievabilityDerivative :: Parameters -> Days -> MemoryState -> Double +retrievabilityDerivative params t state = + (w1 * d1 + w2 * d2) / (w1 + w2) * (1 - 2 * retrievabilityFloor) where + cp = curveParts params t state + d1 = cpDecay1 cp * cpInner1 cp ** (cpDecay1 cp - 1) * cpRate1 cp + d2 = cpDecay2 cp * cpInner2 cp ** (cpDecay2 cp - 1) * cpRate2 cp + w1 = cpWeight1 cp + w2 = cpWeight2 cp + +-- | The fast trace's /own/ recall probability — the mixture's fast component +-- on its own, unrescaled and with no contribution from the slow trace. +-- +-- This is what drives the fast trace's stability update in 'nextStability': +-- the fast trace responds to how well /it/ was doing, not to the mixture. +fastTraceRetrievability :: Parameters -> Days -> Stability -> Retrievability +fastTraceRetrievability params t0 sFast0 = (1 + rate * t) ** decay + where cw = curveWeights params - tOverS = t / s - slope base decay = decay * inner ** (decay - 1) * (factor / s) - where - factor = base ** (1 / decay) - 1 - inner = 1 + factor * tOverS - d1 = slope (cwBase1 cw) (cwDecay1 cw) - d2 = slope (cwBase2 cw) (cwDecay2 cw) - weight1 = cwWeight1 cw * s ** negate (cwStabilityPower1 cw) - weight2 = cwWeight2 cw * s ** cwStabilityPower2 cw + t = max 0 t0 + sFast = clampStability sFast0 + decay = fastDecay cw sFast + rate = shapeFactor1 cw decay / sFast --- | The interval, in days, after which a card of the given stability will have +-- | The interval, in days, after which a card in the given state will have -- decayed to exactly the desired retention. -- -- The FSRS-7 forgetting curve has no closed-form inverse, so this is a -- root-find: Newton's method in @log t@ (which is what makes the problem --- well-conditioned — see the upstream @fsrs_v7_interval_penalty@ module), --- safeguarded by a bracketing bisection so that it cannot diverge. +-- well-conditioned), safeguarded by a bracketing bisection so that it cannot +-- diverge. -- -- The result is always within @['minimumIntervalDays', 'maximumIntervalDays']@; -- a desired retention that is unreachable within that window saturates at the --- nearer end. -nextIntervalDays :: Parameters -> Retrievability -> Stability -> Days -nextIntervalDays params target s +-- nearer end. Since retrievability tops out just below @1@, a target of @1@ +-- saturates rather than diverging. +nextIntervalDays :: Parameters -> Retrievability -> MemoryState -> Days +nextIntervalDays params target state | not (target > 0) = maximumIntervalDays -- also catches NaN | target >= 1 = minimumIntervalDays - | retrievability params lo s <= target = lo - | retrievability params hi s >= target = hi + | curve lo <= target = lo + | curve hi >= target = hi | otherwise = exp (search (0 :: Int) (log lo) (log hi) u0) where + curve t = retrievability params t state lo = minimumIntervalDays hi = maximumIntervalDays - -- R(s, s) is near the interesting range, so start there. - u0 = clampTo (log lo) (log hi) (log s) + -- R around the slow stability is near the interesting range, so start + -- there. + u0 = clampTo (log lo) (log hi) (log (clampStability (memoryStability state))) maxIterations = 200 :: Int -- Full double precision in log space. @@ -177,11 +284,11 @@ | otherwise = search (n + 1) a' b' next where t = exp u - fu = retrievability params t s - target + fu = curve t - target -- R is strictly decreasing in t, so the sign of `fu` says which side -- of the root `u` is on. (a', b') = if fu > 0 then (u, b) else (a, u) - slope = retrievabilityDerivative params t s * t + slope = retrievabilityDerivative params t state * t newton = u - fu / slope next | isNaN newton || isInfinite newton || newton <= a' || newton >= b' = @@ -204,17 +311,27 @@ -- | The difficulty a card is born with, given the rating of its first review. initialDifficulty :: Parameters -> Rating -> Difficulty -initialDifficulty params = - clampTo difficultyMin difficultyMax . rawInitialDifficulty params +initialDifficulty params = clampDifficulty . rawInitialDifficulty params -- | Difficulty after a review: a rating-driven step, damped so that it slows -- down as difficulty approaches its maximum, then reverted 1% of the way -- towards the difficulty an 'Easy' first review would have produced. -nextDifficulty :: Parameters -> Difficulty -> Rating -> Difficulty -nextDifficulty params d rating = - clampTo difficultyMin difficultyMax (meanReversion damped) +-- +-- A lapse's step is weighted by how surprising the lapse was, which is why +-- this takes the retrievability at review time: forgetting a card the model +-- expected you to recall says more about the card than forgetting one that was +-- long overdue. +nextDifficulty + :: Parameters + -> Difficulty + -> Retrievability + -- ^ The retrievability at review time, from 'retrievability'. + -> Rating + -> Difficulty +nextDifficulty params d r rating = clampDifficulty (meanReversion damped) where - delta = negate (difficultyDelta params) * fromIntegral (ratingToInt rating - 3) + step = negate (difficultyDelta params) * fromIntegral (ratingToInt rating - 3) + delta = if rating == Again then step * (r + 0.1) else step damped = d + delta * (10 - d) / 9 meanReversion current = 0.01 * rawInitialDifficulty params Easy + 0.99 * current @@ -226,31 +343,33 @@ initialStability :: Parameters -> Rating -> Stability initialStability = initialStabilityWeight --- | One half of the stability update. +-- | One trace's stability update. -- --- Called twice per review — once with 'FSRS.Parameters.longTermWeights' and --- once with 'FSRS.Parameters.shortTermWeights' — and the two results are --- blended by 'nextStability'. +-- Called twice per review — once with 'FSRS.Parameters.slowTraceWeights' and +-- once with 'FSRS.Parameters.fastTraceWeights' — on that trace's own stability +-- and its own retrievability. -- -- On a lapse the new stability is the post-lapse stability, which can never --- exceed the old one. On a success it is the old stability scaled by a factor --- that grows with how overdue the card was, shrinks as the card gets easier --- and more stable, and is scaled again by the hard penalty or the easy bonus. +-- exceed the old one and, in the finished FSRS-7, does not depend on +-- difficulty. On a success it is the old stability scaled by a factor that +-- grows with how overdue the card was, shrinks as the card gets easier and +-- more stable, and is scaled again by the hard penalty or the easy bonus. stabilityAfterReview :: StabilityWeights - -> MemoryState + -> Stability + -- ^ The stability of the trace being updated. + -> Difficulty -> Retrievability - -- ^ The retrievability at review time, from 'retrievability'. + -- ^ That trace's retrievability at review time. -> Rating -> Stability -stabilityAfterReview w (MemoryState s d) r rating - | rating == Again = postLapse - | otherwise = max postLapse (s * increase) +stabilityAfterReview w s d r rating + | rating == Again = clampStability postLapse + | otherwise = clampStability (max postLapse (s * increase)) where postLapse = min s failureStability failureStability = swFailureFactor w - * d ** negate (swFailureDifficultyExponent w) * ((s + 1) ** swFailureStabilityExponent w - 1) * exp ((1 - r) * swFailureRetrievabilityFactor w) hardPenalty = if rating == Hard then swHardPenalty w else 1 @@ -264,40 +383,76 @@ * hardPenalty * easyBonus --- | How much of a long-term review this is: @0@ for a review that happens at --- the same instant as the previous one, tending to @1@ as the gap grows. +-- | Both stabilities after a review, as @(slow, fast)@. -- --- This is the piece that replaces FSRS-6's hard same-day\/not-same-day split. --- The elapsed time is expected to be non-negative. -transitionCoefficient :: Parameters -> Days -> Double -transitionCoefficient params deltaT = - 1 - transitionAmplitude params * exp (negate (transitionRate params) * deltaT) - --- | Stability after a review, blending the long- and short-term updates. +-- The slow trace is updated from the mixed 'retrievability'; the fast trace +-- from its own 'fastTraceRetrievability'. On a lapse the fast trace is pulled +-- down to at most 'fastTraceRatio' of the post-lapse slow stability, so that +-- forgetting a card cannot leave it with a large short-term boost. nextStability :: Parameters -> MemoryState -> Days -- ^ Days since the previous review. -> Rating - -> Stability -nextStability params state deltaT rating = - coefficient * longTerm + (1 - coefficient) * shortTerm + -> (Stability, Stability) +nextStability params state deltaT rating = (slow, fast) where - r = retrievability params deltaT (memoryStability state) - longTerm = stabilityAfterReview (longTermWeights params) state r rating - shortTerm = stabilityAfterReview (shortTermWeights params) state r rating - coefficient = transitionCoefficient params deltaT + (slow, fast, _) = advance params state deltaT rating +-- | The whole update in one pass: both stabilities and the mixed +-- retrievability that the difficulty step also needs, so that the forgetting +-- curve is evaluated exactly once per review. +advance + :: Parameters + -> MemoryState + -> Days + -> Rating + -> (Stability, Stability, Retrievability) +advance params state deltaT rating = (slow, fast, r) + where + t = max 0 deltaT + d = clampDifficulty (memoryDifficulty state) + r = retrievability params t state + slow = + stabilityAfterReview + (slowTraceWeights params) + (clampStability (memoryStability state)) + d + r + rating + rFast = fastTraceRetrievability params t (memoryStabilityFast state) + raw = + stabilityAfterReview + (fastTraceWeights params) + (clampStability (memoryStabilityFast state)) + d + rFast + rating + fast + | rating == Again = min raw (fastTraceRatio * slow) + | otherwise = raw + -- --------------------------------------------------------------------------- -- State transition -- --------------------------------------------------------------------------- +-- | The state a card is born with, given the rating of its first review. The +-- fast trace starts at 'fastTraceRatio' of the slow one. +initialMemoryState :: Parameters -> Rating -> MemoryState +initialMemoryState params rating = + MemoryState + { memoryStability = clampStability s + , memoryDifficulty = initialDifficulty params rating + , memoryStabilityFast = clampStability (fastTraceRatio * s) + } + where + s = initialStability params rating + -- | Advance a card's memory state by one review. -- -- Pass 'Nothing' for a card that has never been reviewed; the elapsed time is --- then ignored and the state is read straight off the initial-stability and --- initial-difficulty weights. +-- then ignored and the state comes from 'initialMemoryState'. nextMemoryState :: Parameters -> Maybe MemoryState @@ -306,21 +461,17 @@ -- ^ Days since the previous review. -> Rating -> MemoryState -nextMemoryState params before deltaT rating = - MemoryState - { memoryStability = clampTo stabilityMin stabilityMax s - , memoryDifficulty = clampTo difficultyMin difficultyMax d - } - where - (s, d) = case before of - Nothing -> - ( initialStability params rating - , initialDifficulty params rating - ) - Just state -> - ( nextStability params state deltaT rating - , nextDifficulty params (memoryDifficulty state) rating - ) +nextMemoryState params before deltaT rating = case before of + Nothing -> initialMemoryState params rating + Just state -> + MemoryState + { memoryStability = clampStability slow + , memoryDifficulty = + nextDifficulty params (clampDifficulty (memoryDifficulty state)) r rating + , memoryStabilityFast = clampStability fast + } + where + (slow, fast, r) = advance params state deltaT rating -- | Fold a whole review history into a memory state. -- diff --git a/src/FSRS/Parameters.hs b/src/FSRS/Parameters.hs --- a/src/FSRS/Parameters.hs +++ b/src/FSRS/Parameters.hs @@ -1,6 +1,6 @@ {-# LANGUAGE DerivingStrategies #-} --- | The 35 weights of FSRS-7, and typed views onto the blocks they form. +-- | The 34 weights of FSRS-7, and typed views onto the blocks they form. -- -- FSRS-7 groups its weights like this: -- @@ -9,17 +9,17 @@ -- +-----------+------------------------------------------------------------+ -- | @w4..w6@ | difficulty | -- +-----------+------------------------------------------------------------+ --- | @w7..w15@ | stability update, long-term block | +-- | @w7..w14@ | stability update, slow trace | -- +-----------+------------------------------------------------------------+ --- | @w16..w24@| stability update, short-term (same-day) block | +-- | @w15..w22@| stability update, fast trace | -- +-----------+------------------------------------------------------------+ --- | @w25,w26@ | the long-\/short-term transition function | +-- | @w23..w30@| the two-component forgetting curve | -- +-----------+------------------------------------------------------------+ --- | @w27..w34@| the two-component forgetting curve | +-- | @w31..w33@| how difficulty and stability modulate that curve | -- +-----------+------------------------------------------------------------+ -- -- The two stability blocks have identical shapes, which is why --- 'longTermWeights' and 'shortTermWeights' both produce a t'StabilityWeights'. +-- 'slowTraceWeights' and 'fastTraceWeights' both produce a t'StabilityWeights'. module FSRS.Parameters ( -- * Parameters Parameters @@ -33,6 +33,7 @@ -- * Validation , ParameterError (..) , parameterBounds + , orderingConstraints , validateParameters -- * Weight blocks @@ -40,17 +41,14 @@ , initialDifficultyBase , initialDifficultyRate , difficultyDelta - , transitionRate - , transitionAmplitude , StabilityWeights (..) - , longTermWeights - , shortTermWeights + , slowTraceWeights + , fastTraceWeights , CurveWeights (..) , curveWeights ) where import Data.Array.Unboxed (UArray, bounds, elems, listArray, (!)) -import Data.Maybe (mapMaybe) import FSRS.Types (Rating, ratingToInt) @@ -66,10 +64,11 @@ showParen (d > 10) $ showString "mkParameters " . showsPrec 11 (parametersToList p) --- | @35@. FSRS-6 had 21 weights; FSRS-7 adds a second stability block, the --- transition function and the six extra forgetting-curve weights. +-- | @34@. FSRS-6 had 21 weights. FSRS-7 keeps two stability blocks of eight +-- weights each — one per memory trace — and spends eleven on a forgetting +-- curve that mixes the two traces and is modulated by difficulty. parameterCount :: Int -parameterCount = 35 +parameterCount = 34 -- | The 0-based weight at the given index. Indices outside -- @[0, 'parameterCount')@ are a programmer error and raise an exception. @@ -89,57 +88,52 @@ -- | The default FSRS-7 parameters, obtained by the upstream authors through -- multi-user optimisation. -- --- These match @models\/fsrs_v7.py@ in --- . --- Note that the @Default Parameters@ section of that repository's README still --- lists @1.15@ for @w15@ and @w24@; that block of the README has not been --- updated since 2026-03-18, while the model was changed to @1.3@ three days --- later. The values below follow the model. +-- These are the @DEFAULT_PARAMETERS@ of the finished FSRS-7 reference +-- implementation, . defaultParameters :: Parameters defaultParameters = Parameters (listArray (0, parameterCount - 1) ws) where ws = [ -- Initial stability, indexed by rating - 1 - 0.041 - , 2.4175 - , 4.1283 - , 11.9709 + 0.1104 + , 2.2395 + , 3.9221 + , 11.7841 , -- Difficulty - 5.6385 - , 0.4468 - , 3.262 - , -- Stability, long-term block - 2.3054 - , 0.1688 - , 1.3325 - , 0.3524 - , 0.0049 - , 0.7503 - , 0.0896 - , 0.6625 - , 1.3 - , -- Stability, short-term block - 0.882 - , 0.3072 - , 3.5875 - , 0.303 - , 0.0107 - , 0.2279 - , 2.6413 - , 0.5594 - , 1.3 - , -- Long-/short-term transition function - 2.5 + 6.1686 + , 0.6457 + , 3.6807 + , -- Stability, slow trace + 1.9795 + , 0.0 + , 1.3826 + , 0.7024 + , 0.5999 + , 0.8146 + , 0.6398 , 1.0 + , -- Stability, fast trace + 1.3207 + , 0.6707 + , 3.8668 + , 0.4416 + , 0.0934 + , 1.8631 + , 0.6162 + , 1.0869 , -- Forgetting curve - 0.0723 - , 0.1634 - , 0.5 - , 0.9555 - , 0.2245 - , 0.6232 - , 0.1362 - , 0.3862 + 0.1567 + , 0.0801 + , 0.2421 + , 0.9464 + , 0.1433 + , 0.7145 + , 0.0 + , 0.5667 + , -- Modulation of the curve by difficulty and stability + 0.3734 + , 0.5333 + , 0.3048 ] -- | Why a list of weights is not a valid parameter vector. @@ -170,43 +164,44 @@ (1.0, 10.0) , (0.001, 4.0) , (0.1, 4.0) - , -- Stability, long-term block + , -- Stability, slow trace (0.0, 4.0) , (0.0, 1.2) , (0.3, 3.0) , (0.01, 1.5) - , (0.001, 0.9) , (0.1, 1.0) , (0.0, 3.5) , (0.0, 1.0) , (1.0, 7.0) - , -- Stability, short-term block + , -- Stability, fast trace (0.0, 4.0) , (0.0, 2.0) , (0.5, 6.0) , (0.001, 1.5) - , (0.001, 2.0) , (0.001, 1.0) , (0.0, 5.0) , (0.0, 1.0) , (1.0, 7.0) - , -- Transition function - (2.5, 15.0) - , (0.0, 1.0) , -- Forgetting curve (0.01, 0.25) , (0.01, 0.95) - , (0.5, 0.85) + , (0.2, 0.85) , (0.5, 0.99) , (0.01, 1.0) , (0.1, 1.0) , (0.0, 0.9) , (0.1, 1.1) + , -- Modulation of the curve + (0.0, 1.0) + , (0.0, 0.6) + , (0.0, 0.6) ] --- | Pairs @(i, j)@ for which @w[i] <= w[j]@ must hold. +-- | Pairs @(i, j)@ for which @w[i] <= w[j]@ must hold: the initial stabilities +-- rise with the rating, and the slow component of the forgetting curve starts +-- above the fast one. orderingConstraints :: [(Int, Int)] -orderingConstraints = [(0, 1), (1, 2), (2, 3), (27, 28), (29, 30)] +orderingConstraints = [(0, 1), (1, 2), (2, 3), (25, 26)] -- | Every problem with a candidate weight list, or @[]@ if there is none. validateParameters :: [Double] -> [ParameterError] @@ -220,10 +215,14 @@ | isNaN w || isInfinite w = [ParameterNotFinite i w] | w < lo || w > hi = [ParameterOutOfBounds i w lo hi] | otherwise = [] - orderErrors = mapMaybe checkOrder orderingConstraints + -- Only meaningful once every weight is known to be finite; otherwise a + -- NaN would be reported twice, once as itself and once as out of order. + orderErrors + | null boundErrors = concatMap checkOrder orderingConstraints + | otherwise = [] checkOrder (i, j) - | wi <= wj = Nothing - | otherwise = Just (ParameterOutOfOrder i j wi wj) + | wi <= wj = [] + | otherwise = [ParameterOutOfOrder i j wi wj] where wi = ws !! i wj = ws !! j @@ -235,23 +234,23 @@ errs -> Left errs -- | Build a parameter vector by pulling every weight into its valid range, --- exactly as the upstream optimiser's clipper does: bounds first, in index --- order, so that the ordering constraints are resolved against already-clamped --- neighbours. Only a wrong number of weights can still fail. +-- exactly as the upstream optimiser's clipper does: every weight is clamped to +-- its own bounds first, and only then are the ordering constraints restored by +-- raising the /larger/ index. Only a wrong number of weights can still fail. clampParameters :: [Double] -> Either [ParameterError] Parameters clampParameters ws | length ws /= parameterCount = Left [WrongParameterCount (length ws)] - | otherwise = Right (Parameters (listArray (0, parameterCount - 1) clamped)) + | otherwise = Right (Parameters (listArray (0, parameterCount - 1) ordered)) where - clamped = foldl step [] (zip3 [0 :: Int ..] ws parameterBounds) - -- `acc` is the already-clamped prefix, in order. - step acc (i, w, (lo, hi)) = acc <> [clamp lo' hi' w] - where - lo' = maximum (lo : [acc !! j | (j, k) <- orderingConstraints, k == i]) - hi' = max lo' hi - clamp lo hi x + boxed = zipWith clampInto ws parameterBounds + clampInto x (lo, hi) | isNaN x = lo | otherwise = min hi (max lo x) + -- The constraints are listed in increasing order and chain through the + -- initial stabilities, so a single left-to-right pass settles them. + ordered = foldl raise boxed orderingConstraints + raise acc (i, j) = setAt j (max (acc !! j) (acc !! i)) acc + setAt i x xs = take i xs <> [x] <> drop (i + 1) xs -- | @w[rating - 1]@: the stability a card is born with after its first review. initialStabilityWeight :: Parameters -> Rating -> Double @@ -269,34 +268,25 @@ difficultyDelta :: Parameters -> Double difficultyDelta p = parameterAt p 6 --- | @w25@: how fast a review stops counting as same-day. -transitionRate :: Parameters -> Double -transitionRate p = parameterAt p 25 - --- | @w26@: how much of the short-term behaviour applies at zero elapsed time. -transitionAmplitude :: Parameters -> Double -transitionAmplitude p = parameterAt p 26 - --- | One of the two nine-weight blocks that drive the stability update. +-- | One of the two eight-weight blocks that drive the stability update, one +-- per memory trace. data StabilityWeights = StabilityWeights { swIncreaseBase :: !Double - -- ^ @w7@ \/ @w16@, used as @exp (base - 1.5)@. + -- ^ @w7@ \/ @w15@, used as @exp (base - 1.5)@. , swIncreaseStabilityExponent :: !Double - -- ^ @w8@ \/ @w17@. + -- ^ @w8@ \/ @w16@. , swIncreaseRetrievabilityFactor :: !Double - -- ^ @w9@ \/ @w18@. + -- ^ @w9@ \/ @w17@. , swFailureFactor :: !Double - -- ^ @w10@ \/ @w19@. - , swFailureDifficultyExponent :: !Double - -- ^ @w11@ \/ @w20@. + -- ^ @w10@ \/ @w18@. , swFailureStabilityExponent :: !Double - -- ^ @w12@ \/ @w21@. + -- ^ @w11@ \/ @w19@. , swFailureRetrievabilityFactor :: !Double - -- ^ @w13@ \/ @w22@. + -- ^ @w12@ \/ @w20@. , swHardPenalty :: !Double - -- ^ @w14@ \/ @w23@. + -- ^ @w13@ \/ @w21@. , swEasyBonus :: !Double - -- ^ @w15@ \/ @w24@. + -- ^ @w14@ \/ @w22@. } deriving stock (Eq, Show) @@ -307,42 +297,57 @@ , swIncreaseStabilityExponent = at 1 , swIncreaseRetrievabilityFactor = at 2 , swFailureFactor = at 3 - , swFailureDifficultyExponent = at 4 - , swFailureStabilityExponent = at 5 - , swFailureRetrievabilityFactor = at 6 - , swHardPenalty = at 7 - , swEasyBonus = at 8 + , swFailureStabilityExponent = at 4 + , swFailureRetrievabilityFactor = at 5 + , swHardPenalty = at 6 + , swEasyBonus = at 7 } where at k = parameterAt p (base + k) --- | @w7..w15@: the block used for reviews separated by a real interval. -longTermWeights :: Parameters -> StabilityWeights -longTermWeights = stabilityWeightsAt 7 +-- | @w7..w14@: the block that updates the slow trace. +slowTraceWeights :: Parameters -> StabilityWeights +slowTraceWeights = stabilityWeightsAt 7 --- | @w16..w24@: the block used for same-day reviews. -shortTermWeights :: Parameters -> StabilityWeights -shortTermWeights = stabilityWeightsAt 16 +-- | @w15..w22@: the block that updates the fast trace. +fastTraceWeights :: Parameters -> StabilityWeights +fastTraceWeights = stabilityWeightsAt 15 --- | @w27..w34@: the mixture of two power laws that makes up the FSRS-7 --- forgetting curve. +-- | @w23..w33@: the mixture of two power laws that makes up the FSRS-7 +-- forgetting curve, and the three weights that modulate it. +-- +-- The last three are stored the way the reference stores them — shifted so +-- that their range starts at zero — and the formulas in "FSRS.Algorithm" +-- offset them back. The field documentation gives the offset each one carries. data CurveWeights = CurveWeights - { cwDecay1 :: !Double - -- ^ @negate w27@ — already carries the minus sign the formula wants. + { cwDecayBase1 :: !Double + -- ^ @w23@: sets the fast component's decay, which is also scaled by the + -- fast stability, so unlike every earlier version of FSRS the decay is not + -- a constant. , cwDecay2 :: !Double - -- ^ @negate w28@. + -- ^ @w24@: the slow component's decay magnitude. , cwBase1 :: !Double - -- ^ @w29@: the recall probability of the first component at @t == s@. + -- ^ @w25@: the fast component's recall probability at @t == s_fast@. , cwBase2 :: !Double - -- ^ @w30@: likewise for the second component. + -- ^ @w26@: likewise for the slow component at @t == s@. , cwWeight1 :: !Double - -- ^ @w31@. + -- ^ @w27@: how much the fast component counts in the mixture. , cwWeight2 :: !Double - -- ^ @w32@. + -- ^ @w28@: likewise for the slow component. , cwStabilityPower1 :: !Double - -- ^ @w33@; applied as @s ** negate cwStabilityPower1@. + -- ^ @w29@; applied as @s_fast ** negate cwStabilityPower1@. , cwStabilityPower2 :: !Double - -- ^ @w34@; applied as @s ** cwStabilityPower2@. + -- ^ @w30@; applied as @s ** cwStabilityPower2@. + , cwDifficultyWeight :: !Double + -- ^ @w31@; the mixture weight of the slow component is scaled by + -- @exp ((d - 5) * (cwDifficultyWeight - 0.5))@. + , cwDifficultyDecay :: !Double + -- ^ @w32@; the slow component sees time scaled by + -- @exp ((d - 5) * (cwDifficultyDecay - 0.3))@, so a hard card experiences + -- time faster while decaying with the same slope. + , cwStabilityDecay1 :: !Double + -- ^ @w33@; the fast component's decay is scaled by + -- @s_fast ** (cwStabilityDecay1 - 0.3)@. } deriving stock (Eq, Show) @@ -350,12 +355,15 @@ curveWeights :: Parameters -> CurveWeights curveWeights p = CurveWeights - { cwDecay1 = negate (parameterAt p 27) - , cwDecay2 = negate (parameterAt p 28) - , cwBase1 = parameterAt p 29 - , cwBase2 = parameterAt p 30 - , cwWeight1 = parameterAt p 31 - , cwWeight2 = parameterAt p 32 - , cwStabilityPower1 = parameterAt p 33 - , cwStabilityPower2 = parameterAt p 34 + { cwDecayBase1 = parameterAt p 23 + , cwDecay2 = parameterAt p 24 + , cwBase1 = parameterAt p 25 + , cwBase2 = parameterAt p 26 + , cwWeight1 = parameterAt p 27 + , cwWeight2 = parameterAt p 28 + , cwStabilityPower1 = parameterAt p 29 + , cwStabilityPower2 = parameterAt p 30 + , cwDifficultyWeight = parameterAt p 31 + , cwDifficultyDecay = parameterAt p 32 + , cwStabilityDecay1 = parameterAt p 33 } diff --git a/src/FSRS/Scheduler.hs b/src/FSRS/Scheduler.hs --- a/src/FSRS/Scheduler.hs +++ b/src/FSRS/Scheduler.hs @@ -14,7 +14,7 @@ -- -- * Elapsed time is measured in fractional days rather than truncated to whole -- days, and it is fed to the model directly. There is no same-day special --- case, because 'FSRS.Algorithm.transitionCoefficient' already is one. +-- case, because FSRS-7's fast memory trace already is one. -- * Scheduled intervals are not rounded to whole days. Set -- 'schedulerMinimumInterval' to @1@ (the default) to keep review-queue -- intervals at a day or more anyway, or lower it to let FSRS-7 schedule @@ -61,7 +61,6 @@ , MemoryState (..) , Rating (..) , Retrievability - , Stability , allRatings ) @@ -131,15 +130,19 @@ minutes :: Integer -> NominalDiffTime minutes n = fromInteger (n * 60) --- | The interval a graduated card of the given stability earns, clamped to the +-- | The interval a graduated card in the given state earns, clamped to the -- scheduler's interval bounds. -nextReviewInterval :: Scheduler -> Stability -> Days -nextReviewInterval sched stability = +-- +-- This takes a whole t'MemoryState' rather than a stability, because the +-- FSRS-7 forgetting curve is a mixture of both memory traces and is shaped by +-- the difficulty too. +nextReviewInterval :: Scheduler -> MemoryState -> Days +nextReviewInterval sched memory = clampTo (schedulerMinimumInterval sched) (schedulerMaximumInterval sched) $ nextIntervalDays (schedulerParameters sched) (schedulerDesiredRetention sched) - stability + memory -- | What happened in a single review. data ReviewLog = ReviewLog @@ -219,7 +222,7 @@ where graduate = (Review, Nothing, daysToDiffTime fuzzed) where - plain = nextReviewInterval sched (memoryStability memory) + plain = nextReviewInterval sched memory fuzzed = maybe plain (\u -> fuzzInterval sched u plain) sample current = max 0 (fromMaybe 0 (cardStep card)) @@ -257,7 +260,7 @@ memory <- cardMemory card previous <- cardLastReview card let elapsed = max 0 (realToFrac (diffUTCTime now previous) / 86400) - pure (retrievability (schedulerParameters sched) elapsed (memoryStability memory)) + pure (retrievability (schedulerParameters sched) elapsed memory) -- | The interval each of the four ratings would earn, without reviewing. -- Handy for showing the four buttons' answers in a UI. diff --git a/src/FSRS/Types.hs b/src/FSRS/Types.hs --- a/src/FSRS/Types.hs +++ b/src/FSRS/Types.hs @@ -51,7 +51,9 @@ -- | How hard the card is for this reviewer, on a @[1, 10]@ scale. type Difficulty = Double --- | Probability of recall, in @(0, 1]@. +-- | Probability of recall. FSRS-7 squeezes it into @[1e-5, 1 - 1e-5]@ so that +-- neither it nor its logarithm can saturate, so a card reviewed a moment ago +-- has a retrievability just short of @1@ rather than exactly @1@. type Retrievability = Double -- | A duration in days. Fractional values are meaningful throughout FSRS-7: @@ -59,8 +61,25 @@ type Days = Double -- | Everything FSRS remembers about a card. +-- +-- FSRS-7 tracks /two/ memory traces rather than one. Both are stabilities in +-- the same units; they differ only in how fast they decay and in which weights +-- update them. +-- +-- * 'memoryStability' is the slow trace — the durable memory, and the one a +-- scheduler turns into an interval. +-- * 'memoryStabilityFast' is the fast trace, which carries the short-lived +-- boost a review gives you. It is what makes same-day reviews behave +-- differently from spaced ones, and it replaces the elapsed-time blend +-- between a long- and a short-term update that earlier drafts of FSRS-7 +-- used. +-- +-- The forgetting curve is a mixture of the two, so 'retrievability' needs a +-- whole 'MemoryState' — including the difficulty, which in FSRS-7 shapes the +-- curve as well. data MemoryState = MemoryState { memoryStability :: !Stability , memoryDifficulty :: !Difficulty + , memoryStabilityFast :: !Stability } deriving stock (Eq, Ord, Show, Read) diff --git a/test/Test/FSRS/Gen.hs b/test/Test/FSRS/Gen.hs --- a/test/Test/FSRS/Gen.hs +++ b/test/Test/FSRS/Gen.hs @@ -12,7 +12,10 @@ , genStability , genDifficulty , genMemoryState + , genNaturalMemoryState + , genGrowableState , genElapsedDays + , genRetrievability , genDesiredRetention , genReviewHistory , genUTCTime @@ -40,7 +43,7 @@ genRandomParameters :: Gen Parameters genRandomParameters = do ws <- traverse choose parameterBounds - -- `clampParameters` only re-establishes the three ordering constraints; the + -- `clampParameters` only re-establishes the ordering constraints; the -- weights are already inside their individual bounds. case clampParameters ws of Right p -> pure p @@ -67,15 +70,71 @@ , (8, choose (difficultyMin, difficultyMax)) ] +-- | A whole memory state. The fast trace is usually a modest multiple of the +-- slow one, as it is in practice, but sometimes wildly different so that +-- nothing may assume a relationship between them. genMemoryState :: Gen MemoryState -genMemoryState = MemoryState <$> genStability <*> genDifficulty +genMemoryState = do + s <- genStability + d <- genDifficulty + sFast <- + frequency + [ (6, pure (clampStability (s * fastTraceRatio))) + , (2, (\k -> clampStability (s * k)) <$> choose (0.05, 20)) + , (2, genStability) + ] + pure (MemoryState s d sFast) + where + clampStability = min stabilityMax . max stabilityMin +-- | A state whose fast trace sits at exactly the ratio to the slow one that +-- the model itself establishes for a new card. +-- +-- Properties about what /more stability/ or /more difficulty/ does need this: +-- the FSRS-7 curve weights its two components by their own stabilities, so for +-- a wildly lopsided pair of traces those questions have no monotone answer — +-- raising difficulty slows the slow component but also shifts mixture weight +-- onto the fast one, and which effect wins depends on the ratio. +genNaturalMemoryState :: Gen MemoryState +genNaturalMemoryState = do + s <- choose (log naturalStabilityMin, log stabilityMax) + d <- genDifficulty + pure (naturalState (exp s) d) + +-- | A 'genNaturalMemoryState' together with a factor by which both of its +-- traces can be multiplied without either leaving its range — so that scaling +-- really does scale, instead of saturating one trace and skewing the ratio. +genGrowableState :: Gen (MemoryState, Double) +genGrowableState = do + growth <- exp <$> choose (1.0e-6, 5) + s <- choose (log naturalStabilityMin, log (stabilityMax / growth)) + d <- genDifficulty + pure (naturalState (exp s) d, growth) + +-- | The smallest slow stability whose fast trace is still above the floor, so +-- that the ratio is exact rather than clamped. +naturalStabilityMin :: Stability +naturalStabilityMin = stabilityMin / fastTraceRatio + +naturalState :: Stability -> Difficulty -> MemoryState +naturalState s d = MemoryState s d (fastTraceRatio * s) + -- | Anything from "the same instant" to ten years, log-uniform in between. genElapsedDays :: Gen Days genElapsedDays = frequency [ (2, pure 0) , (8, exp <$> choose (log (1 / 86400), log 3650)) + ] + +-- | Anything the forgetting curve could plausibly have returned, including the +-- extremes it is rescaled into. +genRetrievability :: Gen Retrievability +genRetrievability = + frequency + [ (1, pure retrievabilityFloor) + , (1, pure (1 - retrievabilityFloor)) + , (8, choose (retrievabilityFloor, 1 - retrievabilityFloor)) ] genDesiredRetention :: Gen Retrievability diff --git a/test/Test/FSRS/Golden.hs b/test/Test/FSRS/Golden.hs --- a/test/Test/FSRS/Golden.hs +++ b/test/Test/FSRS/Golden.hs @@ -1,5 +1,5 @@ -- | Every function of the model, checked against vectors produced by the --- pure-Python transcription of the upstream reference implementation. +-- pure-Python transcription of the reference implementation. -- -- The two implementations perform the same floating-point operations in the -- same order on the same libm, so agreement is expected to the last few bits; @@ -36,9 +36,9 @@ , testCase "the first golden parameter set is the default one" $ take 1 goldenParameterSets @?= [parametersToList defaultParameters] , labelled "forgetting curve" goldenCurveVectors checkCurve + , labelled "fast-trace recall" goldenFastRecallVectors checkFastRecall , labelled "difficulty" goldenDifficultyVectors checkDifficulty , labelled "stability blocks" goldenHalfStabilityVectors checkHalfStability - , labelled "transition function" goldenTransitionVectors checkTransition , labelled "memory-state transition" goldenStepVectors checkStep , labelled "interval inversion" goldenIntervalVectors checkInterval , labelled "replayed review histories" goldenReplayVectors checkReplay @@ -59,6 +59,10 @@ Just r -> r Nothing -> error ("golden vector has a bad rating: " <> show n) +-- | The vectors spell states out as @(S, D, S_fast)@ triples. +stateOf :: (Double, Double, Double) -> MemoryState +stateOf (s, d, sFast) = MemoryState s d sFast + close :: Double -> String -> Double -> Double -> Assertion close t label expected actual = unless (approxEqual t t actual expected) $ @@ -71,17 +75,28 @@ <> "\n relative error: " <> show (relativeError actual expected) +closeState :: Double -> String -> (Double, Double, Double) -> MemoryState -> Assertion +closeState t label (s, d, sFast) actual = do + close t (label <> " [stability]") s (memoryStability actual) + close t (label <> " [difficulty]") d (memoryDifficulty actual) + close t (label <> " [fast stability]") sFast (memoryStabilityFast actual) + checkCurve :: CurveVector -> Assertion checkCurve v = close tol (show v) (cvRetrievability v) $ - retrievability (paramsAt (cvParams v)) (cvElapsedDays v) (cvStability v) + retrievability (paramsAt (cvParams v)) (cvElapsedDays v) (stateOf (cvState v)) +checkFastRecall :: FastRecallVector -> Assertion +checkFastRecall v = + close tol (show v) (frRecall v) $ + fastTraceRetrievability (paramsAt (frParams v)) (frElapsedDays v) (frStabilityFast v) + checkDifficulty :: DifficultyVector -> Assertion checkDifficulty v = close tol (show v) (dvNextDifficulty v) $ case dvDifficulty v of Nothing -> initialDifficulty params rating - Just d -> nextDifficulty params d rating + Just d -> nextDifficulty params d (dvRetrievability v) rating where params = paramsAt (dvParams v) rating = ratingAt (dvRating v) @@ -91,43 +106,31 @@ close tol (show v) (hsNextStability v) $ stabilityAfterReview block - (MemoryState (hsStability v) (hsDifficulty v)) + (hsStability v) + (hsDifficulty v) (hsRetrievability v) (ratingAt (hsRating v)) where params = paramsAt (hsParams v) - block = (if hsLongTerm v then longTermWeights else shortTermWeights) params - -checkTransition :: TransitionVector -> Assertion -checkTransition v = - close tol (show v) (tvCoefficient v) $ - transitionCoefficient (paramsAt (tvParams v)) (tvElapsedDays v) + block = (if hsSlowTrace v then slowTraceWeights else fastTraceWeights) params checkStep :: StepVector -> Assertion -checkStep v = do - close tol (show v <> " [stability]") expectedS (memoryStability actual) - close tol (show v <> " [difficulty]") expectedD (memoryDifficulty actual) - where - (expectedS, expectedD) = svNextState v - actual = - nextMemoryState - (paramsAt (svParams v)) - (uncurry MemoryState <$> svState v) - (svElapsedDays v) - (ratingAt (svRating v)) +checkStep v = closeState tol (show v) (svNextState v) $ + nextMemoryState + (paramsAt (svParams v)) + (stateOf <$> svState v) + (svElapsedDays v) + (ratingAt (svRating v)) checkInterval :: IntervalVector -> Assertion checkInterval v = close intervalTol (show v) (ivInterval v) $ - nextIntervalDays (paramsAt (ivParams v)) (ivDesiredRetention v) (ivStability v) + nextIntervalDays (paramsAt (ivParams v)) (ivDesiredRetention v) (stateOf (ivState v)) checkReplay :: ReplayVector -> Assertion checkReplay v = case replayReviews params reviews of Nothing -> assertFailure (show v <> ": replayReviews returned Nothing") - Just actual -> do - close tol (show v <> " [stability]") expectedS (memoryStability actual) - close tol (show v <> " [difficulty]") expectedD (memoryDifficulty actual) + Just actual -> closeState tol (show v) (rvFinalState v) actual where params = paramsAt (rvParams v) reviews = [(dt, ratingAt g) | (dt, g) <- rvReviews v] - (expectedS, expectedD) = rvFinalState v diff --git a/test/Test/FSRS/GoldenData.hs b/test/Test/FSRS/GoldenData.hs --- a/test/Test/FSRS/GoldenData.hs +++ b/test/Test/FSRS/GoldenData.hs @@ -7,2717 +7,5721 @@ -- | Golden vectors for the FSRS-7 implementation. -- -- Generated by @reference\/gen_golden.py@ from the pure-Python --- transcription of the official benchmark model. Do not edit by hand; --- regenerate with @python3 reference\/gen_golden.py@. -module Test.FSRS.GoldenData - ( goldenParameterSets - , CurveVector (..) - , goldenCurveVectors - , DifficultyVector (..) - , goldenDifficultyVectors - , HalfStabilityVector (..) - , goldenHalfStabilityVectors - , TransitionVector (..) - , goldenTransitionVectors - , StepVector (..) - , goldenStepVectors - , IntervalVector (..) - , goldenIntervalVectors - , ReplayVector (..) - , goldenReplayVectors - ) where - --- | The parameter sets the vectors below refer to by index. --- Index 0 is the FSRS-7 default parameter set. -goldenParameterSets :: [[Double]] -goldenParameterSets = - [ [0.041, 2.4175, 4.1283, 11.9709, 5.6385, 0.4468, 3.262, 2.3054, 0.1688, 1.3325, 0.3524, 0.0049, 0.7503, 0.0896, 0.6625, 1.3, 0.882, 0.3072, 3.5875, 0.303, 0.0107, 0.2279, 2.6413, 0.5594, 1.3, 2.5, 1.0, 0.0723, 0.1634, 0.5, 0.9555, 0.2245, 0.6232, 0.1362, 0.3862] - , [21.160516, 50.940793, 64.835975, 64.835975, 8.15903, 2.002545, 2.260348, 0.261677, 1.007671, 0.835788, 1.121191, 0.482646, 0.805315, 1.109673, 0.243581, 5.499531, 1.698145, 1.144289, 3.924479, 0.305639, 1.731898, 0.979642, 2.748763, 0.621608, 3.323164, 12.353494, 0.589693, 0.023181, 0.916871, 0.810769, 0.810769, 0.643876, 0.388689, 0.492485, 0.639409] - , [2.462798, 11.949056, 79.640406, 79.640406, 7.614116, 1.181111, 0.390871, 2.724834, 0.753779, 2.243577, 0.730412, 0.835923, 0.322241, 1.039029, 0.595056, 6.951994, 3.326003, 0.777298, 2.338648, 0.894925, 0.32714, 0.712525, 3.444161, 0.965072, 6.509826, 5.536095, 0.438431, 0.018217, 0.26739, 0.581093, 0.581093, 0.397612, 0.469117, 0.180743, 0.357585] - ] - --- | @R(t, s)@, the probability of recall. -data CurveVector = CurveVector - { cvParams :: !Int - , cvElapsedDays :: !Double - , cvStability :: !Double - , cvRetrievability :: !Double - } - deriving stock (Eq, Show) - -goldenCurveVectors :: [CurveVector] -goldenCurveVectors = - [ CurveVector 0 0.0 0.0001 1.0 - , CurveVector 0 0.0 0.01 1.0 - , CurveVector 0 0.0 0.5 1.0 - , CurveVector 0 0.0 1.0 1.0 - , CurveVector 0 0.0 4.1283 1.0 - , CurveVector 0 0.0 15.0 1.0 - , CurveVector 0 0.0 100.0 1.0 - , CurveVector 0 0.0 1000.0 1.0 - , CurveVector 0 0.0 36500.0 1.0 - , CurveVector 0 1.1574074074074073e-5 0.0001 0.5933860064644932 - , CurveVector 0 1.1574074074074073e-5 0.01 0.8495113580744659 - , CurveVector 0 1.1574074074074073e-5 0.5 0.9929070497623003 - , CurveVector 0 1.1574074074074073e-5 1.0 0.9970315864605649 - , CurveVector 0 1.1574074074074073e-5 4.1283 0.9995760691373587 - , CurveVector 0 1.1574074074074073e-5 15.0 0.9999349085685156 - , CurveVector 0 1.1574074074074073e-5 100.0 0.9999961594473195 - , CurveVector 0 1.1574074074074073e-5 1000.0 0.9999998815426243 - , CurveVector 0 1.1574074074074073e-5 36500.0 0.9999999994861863 - , CurveVector 0 0.0006944444444444445 0.0001 0.4432668218647261 - , CurveVector 0 0.0006944444444444445 0.01 0.6844202927268608 - , CurveVector 0 0.0006944444444444445 0.5 0.9323536480673809 - , CurveVector 0 0.0006944444444444445 1.0 0.9576427479174111 - , CurveVector 0 0.0006944444444444445 4.1283 0.9874342644794948 - , CurveVector 0 0.0006944444444444445 15.0 0.9970520789455777 - , CurveVector 0 0.0006944444444444445 100.0 0.999781044413337 - , CurveVector 0 0.0006944444444444445 1000.0 0.9999929300276222 - , CurveVector 0 0.0006944444444444445 36500.0 0.9999999691755385 - , CurveVector 0 0.006944444444444444 0.0001 0.3730533620906363 - , CurveVector 0 0.006944444444444444 0.01 0.6043230466193572 - , CurveVector 0 0.006944444444444444 0.5 0.8907215861983732 - , CurveVector 0 0.006944444444444444 1.0 0.9244321330914924 - , CurveVector 0 0.006944444444444444 4.1283 0.9693189917294772 - , CurveVector 0 0.006944444444444444 15.0 0.9889027240570584 - , CurveVector 0 0.006944444444444444 100.0 0.9984451422665508 - , CurveVector 0 0.006944444444444444 1000.0 0.9999325077444561 - , CurveVector 0 0.006944444444444444 36500.0 0.9999996921537052 - , CurveVector 0 0.25 0.0001 0.2851191592785943 - , CurveVector 0 0.25 0.01 0.456616482214346 - , CurveVector 0 0.25 0.5 0.8224198592478944 - , CurveVector 0 0.25 1.0 0.8723190093653708 - , CurveVector 0 0.25 4.1283 0.9404929608601553 - , CurveVector 0 0.25 15.0 0.9728008245439088 - , CurveVector 0 0.25 100.0 0.9926213962042669 - , CurveVector 0 0.25 1000.0 0.9989715171159107 - , CurveVector 0 0.25 36500.0 0.9999894395613305 - , CurveVector 0 1.0 0.0001 0.25713379769027217 - , CurveVector 0 1.0 0.01 0.39965839215670973 - , CurveVector 0 1.0 0.5 0.7698463681144272 - , CurveVector 0 1.0 1.0 0.8348679957532145 - , CurveVector 0 1.0 4.1283 0.9242342483541028 - , CurveVector 0 1.0 15.0 0.965276266166443 - , CurveVector 0 1.0 100.0 0.9899633108373221 - , CurveVector 0 1.0 1000.0 0.9982079823122783 - , CurveVector 0 1.0 36500.0 0.9999628548326086 - , CurveVector 0 3.0 0.0001 0.2369807334603691 - , CurveVector 0 3.0 0.01 0.3595136620236083 - , CurveVector 0 3.0 0.5 0.7027042985360686 - , CurveVector 0 3.0 1.0 0.7807132698581536 - , CurveVector 0 3.0 4.1283 0.8996583671005782 - , CurveVector 0 3.0 15.0 0.9554107397126494 - , CurveVector 0 3.0 100.0 0.9872853400435361 - , CurveVector 0 3.0 1000.0 0.9975222007805449 - , CurveVector 0 3.0 36500.0 0.9999133375629187 - , CurveVector 0 7.5 0.0001 0.22142030501492593 - , CurveVector 0 7.5 0.01 0.3294480191014634 - , CurveVector 0 7.5 0.5 0.6343961597998443 - , CurveVector 0 7.5 1.0 0.7161183991831989 - , CurveVector 0 7.5 4.1283 0.8618548545083785 - , CurveVector 0 7.5 15.0 0.9397110393641435 - , CurveVector 0 7.5 100.0 0.9837439115086568 - , CurveVector 0 7.5 1000.0 0.9968247800782952 - , CurveVector 0 7.5 36500.0 0.9998474481935904 - , CurveVector 0 30.0 0.0001 0.19984766152161007 - , CurveVector 0 30.0 0.01 0.28929613460097364 - , CurveVector 0 30.0 0.5 0.5298364300580066 - , CurveVector 0 30.0 1.0 0.6031223500178141 - , CurveVector 0 30.0 4.1283 0.7644685415426927 - , CurveVector 0 30.0 15.0 0.886172361687806 - , CurveVector 0 30.0 100.0 0.971243149616753 - , CurveVector 0 30.0 1000.0 0.9950103052406525 - , CurveVector 0 30.0 36500.0 0.9997052031663322 - , CurveVector 0 365.0 0.0001 0.16624187657470219 - , CurveVector 0 365.0 0.01 0.2304175269361819 - , CurveVector 0 365.0 0.5 0.37581378678844907 - , CurveVector 0 365.0 1.0 0.42347782141604523 - , CurveVector 0 365.0 4.1283 0.5441682159716109 - , CurveVector 0 365.0 15.0 0.6762521980608913 - , CurveVector 0 365.0 100.0 0.867529117768457 - 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, CurveVector 1 1.1574074074074073e-5 1.0 0.9986422759813346 - , CurveVector 1 1.1574074074074073e-5 4.1283 0.9998630293353797 - , CurveVector 1 1.1574074074074073e-5 15.0 0.9999889480490822 - , CurveVector 1 1.1574074074074073e-5 100.0 0.9999997688242355 - , CurveVector 1 1.1574074074074073e-5 1000.0 0.9999999957537147 - , CurveVector 1 1.1574074074074073e-5 36500.0 0.9999999999245476 - , CurveVector 1 0.0006944444444444445 0.0001 0.7751473949811729 - , CurveVector 1 0.0006944444444444445 0.01 0.8628468758887021 - , CurveVector 1 0.0006944444444444445 0.5 0.9549077686473312 - , CurveVector 1 0.0006944444444444445 1.0 0.9726123591278394 - , CurveVector 1 0.0006944444444444445 4.1283 0.994878960710534 - , CurveVector 1 0.0006944444444444445 15.0 0.9994396296146354 - , CurveVector 1 0.0006944444444444445 100.0 0.9999864797130398 - , CurveVector 1 0.0006944444444444445 1000.0 0.9999997454930079 - , CurveVector 1 0.0006944444444444445 36500.0 0.9999999954728627 - , CurveVector 1 0.006944444444444444 0.0001 0.7348526048890944 - 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, CurveVector 1 1.0 0.5 0.7731740600264984 - , CurveVector 1 1.0 1.0 0.810769 - , CurveVector 1 1.0 4.1283 0.9190823327933287 - , CurveVector 1 1.0 15.0 0.975841522705037 - , CurveVector 1 1.0 100.0 0.9967920795404497 - , CurveVector 1 1.0 1000.0 0.999730641866046 - , CurveVector 1 1.0 36500.0 0.9999934873029269 - , CurveVector 1 3.0 0.0001 0.6384198660053784 - , CurveVector 1 3.0 0.01 0.708088035759968 - , CurveVector 1 3.0 0.5 0.701602618114653 - , CurveVector 1 3.0 1.0 0.715726404952451 - , CurveVector 1 3.0 4.1283 0.8452125848714827 - , CurveVector 1 3.0 15.0 0.9469306801277422 - , CurveVector 1 3.0 100.0 0.9919643351359503 - , CurveVector 1 3.0 1000.0 0.9992451543075624 - , CurveVector 1 3.0 36500.0 0.9999804885340793 - , CurveVector 1 7.5 0.0001 0.6250024841695064 - , CurveVector 1 7.5 0.01 0.6931736699730552 - , CurveVector 1 7.5 0.5 0.6477065571889125 - , CurveVector 1 7.5 1.0 0.6230688725366799 - , CurveVector 1 7.5 4.1283 0.7276607711422548 - , CurveVector 1 7.5 15.0 0.8899496169066309 - , CurveVector 1 7.5 100.0 0.9815538224427173 - , CurveVector 1 7.5 1000.0 0.9981752619340438 - , CurveVector 1 7.5 36500.0 0.9999513066062199 - , CurveVector 1 30.0 0.0001 0.6052368883847312 - , CurveVector 1 30.0 0.01 0.671234178061259 - , CurveVector 1 30.0 0.5 0.5947036849457923 - , CurveVector 1 30.0 1.0 0.5189670702148328 - , CurveVector 1 30.0 4.1283 0.47889902062470296 - , CurveVector 1 30.0 15.0 0.6917999200125268 - , CurveVector 1 30.0 100.0 0.9332515717445918 - , CurveVector 1 30.0 1000.0 0.9929049778715002 - , CurveVector 1 30.0 36500.0 0.9998057738948768 - , CurveVector 1 365.0 0.0001 0.5711760994954371 - , CurveVector 1 365.0 0.01 0.6334530598009184 - , CurveVector 1 365.0 0.5 0.5473455073533272 - , CurveVector 1 365.0 1.0 0.4467423870943384 - , CurveVector 1 365.0 4.1283 0.2236204733666933 - , CurveVector 1 365.0 15.0 0.20485637040312182 - , CurveVector 1 365.0 100.0 0.5472460692590585 - , CurveVector 1 365.0 1000.0 0.9209964297111749 - , CurveVector 1 365.0 36500.0 0.9976476169878027 - , CurveVector 1 3650.0 0.0001 0.5414882365587022 - , CurveVector 1 3650.0 0.01 0.600527626709789 - , CurveVector 1 3650.0 0.5 0.5174338916915161 - , CurveVector 1 3650.0 1.0 0.4187361900293764 - , CurveVector 1 3650.0 4.1283 0.17815726304772947 - , CurveVector 1 3650.0 15.0 0.07182364534647995 - , CurveVector 1 3650.0 100.0 0.12261437863592996 - , CurveVector 1 3650.0 1000.0 0.5452451752481946 - , CurveVector 1 3650.0 36500.0 0.9769943425928189 - , CurveVector 2 0.0 0.0001 1.0 - , CurveVector 2 0.0 0.01 1.0 - , CurveVector 2 0.0 0.5 1.0 - , CurveVector 2 0.0 1.0 1.0 - , CurveVector 2 0.0 4.1283 1.0 - , CurveVector 2 0.0 15.0 1.0 - , CurveVector 2 0.0 100.0 1.0 - , CurveVector 2 0.0 1000.0 1.0 - , CurveVector 2 0.0 36500.0 1.0 - , CurveVector 2 1.1574074074074073e-5 0.0001 0.606467529772504 - , CurveVector 2 1.1574074074074073e-5 0.01 0.6879249664472816 - , CurveVector 2 1.1574074074074073e-5 0.5 0.8376629751583106 - , CurveVector 2 1.1574074074074073e-5 1.0 0.8691455215882177 - , CurveVector 2 1.1574074074074073e-5 4.1283 0.9245200592994596 - , CurveVector 2 1.1574074074074073e-5 15.0 0.9589607675714509 - , CurveVector 2 1.1574074074074073e-5 100.0 0.9852302440781773 - , CurveVector 2 1.1574074074074073e-5 1000.0 0.9961835844156868 - , CurveVector 2 1.1574074074074073e-5 36500.0 0.9996023459553239 - , CurveVector 2 0.0006944444444444445 0.0001 0.5592622855394497 - , CurveVector 2 0.0006944444444444445 0.01 0.6364681643081666 - , CurveVector 2 0.0006944444444444445 0.5 0.8085965033237014 - , CurveVector 2 0.0006944444444444445 1.0 0.8449260419015837 - , CurveVector 2 0.0006944444444444445 4.1283 0.9093808945594827 - , CurveVector 2 0.0006944444444444445 15.0 0.9500009198888169 - , CurveVector 2 0.0006944444444444445 100.0 0.9815131069373282 - , CurveVector 2 0.0006944444444444445 1000.0 0.9950082011084547 - , CurveVector 2 0.0006944444444444445 36500.0 0.9994183653980044 - , CurveVector 2 0.006944444444444444 0.0001 0.5350670232767891 - , CurveVector 2 0.006944444444444444 0.01 0.589113601405182 - , CurveVector 2 0.006944444444444444 0.5 0.7844310926509394 - 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, CurveVector 2 1.0 15.0 0.8580842903071186 - , CurveVector 2 1.0 100.0 0.9597307808999423 - , CurveVector 2 1.0 1000.0 0.991401983249404 - , CurveVector 2 1.0 36500.0 0.9990753188455495 - , CurveVector 2 3.0 0.0001 0.47795520962718263 - , CurveVector 2 3.0 0.01 0.48842523115540376 - , CurveVector 2 3.0 0.5 0.4767232073536098 - , CurveVector 2 3.0 1.0 0.5015673153236732 - , CurveVector 2 3.0 4.1283 0.6133617183123362 - , CurveVector 2 3.0 15.0 0.7652883605652564 - , CurveVector 2 3.0 100.0 0.9306360628988384 - , CurveVector 2 3.0 1000.0 0.9877295789699271 - , CurveVector 2 3.0 36500.0 0.9989374948726737 - , CurveVector 2 7.5 0.0001 0.4699801195648465 - , CurveVector 2 7.5 0.01 0.47796923981833955 - , CurveVector 2 7.5 0.5 0.4359460557309245 - , CurveVector 2 7.5 1.0 0.44650478450469305 - , CurveVector 2 7.5 4.1283 0.5236779738387979 - , CurveVector 2 7.5 15.0 0.6621824742906998 - , CurveVector 2 7.5 100.0 0.8787205126459078 - , CurveVector 2 7.5 1000.0 0.9800441454347029 - , CurveVector 2 7.5 36500.0 0.9986865595421579 - , CurveVector 2 30.0 0.0001 0.4581895710614185 - , CurveVector 2 30.0 0.01 0.46341631653021614 - , CurveVector 2 30.0 0.5 0.3880162263777013 - , CurveVector 2 30.0 1.0 0.3819137459401326 - , CurveVector 2 30.0 4.1283 0.4118207123301889 - , CurveVector 2 30.0 15.0 0.5051701223166598 - , CurveVector 2 30.0 100.0 0.7363682560284641 - , CurveVector 2 30.0 1000.0 0.9460279362095325 - , CurveVector 2 30.0 36500.0 0.9975540277157354 - , CurveVector 2 365.0 0.0001 0.43772550284476164 - , CurveVector 2 365.0 0.01 0.43996830916988416 - , CurveVector 2 365.0 0.5 0.3307292574698105 - , CurveVector 2 365.0 1.0 0.3068347504530301 - , CurveVector 2 365.0 4.1283 0.2820726268682856 - , CurveVector 2 365.0 15.0 0.30463737786259887 - , CurveVector 2 365.0 100.0 0.43185104483801695 - , CurveVector 2 365.0 1000.0 0.7175121426626243 - , CurveVector 2 365.0 36500.0 0.9819794894033199 - , CurveVector 2 3650.0 0.0001 0.4197078090483988 - , CurveVector 2 3650.0 0.01 0.42052494087116143 - , CurveVector 2 3650.0 0.5 0.29772170181139634 - , CurveVector 2 3650.0 1.0 0.266007008010134 - , CurveVector 2 3650.0 4.1283 0.21591765051843548 - , CurveVector 2 3650.0 15.0 0.20257783586795206 - , CurveVector 2 3650.0 100.0 0.25116200187670906 - , CurveVector 2 3650.0 1000.0 0.4251397867408951 - , CurveVector 2 3650.0 36500.0 0.8722585713639893 - ] - --- | Initial and subsequent difficulty. -data DifficultyVector = DifficultyVector - { dvParams :: !Int - , dvDifficulty :: !(Maybe Double) - -- ^ 'Nothing' for the initial difficulty of a brand-new card. - , dvRating :: !Int - , dvNextDifficulty :: !Double - } - deriving stock (Eq, Show) - -goldenDifficultyVectors :: [DifficultyVector] -goldenDifficultyVectors = - [ DifficultyVector 0 Nothing 1 5.6385 - , DifficultyVector 0 Nothing 2 5.075198392303237 - , DifficultyVector 0 Nothing 3 4.194588083372719 - , DifficultyVector 0 Nothing 4 2.817928571667297 - , DifficultyVector 0 (Just 1.0) 1 7.476939285716673 - , DifficultyVector 0 (Just 1.0) 2 4.247559285716673 - , DifficultyVector 0 (Just 1.0) 3 1.018179285716673 - , DifficultyVector 0 (Just 1.0) 4 1.0 - , DifficultyVector 0 (Just 2.5) 1 7.885479285716673 - , DifficultyVector 0 (Just 2.5) 2 5.194329285716673 - , DifficultyVector 0 (Just 2.5) 3 2.5031792857166733 - , DifficultyVector 0 (Just 2.5) 4 1.0 - , DifficultyVector 0 (Just 4.194588083372719) 1 8.347017296104067 - , DifficultyVector 0 (Just 4.194588083372719) 2 6.263919392179866 - , DifficultyVector 0 (Just 4.194588083372719) 3 4.180821488255665 - , DifficultyVector 0 (Just 4.194588083372719) 4 2.097723584331464 - , DifficultyVector 0 (Just 7.0) 1 9.111099285716673 - , DifficultyVector 0 (Just 7.0) 2 8.034639285716674 - , DifficultyVector 0 (Just 7.0) 3 6.958179285716673 - , DifficultyVector 0 (Just 7.0) 4 5.881719285716673 - , DifficultyVector 0 (Just 10.0) 1 9.928179285716674 - , DifficultyVector 0 (Just 10.0) 2 9.928179285716674 - , DifficultyVector 0 (Just 10.0) 3 9.928179285716674 - , DifficultyVector 0 (Just 10.0) 4 9.928179285716674 - , DifficultyVector 1 Nothing 1 8.15903 - , DifficultyVector 1 Nothing 2 1.7511448034338732 - , DifficultyVector 1 Nothing 3 1.0 - , DifficultyVector 1 Nothing 4 1.0 - , DifficultyVector 1 (Just 1.0) 1 1.4918717310343146 - , DifficultyVector 1 (Just 1.0) 2 1.0 - , DifficultyVector 1 (Just 1.0) 3 1.0 - , DifficultyVector 1 (Just 1.0) 4 1.0 - , DifficultyVector 1 (Just 2.5) 1 2.2309568910343147 - , DifficultyVector 1 (Just 2.5) 2 1.0 - , DifficultyVector 1 (Just 2.5) 3 1.0 - , DifficultyVector 1 (Just 2.5) 4 1.0 - , DifficultyVector 1 (Just 4.194588083372719) 1 3.065920160856728 - , DifficultyVector 1 (Just 4.194588083372719) 2 1.6224725272150176 - , DifficultyVector 1 (Just 4.194588083372719) 3 1.0 - , DifficultyVector 1 (Just 4.194588083372719) 4 1.0 - , DifficultyVector 1 (Just 7.0) 1 4.448212371034315 - , DifficultyVector 1 (Just 7.0) 2 3.702297531034315 - , DifficultyVector 1 (Just 7.0) 3 2.9563826910343147 - , DifficultyVector 1 (Just 7.0) 4 2.2104678510343154 - , DifficultyVector 1 (Just 10.0) 1 5.926382691034315 - , DifficultyVector 1 (Just 10.0) 2 5.926382691034315 - , DifficultyVector 1 (Just 10.0) 3 5.926382691034315 - , DifficultyVector 1 (Just 10.0) 4 5.926382691034315 - , DifficultyVector 2 Nothing 1 7.614116 - , DifficultyVector 2 Nothing 2 5.356124178155698 - , DifficultyVector 2 Nothing 3 1.0 - , DifficultyVector 2 Nothing 4 1.0 - , DifficultyVector 2 (Just 1.0) 1 1.5042458491001744 - , DifficultyVector 2 (Just 1.0) 2 1.1172835591001746 - , DifficultyVector 2 (Just 1.0) 3 1.0 - , DifficultyVector 2 (Just 1.0) 4 1.0 - , DifficultyVector 2 (Just 2.5) 1 2.8602584191001745 - , DifficultyVector 2 (Just 2.5) 2 2.5377898441001747 - , DifficultyVector 2 (Just 2.5) 3 2.215321269100175 - , DifficultyVector 2 (Just 2.5) 4 1.8928526941001744 - , DifficultyVector 2 (Just 4.194588083372719) 1 4.392180247117252 - , DifficultyVector 2 (Just 4.194588083372719) 2 4.142571859378209 - , DifficultyVector 2 (Just 4.194588083372719) 3 3.892963471639167 - , DifficultyVector 2 (Just 4.194588083372719) 4 3.643355083900124 - , DifficultyVector 2 (Just 7.0) 1 6.928296129100175 - , DifficultyVector 2 (Just 7.0) 2 6.799308699100174 - , DifficultyVector 2 (Just 7.0) 3 6.6703212691001745 - , DifficultyVector 2 (Just 7.0) 4 6.541333839100175 - , DifficultyVector 2 (Just 10.0) 1 9.640321269100175 - , DifficultyVector 2 (Just 10.0) 2 9.640321269100175 - , DifficultyVector 2 (Just 10.0) 3 9.640321269100175 - , DifficultyVector 2 (Just 10.0) 4 9.640321269100175 - ] - --- | One half of the stability update, before the two are blended. -data HalfStabilityVector = HalfStabilityVector - { hsParams :: !Int - , hsLongTerm :: !Bool - -- ^ 'True' for the long-term block, 'False' for the short-term one. - , hsStability :: !Double - , hsDifficulty :: !Double - , hsRetrievability :: !Double - , hsRating :: !Int - , hsNextStability :: !Double - } - deriving stock (Eq, Show) - -goldenHalfStabilityVectors :: [HalfStabilityVector] -goldenHalfStabilityVectors = - [ HalfStabilityVector 0 True 0.01 1.0 0.05 1 0.00287539614361996 - , HalfStabilityVector 0 False 0.01 1.0 0.05 1 0.008457926427604777 - , HalfStabilityVector 0 True 0.01 1.0 0.05 2 0.8312175079505889 - , HalfStabilityVector 0 False 0.01 1.0 0.05 2 3.634419609530054 - , HalfStabilityVector 0 True 0.01 1.0 0.05 3 1.2495735969065493 - , HalfStabilityVector 0 False 0.01 1.0 0.05 3 6.489119788219617 - , HalfStabilityVector 0 True 0.01 1.0 0.05 4 1.6214456759785143 - , HalfStabilityVector 0 False 0.01 1.0 0.05 4 8.432855724685503 - , HalfStabilityVector 0 True 0.01 1.0 0.5 1 0.0027617663415225664 - , HalfStabilityVector 0 False 0.01 1.0 0.5 1 0.00257672455606105 - , HalfStabilityVector 0 True 0.01 1.0 0.5 2 0.3154085317282906 - , HalfStabilityVector 0 False 0.01 1.0 0.5 2 0.6319216021560662 - , HalfStabilityVector 0 True 0.01 1.0 0.5 3 0.4709940101559103 - , HalfStabilityVector 0 False 0.01 1.0 0.5 3 1.121765466850315 - , HalfStabilityVector 0 True 0.01 1.0 0.5 4 0.6092922132026835 - , HalfStabilityVector 0 False 0.01 1.0 0.5 4 1.4552951069054094 - , HalfStabilityVector 0 True 0.01 1.0 1.0 1 0.0026407697690489216 - , HalfStabilityVector 0 False 0.01 1.0 1.0 1 0.0006878868205852286 - , HalfStabilityVector 0 True 0.01 1.0 1.0 2 0.01 - , HalfStabilityVector 0 False 0.01 1.0 1.0 2 0.01 - , HalfStabilityVector 0 True 0.01 1.0 1.0 3 0.01 - , HalfStabilityVector 0 False 0.01 1.0 1.0 3 0.01 - , HalfStabilityVector 0 True 0.01 1.0 1.0 4 0.01 - , HalfStabilityVector 0 False 0.01 1.0 1.0 4 0.01 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.05 1 0.0028552655688472766 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.05 1 0.008329158514656381 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.05 2 0.5688723414749896 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.05 2 2.4765668401553422 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.05 3 0.8535808927924372 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.05 3 4.419307901600541 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.05 4 1.1066551606301684 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.05 4 5.7421002720807035 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.5 1 0.0027424312860847063 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.5 1 0.0025374951484554284 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.5 2 0.21784308612633496 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.5 2 0.4332432682520823 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.5 3 0.3237254130208829 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.5 3 0.7666021956597825 - , HalfStabilityVector 0 True 0.01 4.194588083372719 0.5 4 0.41784303692714786 - , HalfStabilityVector 0 False 0.01 4.194588083372719 0.5 4 0.9935828543577173 - , HalfStabilityVector 0 True 0.01 4.194588083372719 1.0 1 0.0026222818075166522 - , HalfStabilityVector 0 False 0.01 4.194588083372719 1.0 1 0.0006774140704390025 - , HalfStabilityVector 0 True 0.01 4.194588083372719 1.0 2 0.01 - , HalfStabilityVector 0 False 0.01 4.194588083372719 1.0 2 0.01 - , HalfStabilityVector 0 True 0.01 4.194588083372719 1.0 3 0.01 - , HalfStabilityVector 0 False 0.01 4.194588083372719 1.0 3 0.01 - , HalfStabilityVector 0 True 0.01 4.194588083372719 1.0 4 0.01 - , HalfStabilityVector 0 False 0.01 4.194588083372719 1.0 4 0.01 - , HalfStabilityVector 0 True 0.01 10.0 0.05 1 0.0028431363371105457 - , HalfStabilityVector 0 False 0.01 10.0 0.05 1 0.008252088996248524 - , HalfStabilityVector 0 True 0.01 10.0 0.05 2 0.09212175079505888 - , HalfStabilityVector 0 False 0.01 10.0 0.05 2 0.37244196095300536 - , HalfStabilityVector 0 True 0.01 10.0 0.05 3 0.13395735969065492 - , HalfStabilityVector 0 False 0.01 10.0 0.05 3 0.6579119788219617 - , HalfStabilityVector 0 True 0.01 10.0 0.05 4 0.17114456759785143 - , HalfStabilityVector 0 False 0.01 10.0 0.05 4 0.8522855724685503 - , HalfStabilityVector 0 True 0.01 10.0 0.5 1 0.002730781376894504 - , HalfStabilityVector 0 False 0.01 10.0 0.5 1 0.0025140157623074026 - , HalfStabilityVector 0 True 0.01 10.0 0.5 2 0.040540853172829065 - , HalfStabilityVector 0 False 0.01 10.0 0.5 2 0.07219216021560662 - , HalfStabilityVector 0 True 0.01 10.0 0.5 3 0.056099401015591036 - , HalfStabilityVector 0 False 0.01 10.0 0.5 3 0.1211765466850315 - , HalfStabilityVector 0 True 0.01 10.0 0.5 4 0.06992922132026835 - , HalfStabilityVector 0 False 0.01 10.0 0.5 4 0.15452951069054094 - , HalfStabilityVector 0 True 0.01 10.0 1.0 1 0.0026111422959877043 - , HalfStabilityVector 0 False 0.01 10.0 1.0 1 0.000671145973118058 - , HalfStabilityVector 0 True 0.01 10.0 1.0 2 0.01 - , HalfStabilityVector 0 False 0.01 10.0 1.0 2 0.01 - , HalfStabilityVector 0 True 0.01 10.0 1.0 3 0.01 - , HalfStabilityVector 0 False 0.01 10.0 1.0 3 0.01 - , HalfStabilityVector 0 True 0.01 10.0 1.0 4 0.01 - , HalfStabilityVector 0 False 0.01 10.0 1.0 4 0.01 - , HalfStabilityVector 0 True 1.0 1.0 0.05 1 0.2617448884635849 - , HalfStabilityVector 0 False 1.0 1.0 0.05 1 0.6375484000895719 - , HalfStabilityVector 0 True 1.0 1.0 0.05 2 38.744893102401065 - , HalfStabilityVector 0 False 1.0 1.0 0.05 2 89.07212425705278 - , HalfStabilityVector 0 True 1.0 1.0 0.05 3 57.97342355079406 - , HalfStabilityVector 0 False 1.0 1.0 0.05 3 158.44033653388055 - , HalfStabilityVector 0 True 1.0 1.0 0.05 4 75.06545061603228 - , HalfStabilityVector 0 False 1.0 1.0 0.05 4 205.67243749404471 - , HalfStabilityVector 0 True 1.0 1.0 0.5 1 0.25140126331053797 - , HalfStabilityVector 0 False 1.0 1.0 0.5 1 0.19423042187108028 - , HalfStabilityVector 0 True 1.0 1.0 0.5 2 15.037221894371966 - , HalfStabilityVector 0 False 1.0 1.0 0.5 2 16.112476623625945 - , HalfStabilityVector 0 True 1.0 1.0 0.5 3 22.188259463202968 - , HalfStabilityVector 0 False 1.0 1.0 0.5 3 28.015510589249097 - , HalfStabilityVector 0 True 1.0 1.0 0.5 4 28.54473730216386 - , HalfStabilityVector 0 False 1.0 1.0 0.5 4 36.12016376602383 - , HalfStabilityVector 0 True 1.0 1.0 1.0 1 0.24038704725656526 - , HalfStabilityVector 0 False 1.0 1.0 1.0 1 0.05185208758442845 - , HalfStabilityVector 0 True 1.0 1.0 1.0 2 1.0 - , HalfStabilityVector 0 False 1.0 1.0 1.0 2 1.0 - , HalfStabilityVector 0 True 1.0 1.0 1.0 3 1.0 - , HalfStabilityVector 0 False 1.0 1.0 1.0 3 1.0 - , HalfStabilityVector 0 True 1.0 1.0 1.0 4 1.0 - , HalfStabilityVector 0 False 1.0 1.0 1.0 4 1.0 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.05 1 0.25991241920181896 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.05 1 0.6278420284882321 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.05 2 26.686954531090308 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.05 2 60.93670839416256 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.05 3 39.77276155636273 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.05 3 108.14463424054802 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.05 4 51.40459002327155 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.05 4 140.2880245127124 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.5 1 0.24964120950360458 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.5 1 0.19127335594369213 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.5 2 10.552907715630036 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.5 2 11.284662850417522 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.5 3 15.419483344347224 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.5 3 19.38516776978463 - , HalfStabilityVector 0 True 1.0 4.194588083372719 0.5 4 19.74532834765139 - , HalfStabilityVector 0 False 1.0 4.194588083372719 0.5 4 24.90071810072002 - , HalfStabilityVector 0 True 1.0 4.194588083372719 1.0 1 0.23870410369419032 - , HalfStabilityVector 0 False 1.0 4.194588083372719 1.0 1 0.05106266417699935 - , HalfStabilityVector 0 True 1.0 4.194588083372719 1.0 2 1.0 - , HalfStabilityVector 0 False 1.0 4.194588083372719 1.0 2 1.0 - , HalfStabilityVector 0 True 1.0 4.194588083372719 1.0 3 1.0 - , HalfStabilityVector 0 False 1.0 4.194588083372719 1.0 3 1.0 - , HalfStabilityVector 0 True 1.0 4.194588083372719 1.0 4 1.0 - , HalfStabilityVector 0 False 1.0 4.194588083372719 1.0 4 1.0 - , HalfStabilityVector 0 True 1.0 10.0 0.05 1 0.2588083054555709 - , HalfStabilityVector 0 False 1.0 10.0 0.05 1 0.6220326201684536 - , HalfStabilityVector 0 True 1.0 10.0 0.05 2 4.7744893102401065 - , HalfStabilityVector 0 False 1.0 10.0 0.05 2 9.807212425705277 - , HalfStabilityVector 0 True 1.0 10.0 0.05 3 6.697342355079406 - , HalfStabilityVector 0 False 1.0 10.0 0.05 3 16.744033653388055 - , HalfStabilityVector 0 True 1.0 10.0 0.05 4 8.406545061603229 - , HalfStabilityVector 0 False 1.0 10.0 0.05 4 21.46724374940447 - , HalfStabilityVector 0 True 1.0 10.0 0.5 1 0.24858072808494294 - , HalfStabilityVector 0 False 1.0 10.0 0.5 1 0.18950350783708025 - , HalfStabilityVector 0 True 1.0 10.0 0.5 2 2.4037221894371967 - , HalfStabilityVector 0 False 1.0 10.0 0.5 2 2.5112476623625946 - , HalfStabilityVector 0 True 1.0 10.0 0.5 3 3.118825946320297 - , HalfStabilityVector 0 False 1.0 10.0 0.5 3 3.7015510589249097 - , HalfStabilityVector 0 True 1.0 10.0 0.5 4 3.754473730216386 - , HalfStabilityVector 0 False 1.0 10.0 0.5 4 4.512016376602382 - , HalfStabilityVector 0 True 1.0 10.0 1.0 1 0.23769008334462816 - , HalfStabilityVector 0 False 1.0 10.0 1.0 1 0.05059018248154134 - , HalfStabilityVector 0 True 1.0 10.0 1.0 2 1.0 - , HalfStabilityVector 0 False 1.0 10.0 1.0 2 1.0 - , HalfStabilityVector 0 True 1.0 10.0 1.0 3 1.0 - , HalfStabilityVector 0 False 1.0 10.0 1.0 3 1.0 - , HalfStabilityVector 0 True 1.0 10.0 1.0 4 1.0 - , HalfStabilityVector 0 False 1.0 10.0 1.0 4 1.0 - , HalfStabilityVector 0 True 4.1283 1.0 0.05 1 0.9245562153616427 - , HalfStabilityVector 0 False 4.1283 1.0 0.05 1 1.6819069920331728 - , HalfStabilityVector 0 True 4.1283 1.0 0.05 2 126.78386642337001 - , HalfStabilityVector 0 False 4.1283 1.0 0.05 2 239.3323486572463 - , HalfStabilityVector 0 True 4.1283 1.0 0.05 3 189.26877762018117 - , HalfStabilityVector 0 False 4.1283 1.0 0.05 3 424.5860201595393 - , HalfStabilityVector 0 True 4.1283 1.0 0.05 4 244.8109209062355 - , HalfStabilityVector 0 False 4.1283 1.0 0.05 4 550.7233362074012 - , HalfStabilityVector 0 True 4.1283 1.0 0.5 1 0.8880196358671743 - , HalfStabilityVector 0 False 4.1283 1.0 0.5 1 0.5123963993394485 - , HalfStabilityVector 0 True 4.1283 1.0 0.5 2 49.74356768121113 - , HalfStabilityVector 0 False 4.1283 1.0 0.5 2 44.4874456104815 - , HalfStabilityVector 0 True 4.1283 1.0 0.5 3 72.98153423579039 - , HalfStabilityVector 0 False 4.1283 1.0 0.5 3 76.27550345098588 - , HalfStabilityVector 0 True 4.1283 1.0 0.5 4 93.63750450652752 - , HalfStabilityVector 0 False 4.1283 1.0 0.5 4 97.91966448628165 - , HalfStabilityVector 0 True 4.1283 1.0 1.0 1 0.849114341594529 - , HalfStabilityVector 0 False 4.1283 1.0 1.0 1 0.13679022431475651 - , HalfStabilityVector 0 True 4.1283 1.0 1.0 2 4.1283 - , HalfStabilityVector 0 False 4.1283 1.0 1.0 2 4.1283 - , HalfStabilityVector 0 True 4.1283 1.0 1.0 3 4.1283 - , HalfStabilityVector 0 False 4.1283 1.0 1.0 3 4.1283 - , HalfStabilityVector 0 True 4.1283 1.0 1.0 4 4.1283 - , HalfStabilityVector 0 False 4.1283 1.0 1.0 4 4.1283 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.05 1 0.9180834209725344 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.05 1 1.6563007568653456 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.05 2 87.60046533782713 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.05 2 164.19434355710067 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.05 3 130.1240212646447 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.05 3 290.26709792116674 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.05 4 167.92273764403814 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.05 4 376.10873729751677 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.5 1 0.8818026331355332 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.5 1 0.5045954075112541 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.5 2 35.17136862578576 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.5 2 31.594361048246647 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.5 3 50.98576207665775 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.5 3 53.22744381166723 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 0.5 4 65.04300069965508 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 0.5 4 67.9571869551674 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 1.0 1 0.8431697138318628 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 1.0 1 0.13470765811516586 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 1.0 2 4.1283 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 1.0 2 4.1283 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 1.0 3 4.1283 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 1.0 3 4.1283 - , HalfStabilityVector 0 True 4.1283 4.194588083372719 1.0 4 4.1283 - , HalfStabilityVector 0 False 4.1283 4.194588083372719 1.0 4 4.1283 - , HalfStabilityVector 0 True 4.1283 10.0 0.05 1 0.9141833821501835 - , HalfStabilityVector 0 False 4.1283 10.0 0.05 1 1.640975042815654 - , HalfStabilityVector 0 True 4.1283 10.0 0.05 2 16.393856642337 - , HalfStabilityVector 0 False 4.1283 10.0 0.05 2 27.648704865724625 - , HalfStabilityVector 0 True 4.1283 10.0 0.05 3 22.642347762018115 - , HalfStabilityVector 0 False 4.1283 10.0 0.05 3 46.174072015953925 - , HalfStabilityVector 0 True 4.1283 10.0 0.05 4 28.196562090623548 - , HalfStabilityVector 0 False 4.1283 10.0 0.05 4 58.78780362074011 - , HalfStabilityVector 0 True 4.1283 10.0 0.5 1 0.8780567159080586 - , HalfStabilityVector 0 False 4.1283 10.0 0.5 1 0.4999263974330719 - , HalfStabilityVector 0 True 4.1283 10.0 0.5 2 8.689826768121115 - , HalfStabilityVector 0 False 4.1283 10.0 0.5 2 8.16421456104815 - , HalfStabilityVector 0 True 4.1283 10.0 0.5 3 11.01362342357904 - , HalfStabilityVector 0 False 4.1283 10.0 0.5 3 11.343020345098587 - , HalfStabilityVector 0 True 4.1283 10.0 0.5 4 13.079220450652754 - , HalfStabilityVector 0 False 4.1283 10.0 0.5 4 13.507436448628166 - , HalfStabilityVector 0 True 4.1283 10.0 1.0 1 0.839587910106128 - , HalfStabilityVector 0 False 4.1283 10.0 1.0 1 0.13346121115194412 - , HalfStabilityVector 0 True 4.1283 10.0 1.0 2 4.1283 - , HalfStabilityVector 0 False 4.1283 10.0 1.0 2 4.1283 - , HalfStabilityVector 0 True 4.1283 10.0 1.0 3 4.1283 - , HalfStabilityVector 0 False 4.1283 10.0 1.0 3 4.1283 - , HalfStabilityVector 0 True 4.1283 10.0 1.0 4 4.1283 - , HalfStabilityVector 0 False 4.1283 10.0 1.0 4 4.1283 - , HalfStabilityVector 0 True 1000.0 1.0 0.05 1 68.04348456164972 - , HalfStabilityVector 0 False 1000.0 1.0 0.05 1 14.26268886210528 - , HalfStabilityVector 0 True 1000.0 1.0 0.05 2 12761.377775584082 - , HalfStabilityVector 0 False 1000.0 1.0 0.05 2 11549.660200515413 - , HalfStabilityVector 0 True 1000.0 1.0 0.05 3 18753.023057485407 - , HalfStabilityVector 0 False 1000.0 1.0 0.05 3 19858.884877574925 - , HalfStabilityVector 0 True 1000.0 1.0 0.05 4 24078.92997473103 - , HalfStabilityVector 0 False 1000.0 1.0 0.05 4 25516.550340847407 - , HalfStabilityVector 0 True 1000.0 1.0 0.5 1 65.35454456918542 - , HalfStabilityVector 0 False 1000.0 1.0 0.5 1 4.3451572842367145 - , HalfStabilityVector 0 True 1000.0 1.0 0.5 2 5374.024034761578 - , HalfStabilityVector 0 False 1000.0 1.0 0.5 2 2810.2378534910713 - , HalfStabilityVector 0 True 1000.0 1.0 0.5 3 7602.300429828797 - , HalfStabilityVector 0 False 1000.0 1.0 0.5 3 4236.034775636524 - , HalfStabilityVector 0 True 1000.0 1.0 0.5 4 9582.990558777437 - , HalfStabilityVector 0 False 1000.0 1.0 0.5 4 5206.8452083274815 - 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, HalfStabilityVector 2 True 1000.0 1.0 0.05 4 10627.276057290686 - , HalfStabilityVector 2 False 1000.0 1.0 0.05 4 16478.758310505313 - , HalfStabilityVector 2 True 1000.0 1.0 0.5 1 10.14968593201463 - , HalfStabilityVector 2 False 1000.0 1.0 0.5 1 682.9483757192087 - , HalfStabilityVector 2 True 1000.0 1.0 0.5 2 1229.7213103325757 - , HalfStabilityVector 2 False 1000.0 1.0 0.5 2 1619.449039952195 - , HalfStabilityVector 2 True 1000.0 1.0 0.5 3 1386.049901744669 - , HalfStabilityVector 2 False 1000.0 1.0 0.5 3 1641.8682128920898 - , HalfStabilityVector 2 True 1000.0 1.0 0.5 4 3683.816600629527 - , HalfStabilityVector 2 False 1000.0 1.0 0.5 4 5178.450380858463 - , HalfStabilityVector 2 True 1000.0 1.0 1.0 1 6.037127155869641 - , HalfStabilityVector 2 False 1000.0 1.0 1.0 1 122.03876889929109 - , HalfStabilityVector 2 True 1000.0 1.0 1.0 2 1000.0 - , HalfStabilityVector 2 False 1000.0 1.0 1.0 2 1000.0 - , HalfStabilityVector 2 True 1000.0 1.0 1.0 3 1000.0 - , HalfStabilityVector 2 False 1000.0 1.0 1.0 3 1000.0 - , HalfStabilityVector 2 True 1000.0 1.0 1.0 4 1000.0 - , HalfStabilityVector 2 False 1000.0 1.0 1.0 4 1000.0 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.05 1 4.886437328040729 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.05 1 1000.0 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.05 2 1560.7977885392115 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.05 2 2561.63980839527 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.05 3 1942.428592500893 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.05 3 2618.1588610956173 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.05 4 7551.757920494653 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.05 4 11533.932626090638 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.5 1 3.061486018918276 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.5 1 427.24923398391303 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.5 2 1156.3348142840543 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.5 2 1421.5605878233996 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.5 3 1262.722860174596 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.5 3 1436.8177584920086 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 0.5 4 2826.44774759663 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 0.5 4 3843.6076014929977 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 1.0 1 1.821000226600915 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 1.0 1 76.34686951799625 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 1.0 2 1000.0 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 1.0 2 1000.0 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 1.0 3 1000.0 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 1.0 3 1000.0 - , HalfStabilityVector 2 True 1000.0 4.194588083372719 1.0 4 1000.0 - , HalfStabilityVector 2 False 1000.0 4.194588083372719 1.0 4 1000.0 - , HalfStabilityVector 2 True 1000.0 10.0 0.05 1 2.363685311356562 - , HalfStabilityVector 2 False 1000.0 10.0 0.05 1 1000.0 - , HalfStabilityVector 2 True 1000.0 10.0 0.05 2 1082.404679600517 - , HalfStabilityVector 2 False 1000.0 10.0 0.05 2 1229.470284462841 - , HalfStabilityVector 2 True 1000.0 10.0 0.05 3 1138.482226211511 - , HalfStabilityVector 2 False 1000.0 10.0 0.05 3 1237.7753001463527 - , HalfStabilityVector 2 True 1000.0 10.0 0.05 4 1962.7276057290683 - , HalfStabilityVector 2 False 1000.0 10.0 0.05 4 2547.875831050531 - , HalfStabilityVector 2 True 1000.0 10.0 0.5 1 1.480913198725526 - , HalfStabilityVector 2 False 1000.0 10.0 0.5 1 321.5495280333281 - , HalfStabilityVector 2 True 1000.0 10.0 0.5 2 1022.9721310332576 - , HalfStabilityVector 2 False 1000.0 10.0 0.5 2 1061.9449039952196 - , HalfStabilityVector 2 True 1000.0 10.0 0.5 3 1038.604990174467 - , HalfStabilityVector 2 False 1000.0 10.0 0.5 3 1064.1868212892089 - , HalfStabilityVector 2 True 1000.0 10.0 0.5 4 1268.3816600629525 - , HalfStabilityVector 2 False 1000.0 10.0 0.5 4 1417.8450380858462 - , HalfStabilityVector 2 True 1000.0 10.0 1.0 1 0.8808608805629355 - , HalfStabilityVector 2 False 1000.0 10.0 1.0 1 57.458967524464 - , HalfStabilityVector 2 True 1000.0 10.0 1.0 2 1000.0 - , HalfStabilityVector 2 False 1000.0 10.0 1.0 2 1000.0 - , HalfStabilityVector 2 True 1000.0 10.0 1.0 3 1000.0 - , HalfStabilityVector 2 False 1000.0 10.0 1.0 3 1000.0 - , HalfStabilityVector 2 True 1000.0 10.0 1.0 4 1000.0 - , HalfStabilityVector 2 False 1000.0 10.0 1.0 4 1000.0 - ] - --- | The long-\/short-term blending coefficient. -data TransitionVector = TransitionVector - { tvParams :: !Int - , tvElapsedDays :: !Double - , tvCoefficient :: !Double - } - deriving stock (Eq, Show) - -goldenTransitionVectors :: [TransitionVector] -goldenTransitionVectors = - [ TransitionVector 0 0.0 0.0 - , TransitionVector 0 1.1574074074074073e-5 2.8934766566734993e-5 - , TransitionVector 0 0.0006944444444444445 0.0017346049419677545 - , TransitionVector 0 0.006944444444444444 0.0172112753795709 - , TransitionVector 0 0.25 0.4647385714810097 - , TransitionVector 0 1.0 0.9179150013761012 - , TransitionVector 0 3.0 0.9994469156298522 - , TransitionVector 0 7.5 0.9999999928058669 - , TransitionVector 0 30.0 1.0 - , TransitionVector 0 365.0 1.0 - , TransitionVector 0 3650.0 1.0 - , TransitionVector 1 0.0 0.410307 - , TransitionVector 1 1.1574074074074073e-5 0.4103913084279295 - , TransitionVector 1 0.0006944444444444445 0.41534422969275386 - , TransitionVector 1 0.006944444444444444 0.45878646256833155 - , TransitionVector 1 0.25 0.9731241379424495 - , TransitionVector 1 1.0 0.9999974556802093 - , TransitionVector 1 3.0 1.0 - , TransitionVector 1 7.5 1.0 - , TransitionVector 1 30.0 1.0 - , TransitionVector 1 365.0 1.0 - , TransitionVector 1 3650.0 1.0 - , TransitionVector 2 0.0 0.561569 - , TransitionVector 2 1.1574074074074073e-5 0.5615970916424434 - , TransitionVector 2 0.0006944444444444445 0.5632513166324914 - , TransitionVector 2 0.006944444444444444 0.5781046317970904 - , TransitionVector 2 0.25 0.8901430906590875 - , TransitionVector 2 1.0 0.9982717532681704 - , TransitionVector 2 3.0 0.999999973145645 - , TransitionVector 2 7.5 1.0 - , TransitionVector 2 30.0 1.0 - , TransitionVector 2 365.0 1.0 - , TransitionVector 2 3650.0 1.0 - ] - --- | A full memory-state transition. -data StepVector = StepVector - { svParams :: !Int - , svState :: !(Maybe (Double, Double)) - -- ^ @(stability, difficulty)@; 'Nothing' for the first review. - , svElapsedDays :: !Double - , svRating :: !Int - , svNextState :: !(Double, Double) - } - deriving stock (Eq, Show) - -goldenStepVectors :: [StepVector] -goldenStepVectors = - [ StepVector 0 Nothing 0.0 1 (0.041, 5.6385) - , StepVector 0 Nothing 0.0 2 (2.4175, 5.075198392303237) - , StepVector 0 Nothing 0.0 3 (4.1283, 4.194588083372719) - , StepVector 0 Nothing 0.0 4 (11.9709, 2.817928571667297) - , StepVector 0 (Just (0.0001, 1.0)) 0.0 1 (0.0001, 7.476939285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.0 2 (0.0001, 4.247559285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.0 3 (0.0001, 1.018179285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.0 4 (0.0001, 1.0) - , StepVector 0 (Just (0.0001, 1.0)) 0.006944444444444444 1 (0.0001, 7.476939285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.006944444444444444 2 (0.042815393880189796, 4.247559285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.006944444444444444 3 (0.0764154303138622, 1.018179285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.006944444444444444 4 (0.09931005940802089, 1.0) - , StepVector 0 (Just (0.0001, 1.0)) 0.5 1 (0.0001, 7.476939285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.5 2 (0.02687991895595657, 4.247559285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.5 3 (0.045684811910156525, 1.018179285716673) - , StepVector 0 (Just (0.0001, 1.0)) 0.5 4 (0.05936025548320348, 1.0) - , StepVector 0 (Just (0.0001, 1.0)) 1.0 1 (0.0001, 7.476939285716673) - , StepVector 0 (Just (0.0001, 1.0)) 1.0 2 (0.01659503714401098, 4.247559285716673) - , StepVector 0 (Just (0.0001, 1.0)) 1.0 3 (0.026557084707377977, 1.018179285716673) - , StepVector 0 (Just (0.0001, 1.0)) 1.0 4 (0.03449421011959137, 1.0) - , StepVector 0 (Just (0.0001, 1.0)) 45.0 1 (0.0001, 7.476939285716673) - , StepVector 0 (Just (0.0001, 1.0)) 45.0 2 (0.013623815415699077, 4.247559285716673) - , StepVector 0 (Just (0.0001, 1.0)) 45.0 3 (0.02051330628784766, 1.018179285716673) - , StepVector 0 (Just (0.0001, 1.0)) 45.0 4 (0.02663729817420196, 1.0) - , StepVector 0 (Just (0.0001, 1.0)) 400.0 1 (0.0001, 7.476939285716673) - , StepVector 0 (Just (0.0001, 1.0)) 400.0 2 (0.014428231476499855, 4.247559285716673) - , StepVector 0 (Just (0.0001, 1.0)) 400.0 3 (0.021727519209811103, 1.018179285716673) - , StepVector 0 (Just (0.0001, 1.0)) 400.0 4 (0.028215774972754435, 1.0) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.0 1 (0.0001, 8.347017296104067) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.0 2 (0.0001, 6.263919392179866) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.0 3 (0.0001, 4.180821488255665) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.0 4 (0.0001, 2.097723584331464) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.006944444444444444 1 (0.0001, 8.347017296104067) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.006944444444444444 2 (0.029169585053567166, 6.263919392179866) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.006944444444444444 3 (0.05203579388804967, 4.180821488255665) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.006944444444444444 4 (0.06761653205446458, 2.097723584331464) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.5 1 (0.0001, 8.347017296104067) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.5 2 (0.018324837958917966, 6.263919392179866) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.5 3 (0.031122342219059244, 4.180821488255665) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 0.5 4 (0.04042904488477702, 2.097723584331464) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 1.0 1 (0.0001, 8.347017296104067) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 1.0 2 (0.011325552234506195, 6.263919392179866) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 1.0 3 (0.01810513595468075, 4.180821488255665) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 1.0 4 (0.023506676741084975, 2.097723584331464) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 45.0 1 (0.0001, 8.347017296104067) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 45.0 2 (0.009303513458826622, 6.263919392179866) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 45.0 3 (0.01399209578690811, 4.180821488255665) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 45.0 4 (0.018159724522980543, 2.097723584331464) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 400.0 1 (0.0001, 8.347017296104067) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 400.0 2 (0.009850951723436623, 6.263919392179866) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 400.0 3 (0.014818417695753395, 4.180821488255665) - , StepVector 0 (Just (0.0001, 4.194588083372719)) 400.0 4 (0.019233943004479413, 2.097723584331464) - , StepVector 0 (Just (0.0001, 10.0)) 0.0 1 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.0 2 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.0 3 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.0 4 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.006944444444444444 1 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.006944444444444444 2 (0.004371539388018979, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.006944444444444444 3 (0.007731543031386222, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.006944444444444444 4 (0.010021005940802089, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.5 1 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.5 2 (0.002777991895595657, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.5 3 (0.004658481191015653, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 0.5 4 (0.006026025548320348, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 1.0 1 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 1.0 2 (0.001749503714401098, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 1.0 3 (0.002745708470737798, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 1.0 4 (0.0035394210119591377, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 45.0 1 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 45.0 2 (0.0014523815415699078, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 45.0 3 (0.0021413306287847663, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 45.0 4 (0.0027537298174201965, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 400.0 1 (0.0001, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 400.0 2 (0.0015328231476499858, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 400.0 3 (0.0022627519209811107, 9.928179285716674) - , StepVector 0 (Just (0.0001, 10.0)) 400.0 4 (0.0029115774972754437, 9.928179285716674) - , StepVector 0 (Just (1.0, 1.0)) 0.0 1 (0.05185208758442845, 7.476939285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.0 2 (1.0, 4.247559285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.0 3 (1.0, 1.018179285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.0 4 (1.0, 1.0) - , StepVector 0 (Just (1.0, 1.0)) 0.006944444444444444 1 (0.06638267651649077, 7.476939285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.006944444444444444 2 (1.9498457743368915, 4.247559285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.006944444444444444 3 (2.6904530220163196, 1.018179285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.006944444444444444 4 (3.197588928621215, 1.0) - , StepVector 0 (Just (1.0, 1.0)) 0.5 1 (0.1954216491542706, 7.476939285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.5 2 (3.8057614435171345, 4.247559285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.5 3 (5.396628606628578, 1.018179285716673) - , StepVector 0 (Just (1.0, 1.0)) 0.5 4 (6.715617188617151, 1.0) - , StepVector 0 (Just (1.0, 1.0)) 1.0 1 (0.230527366662237, 7.476939285716673) - , StepVector 0 (Just (1.0, 1.0)) 1.0 2 (4.549141883918697, 4.247559285716673) - , StepVector 0 (Just (1.0, 1.0)) 1.0 3 (6.412854677935164, 1.018179285716673) - , StepVector 0 (Just (1.0, 1.0)) 1.0 4 (8.036711081315712, 1.0) - , StepVector 0 (Just (1.0, 1.0)) 45.0 1 (0.24981723569318473, 7.476939285716673) - , StepVector 0 (Just (1.0, 1.0)) 45.0 2 (12.447877746852612, 4.247559285716673) - , StepVector 0 (Just (1.0, 1.0)) 45.0 3 (18.27981546694734, 1.018179285716673) - , StepVector 0 (Just (1.0, 1.0)) 45.0 4 (23.463760107031543, 1.0) - , StepVector 0 (Just (1.0, 1.0)) 400.0 1 (0.25325646949892705, 7.476939285716673) - , StepVector 0 (Just (1.0, 1.0)) 400.0 2 (18.37195723994685, 4.247559285716673) - , StepVector 0 (Just (1.0, 1.0)) 400.0 3 (27.221822248976377, 1.018179285716673) - , StepVector 0 (Just (1.0, 1.0)) 400.0 4 (35.08836892366929, 1.0) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.0 1 (0.05106266417699935, 8.347017296104067) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.0 2 (1.0, 6.263919392179866) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.0 3 (1.0, 4.180821488255665) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.0 4 (1.0, 2.097723584331464) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.006944444444444444 1 (0.06540628679938068, 8.347017296104067) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.006944444444444444 2 (1.6464091751630348, 6.263919392179866) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.006944444444444444 3 (2.150422914052846, 4.180821488255665) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.006944444444444444 4 (2.4955497882686997, 2.097723584331464) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.5 1 (0.1938751351692444, 8.347017296104067) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.5 2 (2.9094362362924873, 6.263919392179866) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.5 3 (3.992086871253452, 4.180821488255665) - , StepVector 0 (Just (1.0, 4.194588083372719)) 0.5 4 (4.889712932629488, 2.097723584331464) - , StepVector 0 (Just (1.0, 4.194588083372719)) 1.0 1 (0.22885931116712982, 8.347017296104067) - , StepVector 0 (Just (1.0, 4.194588083372719)) 1.0 2 (3.41533724706213, 6.263919392179866) - 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, StepVector 2 (Just (1000.0, 1.0)) 0.006944444444444444 4 (1020.0353359083821, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 0.5 1 (9.365326366825816, 1.5042458491001744) - , StepVector 2 (Just (1000.0, 1.0)) 0.5 2 (1001.9849631831362, 1.1172835591001746) - , StepVector 2 (Just (1000.0, 1.0)) 0.5 3 (1003.2473807949993, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 0.5 4 (1022.5129272023743, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 1.0 1 (6.298026982765722, 1.5042458491001744) - , StepVector 2 (Just (1000.0, 1.0)) 1.0 2 (1002.167257364372, 1.1172835591001746) - , StepVector 2 (Just (1000.0, 1.0)) 1.0 3 (1003.6357950413839, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 1.0 4 (1025.2715372505786, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 45.0 1 (6.51766509568746, 1.5042458491001744) - , StepVector 2 (Just (1000.0, 1.0)) 45.0 2 (1019.9544144747115, 1.1172835591001746) - , StepVector 2 (Just (1000.0, 1.0)) 45.0 3 (1033.5336749393527, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 45.0 4 (1233.1259069763294, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 400.0 1 (8.200629394345464, 1.5042458491001744) - , StepVector 2 (Just (1000.0, 1.0)) 400.0 2 (1104.014330705398, 1.1172835591001746) - , StepVector 2 (Just (1000.0, 1.0)) 400.0 3 (1174.797549651458, 1.0) - , StepVector 2 (Just (1000.0, 1.0)) 400.0 4 (2215.191516391638, 1.0) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.0 1 (34.49545162589666, 4.392180247117252) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.0 2 (1000.0, 4.142571859378209) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.0 3 (1000.0, 3.892963471639167) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.0 4 (1000.0, 3.643355083900124) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.006944444444444444 1 (33.89945672815858, 4.392180247117252) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.006944444444444444 2 (1001.6155014155838, 4.142571859378209) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.006944444444444444 3 (1002.0312175143529, 3.892963471639167) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.006944444444444444 4 (1013.6348713744535, 3.643355083900124) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.5 1 (3.9419273987129158, 4.392180247117252) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.5 2 (1001.3508492100582, 4.142571859378209) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.5 3 (1002.2099763960116, 3.892963471639167) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 0.5 4 (1015.32097430612, 3.643355083900124) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 1.0 1 (1.9700777720638714, 4.392180247117252) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 1.0 2 (1001.4749079093896, 4.142571859378209) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 1.0 3 (1002.4743082901048, 3.892963471639167) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 1.0 4 (1017.1983220756576, 3.643355083900124) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 45.0 1 (1.9659466017071279, 4.392180247117252) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 45.0 2 (1013.5798010055521, 4.142571859378209) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 45.0 3 (1022.8210471040575, 3.892963471639167) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 45.0 4 (1158.6517825411256, 3.643355083900124) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 400.0 1 (2.4735851340905017, 4.392180247117252) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 400.0 2 (1070.7860365682527, 4.142571859378209) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 400.0 3 (1118.9569327395282, 3.892963471639167) - , StepVector 2 (Just (1000.0, 4.194588083372719)) 400.0 4 (1826.9878826636022, 3.643355083900124) - , StepVector 2 (Just (1000.0, 10.0)) 0.0 1 (25.686456754555124, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.0 2 (1000.0, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.0 3 (1000.0, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.0 4 (1000.0, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.006944444444444444 1 (25.228152845249443, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.006944444444444444 2 (1000.2373848101151, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.006944444444444444 3 (1000.2984709139192, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.006944444444444444 4 (1002.0035335908382, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.5 1 (2.4867983369157667, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.5 2 (1000.1984963183138, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.5 3 (1000.3247380795, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 0.5 4 (1002.2512927202373, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 1.0 1 (0.9895172887055139, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 1.0 2 (1000.2167257364373, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 1.0 3 (1000.3635795041383, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 1.0 4 (1002.5271537250578, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 45.0 1 (0.9509748705259065, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 45.0 2 (1001.9954414474712, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 45.0 3 (1003.3533674939353, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 45.0 4 (1023.312590697633, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 400.0 1 (1.1965316354899411, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 400.0 2 (1010.4014330705397, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 400.0 3 (1017.4797549651457, 9.640321269100175) - , StepVector 2 (Just (1000.0, 10.0)) 400.0 4 (1121.5191516391635, 9.640321269100175) - , StepVector 2 (Just (36500.0, 1.0)) 0.0 1 (710.2538998690314, 1.5042458491001744) - , StepVector 2 (Just (36500.0, 1.0)) 0.0 2 (36500.0, 1.1172835591001746) - , StepVector 2 (Just (36500.0, 1.0)) 0.0 3 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 0.0 4 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 0.006944444444444444 1 (685.8356643703515, 1.5042458491001744) - , StepVector 2 (Just (36500.0, 1.0)) 0.006944444444444444 2 (36500.0, 1.1172835591001746) - , StepVector 2 (Just (36500.0, 1.0)) 0.006944444444444444 3 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 0.006944444444444444 4 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 0.5 1 (64.26913123751073, 1.5042458491001744) - , StepVector 2 (Just (36500.0, 1.0)) 0.5 2 (36500.0, 1.1172835591001746) - , StepVector 2 (Just (36500.0, 1.0)) 0.5 3 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 0.5 4 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 1.0 1 (23.579993025244807, 1.5042458491001744) - , StepVector 2 (Just (36500.0, 1.0)) 1.0 2 (36500.0, 1.1172835591001746) - , StepVector 2 (Just (36500.0, 1.0)) 1.0 3 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 1.0 4 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 45.0 1 (20.902526842337465, 1.5042458491001744) - , StepVector 2 (Just (36500.0, 1.0)) 45.0 2 (36500.0, 1.1172835591001746) - , StepVector 2 (Just (36500.0, 1.0)) 45.0 3 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 45.0 4 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 400.0 1 (21.261717622500864, 1.5042458491001744) - , StepVector 2 (Just (36500.0, 1.0)) 400.0 2 (36500.0, 1.1172835591001746) - , StepVector 2 (Just (36500.0, 1.0)) 400.0 3 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 1.0)) 400.0 4 (36500.0, 1.0) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.0 1 (440.5412488204074, 4.392180247117252) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.0 2 (36500.0, 4.142571859378209) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.0 3 (36500.0, 3.892963471639167) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.0 4 (36500.0, 3.643355083900124) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.006944444444444444 1 (425.1509580675626, 4.392180247117252) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.006944444444444444 2 (36500.0, 4.142571859378209) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.006944444444444444 3 (36500.0, 3.892963471639167) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.006944444444444444 4 (36500.0, 3.643355083900124) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.5 1 (33.63699546233535, 4.392180247117252) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.5 2 (36500.0, 4.142571859378209) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.5 3 (36500.0, 3.892963471639167) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 0.5 4 (36500.0, 3.643355083900124) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 1.0 1 (8.007431778493624, 4.392180247117252) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 1.0 2 (36500.0, 4.142571859378209) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 1.0 3 (36500.0, 3.892963471639167) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 1.0 4 (36500.0, 3.643355083900124) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 45.0 1 (6.304903828209203, 4.392180247117252) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 45.0 2 (36500.0, 4.142571859378209) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 45.0 3 (36500.0, 3.892963471639167) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 45.0 4 (36500.0, 3.643355083900124) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 400.0 1 (6.413247826137848, 4.392180247117252) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 400.0 2 (36500.0, 4.142571859378209) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 400.0 3 (36500.0, 3.892963471639167) - , StepVector 2 (Just (36500.0, 4.194588083372719)) 400.0 4 (36500.0, 3.643355083900124) - , StepVector 2 (Just (36500.0, 10.0)) 0.0 1 (330.60428380490436, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.0 2 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.0 3 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.0 4 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.006944444444444444 1 (318.9928580228448, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.006944444444444444 2 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.006944444444444444 3 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.006944444444444444 4 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.5 1 (23.670683890481016, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.5 2 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.5 3 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 0.5 4 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 1.0 1 (4.338049711119281, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 1.0 2 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 1.0 3 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 1.0 4 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 45.0 1 (3.0498311075708195, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 45.0 2 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 45.0 3 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 45.0 4 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 400.0 1 (3.102239661960336, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 400.0 2 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 400.0 3 (36500.0, 9.640321269100175) - , StepVector 2 (Just (36500.0, 10.0)) 400.0 4 (36500.0, 9.640321269100175) - ] - --- | The interval that lands exactly on the desired retention. -data IntervalVector = IntervalVector - { ivParams :: !Int - , ivDesiredRetention :: !Double - , ivStability :: !Double - , ivInterval :: !Double - } - deriving stock (Eq, Show) - -goldenIntervalVectors :: [IntervalVector] -goldenIntervalVectors = - [ IntervalVector 0 0.7 0.0001 1.1574074074074073e-5 - , IntervalVector 0 0.7 0.01 0.00045127975239051384 - , IntervalVector 0 0.7 0.5 3.117203331616744 - , IntervalVector 0 0.7 1.0 9.20105680045469 - , IntervalVector 0 0.7 4.1283 62.10906194594796 - , IntervalVector 0 0.7 15.0 284.948503494052 - , IntervalVector 0 0.7 100.0 2225.756072433354 - , IntervalVector 0 0.7 1000.0 23800.027080355834 - , IntervalVector 0 0.7 36500.0 36500.0 - , IntervalVector 0 0.8 0.0001 1.1574074074074073e-5 - , IntervalVector 0 0.8 0.01 3.601728249454452e-5 - , IntervalVector 0 0.8 0.5 0.5024089885355536 - , IntervalVector 0 0.8 1.0 2.150047765631358 - , IntervalVector 0 0.8 4.1283 19.35445042913598 - , IntervalVector 0 0.8 15.0 97.42745289971072 - , IntervalVector 0 0.8 100.0 801.9939743014621 - , IntervalVector 0 0.8 1000.0 8749.841127265681 - , IntervalVector 0 0.8 36500.0 36500.0 - , IntervalVector 0 0.85 0.0001 1.1574074074074073e-5 - , IntervalVector 0 0.85 0.01 1.1574074074074073e-5 - , IntervalVector 0 0.85 0.5 0.07311627017082284 - , IntervalVector 0 0.85 1.0 0.6357738009780464 - , IntervalVector 0 0.85 4.1283 9.281518670005237 - , IntervalVector 0 0.85 15.0 52.320939407195404 - , IntervalVector 0 0.85 100.0 455.33708673914697 - , IntervalVector 0 0.85 1000.0 5067.354602800332 - , IntervalVector 0 0.85 36500.0 36500.0 - , IntervalVector 0 0.9 0.0001 1.1574074074074073e-5 - , IntervalVector 0 0.9 0.01 1.1574074074074073e-5 - , IntervalVector 0 0.9 0.5 0.004070952126970879 - , IntervalVector 0 0.9 1.0 0.04220140211604471 - , IntervalVector 0 0.9 4.1283 2.9669271623721456 - , IntervalVector 0 0.9 15.0 23.130676977447674 - , IntervalVector 0 0.9 100.0 228.64254264799698 - , IntervalVector 0 0.9 1000.0 2650.9394532829792 - , IntervalVector 0 0.9 36500.0 36500.0 - , IntervalVector 0 0.95 0.0001 1.1574074074074073e-5 - , IntervalVector 0 0.95 0.01 1.1574074074074073e-5 - , IntervalVector 0 0.95 0.5 0.0002729212997928062 - , IntervalVector 0 0.95 1.0 0.0011673402673624 - , IntervalVector 0 0.95 4.1283 0.08000910354847687 - , IntervalVector 0 0.95 15.0 4.414772788071169 - , IntervalVector 0 0.95 100.0 77.51137131161089 - , IntervalVector 0 0.95 1000.0 1029.0563316579403 - , IntervalVector 0 0.95 36500.0 36500.0 - , IntervalVector 0 0.97 0.0001 1.1574074074074073e-5 - , IntervalVector 0 0.97 0.01 1.1574074074074073e-5 - , IntervalVector 0 0.97 0.5 8.828059519681088e-5 - , IntervalVector 0 0.97 1.0 0.00029303360834978737 - , IntervalVector 0 0.97 4.1283 0.006386991233059331 - , IntervalVector 0 0.97 15.0 0.4429904100443122 - , IntervalVector 0 0.97 100.0 32.514164306905954 - , IntervalVector 0 0.97 1000.0 536.2719260144573 - , IntervalVector 0 0.97 36500.0 22700.633467170508 - , IntervalVector 0 0.99 0.0001 1.1574074074074073e-5 - , IntervalVector 0 0.99 0.01 1.1574074074074073e-5 - , IntervalVector 0 0.99 0.5 1.7471896134792815e-5 - , IntervalVector 0 0.99 1.0 4.822136328432182e-5 - , IntervalVector 0 0.99 4.1283 0.0004690664752905264 - , IntervalVector 0 0.99 15.0 0.005395816582669202 - , IntervalVector 0 0.99 100.0 0.9825033805227932 - , IntervalVector 0 0.99 1000.0 117.48067393690135 - , IntervalVector 0 0.99 36500.0 6735.646375251022 - , IntervalVector 1 0.7 0.0001 0.056485270434622384 - , IntervalVector 1 0.7 0.01 4.917962841074945 - , IntervalVector 1 0.7 0.5 3.0747826128579723 - , IntervalVector 1 0.7 1.0 3.5035241205529903 - , IntervalVector 1 0.7 4.1283 8.881571776199577 - , IntervalVector 1 0.7 15.0 28.779595370154098 - , IntervalVector 1 0.7 100.0 185.77323261468953 - , IntervalVector 1 0.7 1000.0 1850.306402242769 - , IntervalVector 1 0.7 36500.0 36500.0 - , IntervalVector 1 0.8 0.0001 0.00017803154636673922 - , IntervalVector 1 0.8 0.01 0.017526088717440668 - , IntervalVector 1 0.8 0.5 0.6209748700795628 - , IntervalVector 1 0.8 1.0 1.1624258186863363 - , IntervalVector 1 0.8 4.1283 4.509858675287754 - , IntervalVector 1 0.8 15.0 16.151138483343377 - , IntervalVector 1 0.8 100.0 107.24123174296729 - , IntervalVector 1 0.8 1000.0 1071.8776526967645 - , IntervalVector 1 0.8 36500.0 36500.0 - , IntervalVector 1 0.85 0.0001 1.3014325708657666e-5 - , IntervalVector 1 0.85 0.01 0.0013275784398440527 - , IntervalVector 1 0.85 0.5 0.18019830183924998 - , IntervalVector 1 0.85 1.0 0.5072819008173706 - , IntervalVector 1 0.85 4.1283 2.853572670471599 - , IntervalVector 1 0.85 15.0 11.084784580817049 - , IntervalVector 1 0.85 100.0 75.25530086567957 - , IntervalVector 1 0.85 1000.0 754.2392102615415 - , IntervalVector 1 0.85 36500.0 27534.560520025057 - , IntervalVector 1 0.9 0.0001 1.1574074074074073e-5 - , IntervalVector 1 0.9 0.01 0.00011117565267932369 - , IntervalVector 1 0.9 0.5 0.018717648016651153 - , IntervalVector 1 0.9 1.0 0.10511511284303723 - , IntervalVector 1 0.9 4.1283 1.4637131423968208 - , IntervalVector 1 0.9 15.0 6.655916282644194 - , IntervalVector 1 0.9 100.0 47.011718979983804 - , IntervalVector 1 0.9 1000.0 473.4253654955935 - , IntervalVector 1 0.9 36500.0 17289.509963417844 - , IntervalVector 1 0.95 0.0001 1.1574074074074073e-5 - , IntervalVector 1 0.95 0.01 1.1574074074074073e-5 - , IntervalVector 1 0.95 0.5 0.0009437701786925955 - , IntervalVector 1 0.95 1.0 0.004090102355002918 - , IntervalVector 1 0.95 4.1283 0.3495061226120306 - , IntervalVector 1 0.95 15.0 2.7772828623271026 - , IntervalVector 1 0.95 100.0 21.91235884204184 - , IntervalVector 1 0.95 1000.0 223.46725792535577 - , IntervalVector 1 0.95 36500.0 8169.033979115177 - , IntervalVector 1 0.97 0.0001 1.1574074074074073e-5 - , IntervalVector 1 0.97 0.01 1.1574074074074073e-5 - , IntervalVector 1 0.97 0.5 0.0002569412683931921 - , IntervalVector 1 0.97 1.0 0.0008627094776825766 - , IntervalVector 1 0.97 4.1283 0.06823050658616155 - , IntervalVector 1 0.97 15.0 1.3832728374582621 - , IntervalVector 1 0.97 100.0 12.652613385391312 - , IntervalVector 1 0.97 1000.0 131.0325051789605 - , IntervalVector 1 0.97 36500.0 4795.665879636751 - , IntervalVector 1 0.99 0.0001 1.1574074074074073e-5 - , IntervalVector 1 0.99 0.01 1.1574074074074073e-5 - , IntervalVector 1 0.99 0.5 4.343160931319135e-5 - , IntervalVector 1 0.99 1.0 0.00011831556774026941 - , IntervalVector 1 0.99 4.1283 0.0022932718844632704 - , IntervalVector 1 0.99 15.0 0.1832552247602712 - , IntervalVector 1 0.99 100.0 3.835732740677949 - , IntervalVector 1 0.99 1000.0 42.53363987052 - , IntervalVector 1 0.99 36500.0 1564.6644364198594 - , IntervalVector 2 0.7 0.0001 1.1574074074074073e-5 - , IntervalVector 2 0.7 0.01 1.1574074074074073e-5 - , IntervalVector 2 0.7 0.5 0.08150032655928467 - , IntervalVector 2 0.7 1.0 0.2191302172372853 - , IntervalVector 2 0.7 4.1283 1.280641542930248 - , IntervalVector 2 0.7 15.0 5.426265610662961 - , IntervalVector 2 0.7 100.0 39.94832161945218 - , IntervalVector 2 0.7 1000.0 415.7814582906561 - , IntervalVector 2 0.7 36500.0 15389.855536955905 - , IntervalVector 2 0.8 0.0001 1.1574074074074073e-5 - , IntervalVector 2 0.8 0.01 1.1574074074074073e-5 - , IntervalVector 2 0.8 0.5 0.0019323117414683263 - , IntervalVector 2 0.8 1.0 0.02982261032771186 - , IntervalVector 2 0.8 4.1283 0.397688827723519 - , IntervalVector 2 0.8 15.0 2.104189792791598 - , IntervalVector 2 0.8 100.0 17.48703508290727 - , IntervalVector 2 0.8 1000.0 190.42477333335583 - , IntervalVector 2 0.8 36500.0 7157.847169026045 - , IntervalVector 2 0.85 0.0001 1.1574074074074073e-5 - , IntervalVector 2 0.85 0.01 1.1574074074074073e-5 - , IntervalVector 2 0.85 0.5 1.1574074074074073e-5 - , IntervalVector 2 0.85 1.0 0.00029955593419729983 - , IntervalVector 2 0.85 4.1283 0.15588323083723007 - , IntervalVector 2 0.85 15.0 1.1299878116819286 - , IntervalVector 2 0.85 100.0 10.619072803191733 - , IntervalVector 2 0.85 1000.0 120.33639320854094 - , IntervalVector 2 0.85 36500.0 4582.215684387548 - , IntervalVector 2 0.9 0.0001 1.1574074074074073e-5 - , IntervalVector 2 0.9 0.01 1.1574074074074073e-5 - , IntervalVector 2 0.9 0.5 1.1574074074074073e-5 - , IntervalVector 2 0.9 1.0 1.1574074074074073e-5 - , IntervalVector 2 0.9 4.1283 0.006395903619397388 - , IntervalVector 2 0.9 15.0 0.42381904955941113 - , IntervalVector 2 0.9 100.0 5.496698918051801 - , IntervalVector 2 0.9 1000.0 67.54103651918959 - , IntervalVector 2 0.9 36500.0 2635.459438849799 - , IntervalVector 2 0.95 0.0001 1.1574074074074073e-5 - , IntervalVector 2 0.95 0.01 1.1574074074074073e-5 - , IntervalVector 2 0.95 0.5 1.1574074074074073e-5 - , IntervalVector 2 0.95 1.0 1.1574074074074073e-5 - , IntervalVector 2 0.95 4.1283 1.1574074074074073e-5 - , IntervalVector 2 0.95 15.0 0.0006947402110169297 - , IntervalVector 2 0.95 100.0 1.6297887361214212 - , IntervalVector 2 0.95 1000.0 27.162156921554093 - , IntervalVector 2 0.95 36500.0 1140.9809607840618 - , IntervalVector 2 0.97 0.0001 1.1574074074074073e-5 - , IntervalVector 2 0.97 0.01 1.1574074074074073e-5 - , IntervalVector 2 0.97 0.5 1.1574074074074073e-5 - , IntervalVector 2 0.97 1.0 1.1574074074074073e-5 - , IntervalVector 2 0.97 4.1283 1.1574074074074073e-5 - , IntervalVector 2 0.97 15.0 1.1574074074074073e-5 - , IntervalVector 2 0.97 100.0 0.38856423686691866 - , IntervalVector 2 0.97 1000.0 13.726252993269208 - , IntervalVector 2 0.97 36500.0 641.4142966751779 - , IntervalVector 2 0.99 0.0001 1.1574074074074073e-5 - , IntervalVector 2 0.99 0.01 1.1574074074074073e-5 - , IntervalVector 2 0.99 0.5 1.1574074074074073e-5 - , IntervalVector 2 0.99 1.0 1.1574074074074073e-5 - , IntervalVector 2 0.99 4.1283 1.1574074074074073e-5 - , IntervalVector 2 0.99 15.0 1.1574074074074073e-5 - , IntervalVector 2 0.99 100.0 1.1574074074074073e-5 - , IntervalVector 2 0.99 1000.0 1.7403480423800615 - , IntervalVector 2 0.99 36500.0 188.8949885261801 - ] - --- | A whole review history folded into a final memory state. -data ReplayVector = ReplayVector - { rvParams :: !Int - , rvReviews :: ![(Double, Int)] - -- ^ @(days since the previous review, rating)@. - , rvFinalState :: !(Double, Double) - } - deriving stock (Eq, Show) - -goldenReplayVectors :: [ReplayVector] -goldenReplayVectors = - [ ReplayVector 0 [(0.0, 3)] (4.1283, 4.194588083372719) - , ReplayVector 0 [(0.0, 1)] (0.041, 5.6385) - , ReplayVector 0 [(0.0, 4)] (11.9709, 2.817928571667297) - , ReplayVector 0 [(0.0, 3), (0.006944444444444444, 3)] (5.284074098785149, 4.180821488255665) - , ReplayVector 0 [(0.0, 1), (0.0006944444444444445, 3), (0.006944444444444444, 3), (1.0, 3)] (4.363823678078679, 5.554726208007091) - , ReplayVector 0 [(0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (51.13598657235655, 4.140342205740074) - , ReplayVector 0 [(0.0, 2), (1.0, 2), (2.0, 2), (3.0, 2)] (10.005657593467827, 8.615870652454893) - , ReplayVector 0 [(0.0, 4), (15.0, 4), (90.0, 4), (365.0, 4)] (399.54723405853474, 1.0) - , ReplayVector 0 [(0.0, 3), (5.0, 1), (0.006944444444444444, 3), (1.0, 3), (4.0, 4)] (6.709654019064798, 7.550194020527194) - , ReplayVector 0 [(0.0, 1), (0.0, 1), (0.0, 1), (0.0, 3)] (0.0001844264325618162, 9.517410721695096) - , ReplayVector 0 [(0.0, 3), (100.0, 1), (0.5, 2), (2.0, 3), (6.0, 4), (30.0, 1)] (1.2988830554348012, 9.476663700091226) - , ReplayVector 0 [(0.0, 2), (0.25, 3), (0.75, 4), (2.5, 1), (0.01, 3), (7.0, 3)] (6.155878820322062, 7.9861912704492415) - , ReplayVector 0 [(0.0, 3), (1.0, 3), (2.0, 3), (4.0, 3), (8.0, 3), (16.0, 3), (32.0, 3), (64.0, 3), (128.0, 3), (256.0, 3), (512.0, 3)] (504.34338372214967, 4.062954757444055) - , ReplayVector 0 [(0.0, 4), (1.0, 4), (1.0, 3), (1.0, 2), (1.0, 1), (1.0, 3), (1.0, 4), (1.0, 2), (1.0, 1)] (1.8700202120083298, 9.504197999898857) - , ReplayVector 1 [(0.0, 3)] (64.835975, 1.0) - , ReplayVector 1 [(0.0, 1)] (21.160516, 8.15903) - , ReplayVector 1 [(0.0, 4)] (64.835975, 1.0) - , ReplayVector 1 [(0.0, 3), (0.006944444444444444, 3)] (64.83966034515682, 1.0) - , ReplayVector 1 [(0.0, 1), (0.0006944444444444445, 3), (0.006944444444444444, 3), (1.0, 3)] (21.22186424830409, 1.0) - , ReplayVector 1 [(0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (65.12283435473542, 1.0) - , ReplayVector 1 [(0.0, 2), (1.0, 2), (2.0, 2), (3.0, 2)] (50.96007847033368, 1.0) - , ReplayVector 1 [(0.0, 4), (15.0, 4), (90.0, 4), (365.0, 4)] (77.80278794798323, 1.0) - , ReplayVector 1 [(0.0, 3), (5.0, 1), (0.006944444444444444, 3), (1.0, 3), (4.0, 4)] (32.70121989196062, 1.0) - , ReplayVector 1 [(0.0, 1), (0.0, 1), (0.0, 1), (0.0, 3)] (0.3145624222371321, 1.0) - , ReplayVector 1 [(0.0, 3), (100.0, 1), (0.5, 2), (2.0, 3), (6.0, 4), (30.0, 1)] (26.19569389489973, 1.4918717310343146) - , ReplayVector 1 [(0.0, 2), (0.25, 3), (0.75, 4), (2.5, 1), (0.01, 3), (7.0, 3)] (26.472074461000048, 1.0) - , ReplayVector 1 [(0.0, 3), (1.0, 3), (2.0, 3), (4.0, 3), (8.0, 3), (16.0, 3), (32.0, 3), (64.0, 3), (128.0, 3), (256.0, 3), (512.0, 3)] (69.9098324237063, 1.0) - , ReplayVector 1 [(0.0, 4), (1.0, 4), (1.0, 3), (1.0, 2), (1.0, 1), (1.0, 3), (1.0, 4), (1.0, 2), (1.0, 1)] (17.7943323192371, 1.4918717310343146) - , ReplayVector 2 [(0.0, 3)] (79.640406, 1.0) - , ReplayVector 2 [(0.0, 1)] (2.462798, 7.614116) - , ReplayVector 2 [(0.0, 4)] (79.640406, 1.0) - , ReplayVector 2 [(0.0, 3), (0.006944444444444444, 3)] (86.62079519809366, 1.0) - , ReplayVector 2 [(0.0, 1), (0.0006944444444444445, 3), (0.006944444444444444, 3), (1.0, 3)] (23.961229647935912, 6.61669734203843) - , ReplayVector 2 [(0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (199.62738805973905, 1.0) - , ReplayVector 2 [(0.0, 2), (1.0, 2), (2.0, 2), (3.0, 2)] (43.299666393753476, 5.033143534988341) - , ReplayVector 2 [(0.0, 4), (15.0, 4), (90.0, 4), (365.0, 4)] (2203.3303431594163, 1.0) - , ReplayVector 2 [(0.0, 3), (5.0, 1), (0.006944444444444444, 3), (1.0, 3), (4.0, 4)] (280.96023230120966, 1.0) - , ReplayVector 2 [(0.0, 1), (0.0, 1), (0.0, 1), (0.0, 3)] (0.05224193167244188, 7.032017724078441) - , ReplayVector 2 [(0.0, 3), (100.0, 1), (0.5, 2), (2.0, 3), (6.0, 4), (30.0, 1)] (4.551999327806947, 1.5042458491001744) - , ReplayVector 2 [(0.0, 2), (0.25, 3), (0.75, 4), (2.5, 1), (0.01, 3), (7.0, 3)] (63.18078959050319, 4.076018495507828) - , ReplayVector 2 [(0.0, 3), (1.0, 3), (2.0, 3), (4.0, 3), (8.0, 3), (16.0, 3), (32.0, 3), (64.0, 3), (128.0, 3), (256.0, 3), (512.0, 3)] (890.1169420823825, 1.0) - , ReplayVector 2 [(0.0, 4), (1.0, 4), (1.0, 3), (1.0, 2), (1.0, 1), (1.0, 3), (1.0, 4), (1.0, 2), (1.0, 1)] (2.817832383828903, 1.6102711693629577) +-- transcription of the reference model. Do not edit by hand; +-- regenerate with @python3 reference\/gen_golden.py@. +module Test.FSRS.GoldenData + ( goldenParameterSets + , CurveVector (..) + , goldenCurveVectors + , FastRecallVector (..) + , goldenFastRecallVectors + , DifficultyVector (..) + , goldenDifficultyVectors + , HalfStabilityVector (..) + , goldenHalfStabilityVectors + , StepVector (..) + , goldenStepVectors + , IntervalVector (..) + , goldenIntervalVectors + , ReplayVector (..) + , goldenReplayVectors + ) where + +-- | The parameter sets the vectors below refer to by index. +-- Index 0 is the FSRS-7 default parameter set. +goldenParameterSets :: [[Double]] +goldenParameterSets = + [ [0.1104, 2.2395, 3.9221, 11.7841, 6.1686, 0.6457, 3.6807, 1.9795, 0.0, 1.3826, 0.7024, 0.5999, 0.8146, 0.6398, 1.0, 1.3207, 0.6707, 3.8668, 0.4416, 0.0934, 1.8631, 0.6162, 1.0869, 0.1567, 0.0801, 0.2421, 0.9464, 0.1433, 0.7145, 0.0, 0.5667, 0.3734, 0.5333, 0.3048] + , [21.160516, 50.940793, 64.835975, 64.835975, 8.15903, 2.002545, 2.260348, 0.261677, 1.007671, 0.835788, 1.121191, 0.582182, 2.742892, 0.317049, 2.461488, 2.999687, 0.849073, 3.646794, 0.934326, 0.204025, 4.32941, 0.979622, 4.298516, 0.159186, 0.373962, 0.712382, 0.78895, 0.064371, 0.968281, 0.799121, 0.383215, 0.640278, 0.19246, 0.328323] + , [2.462798, 11.949056, 79.640406, 79.640406, 7.614116, 1.181111, 0.390871, 2.724834, 0.753779, 2.243577, 0.730412, 0.935852, 0.86427, 0.296865, 4.570336, 3.967996, 1.663002, 2.63757, 0.502115, 0.596751, 0.815759, 0.712237, 5.132993, 0.241617, 0.873206, 0.357877, 0.714831, 0.043894, 0.346437, 0.208525, 0.103578, 0.391527, 0.246078, 0.120496] + ] + +-- | @R(t, state)@, the probability of recall. The state is spelled out +-- as a @(stability, difficulty, fast stability)@ triple. +data CurveVector = CurveVector + { cvParams :: !Int + , cvElapsedDays :: !Double + , cvState :: !(Double, Double, Double) + , cvRetrievability :: !Double + } + deriving stock (Eq, Show) + +goldenCurveVectors :: [CurveVector] +goldenCurveVectors = + [ CurveVector 0 0.0 (0.0001, 1.0, 0.0001) 0.9999899999999999 + , CurveVector 0 0.0 (0.0001, 5.0, 0.0001) 0.9999899999999999 + , CurveVector 0 0.0 (0.0001, 10.0, 0.0001) 0.9999899999999999 + , CurveVector 0 0.0 (0.01, 1.0, 0.008) 0.9999899999999999 + , CurveVector 0 0.0 (0.01, 5.0, 0.008) 0.9999899999999999 + , CurveVector 0 0.0 (0.01, 10.0, 0.008) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 1.0, 0.4) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 5.0, 0.4) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 10.0, 0.4) 0.9999899999999999 + , CurveVector 0 0.0 (1.0, 1.0, 0.8) 0.9999899999999999 + , CurveVector 0 0.0 (1.0, 5.0, 0.8) 0.9999899999999999 + , CurveVector 0 0.0 (1.0, 10.0, 0.8) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 1.0, 3.13768) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 5.0, 3.13768) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 10.0, 3.13768) 0.9999899999999999 + , CurveVector 0 0.0 (15.0, 1.0, 12.0) 0.9999899999999999 + , CurveVector 0 0.0 (15.0, 5.0, 12.0) 0.9999899999999999 + , CurveVector 0 0.0 (15.0, 10.0, 12.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 1.0, 80.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 5.0, 80.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 10.0, 80.0) 0.9999899999999999 + , CurveVector 0 0.0 (1000.0, 1.0, 800.0) 0.9999899999999999 + , CurveVector 0 0.0 (1000.0, 5.0, 800.0) 0.9999899999999999 + , CurveVector 0 0.0 (1000.0, 10.0, 800.0) 0.9999899999999999 + , CurveVector 0 0.0 (36500.0, 1.0, 29200.0) 0.9999899999999999 + , CurveVector 0 0.0 (36500.0, 5.0, 29200.0) 0.9999899999999999 + , CurveVector 0 0.0 (36500.0, 10.0, 29200.0) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 2.5, 0.025) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 2.5, 0.5) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 2.5, 10.0) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 7.0, 0.025) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 7.0, 0.5) 0.9999899999999999 + , CurveVector 0 0.0 (0.5, 7.0, 10.0) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 2.5, 0.196105) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 2.5, 3.9221) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 2.5, 78.442) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 7.0, 0.196105) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 7.0, 3.9221) 0.9999899999999999 + , CurveVector 0 0.0 (3.9221, 7.0, 78.442) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 2.5, 5.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 2.5, 100.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 2.5, 2000.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 7.0, 5.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 7.0, 100.0) 0.9999899999999999 + , CurveVector 0 0.0 (100.0, 7.0, 2000.0) 0.9999899999999999 + , CurveVector 0 1.1574074074074073e-5 (0.0001, 1.0, 0.0001) 0.3628373041101308 + , CurveVector 0 1.1574074074074073e-5 (0.0001, 5.0, 0.0001) 0.35172985787323185 + , CurveVector 0 1.1574074074074073e-5 (0.0001, 10.0, 0.0001) 0.3435245955238318 + , CurveVector 0 1.1574074074074073e-5 (0.01, 1.0, 0.008) 0.783919591141654 + , CurveVector 0 1.1574074074074073e-5 (0.01, 5.0, 0.008) 0.7456855096301587 + , CurveVector 0 1.1574074074074073e-5 (0.01, 10.0, 0.008) 0.7090545359056282 + , CurveVector 0 1.1574074074074073e-5 (0.5, 1.0, 0.4) 0.9946679375761777 + , CurveVector 0 1.1574074074074073e-5 (0.5, 5.0, 0.4) 0.9919621861982887 + , CurveVector 0 1.1574074074074073e-5 (0.5, 10.0, 0.4) 0.9874137201352076 + , CurveVector 0 1.1574074074074073e-5 (1.0, 1.0, 0.8) 0.9980250338922181 + , CurveVector 0 1.1574074074074073e-5 (1.0, 5.0, 0.8) 0.9969456754685644 + , CurveVector 0 1.1574074074074073e-5 (1.0, 10.0, 0.8) 0.9949930634344051 + , CurveVector 0 1.1574074074074073e-5 (3.9221, 1.0, 3.13768) 0.9997450897988265 + , CurveVector 0 1.1574074074074073e-5 (3.9221, 5.0, 3.13768) 0.9995972088521423 + , CurveVector 0 1.1574074074074073e-5 (3.9221, 10.0, 3.13768) 0.9993014562402476 + , CurveVector 0 1.1574074074074073e-5 (15.0, 1.0, 12.0) 0.9999603423093698 + , CurveVector 0 1.1574074074074073e-5 (15.0, 5.0, 12.0) 0.9999415786411505 + , CurveVector 0 1.1574074074074073e-5 (15.0, 10.0, 12.0) 0.9999019548721743 + , CurveVector 0 1.1574074074074073e-5 (100.0, 1.0, 80.0) 0.9999885555204889 + , CurveVector 0 1.1574074074074073e-5 (100.0, 5.0, 80.0) 0.9999876138700481 + , CurveVector 0 1.1574074074074073e-5 (100.0, 10.0, 80.0) 0.999985551438797 + , CurveVector 0 1.1574074074074073e-5 (1000.0, 1.0, 800.0) 0.9999899635448196 + , CurveVector 0 1.1574074074074073e-5 (1000.0, 5.0, 800.0) 0.9999899392881023 + , CurveVector 0 1.1574074074074073e-5 (1000.0, 10.0, 800.0) 0.9999898848568648 + , CurveVector 0 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+ , CurveVector 2 3.0 (36500.0, 10.0, 29200.0) 0.9957687256371135 + , CurveVector 2 3.0 (0.5, 2.5, 0.025) 0.23978181514285538 + , CurveVector 2 3.0 (0.5, 2.5, 0.5) 0.2776342404796161 + , CurveVector 2 3.0 (0.5, 2.5, 10.0) 0.2934961803002208 + , CurveVector 2 3.0 (0.5, 7.0, 0.025) 0.2545515174714049 + , CurveVector 2 3.0 (0.5, 7.0, 0.5) 0.3144242904255178 + , CurveVector 2 3.0 (0.5, 7.0, 10.0) 0.34234570191978014 + , CurveVector 2 3.0 (3.9221, 2.5, 0.196105) 0.6783957646367406 + , CurveVector 2 3.0 (3.9221, 2.5, 3.9221) 0.719029137188757 + , CurveVector 2 3.0 (3.9221, 2.5, 78.442) 0.7332025708998837 + , CurveVector 2 3.0 (3.9221, 7.0, 0.196105) 0.6816737916341917 + , CurveVector 2 3.0 (3.9221, 7.0, 3.9221) 0.7457589648657088 + , CurveVector 2 3.0 (3.9221, 7.0, 78.442) 0.7695955124907019 + , CurveVector 2 3.0 (100.0, 2.5, 5.0) 0.9617401117971932 + , CurveVector 2 3.0 (100.0, 2.5, 100.0) 0.9756500748002603 + , CurveVector 2 3.0 (100.0, 2.5, 2000.0) 0.9806647226043007 + , CurveVector 2 3.0 (100.0, 7.0, 5.0) 0.9501408216855228 + , CurveVector 2 3.0 (100.0, 7.0, 100.0) 0.9721255507986069 + , CurveVector 2 3.0 (100.0, 7.0, 2000.0) 0.9801737730150023 + , CurveVector 2 7.5 (0.0001, 1.0, 0.0001) 5.3532178043234786e-5 + , CurveVector 2 7.5 (0.0001, 5.0, 0.0001) 5.16221782914131e-5 + , CurveVector 2 7.5 (0.0001, 10.0, 0.0001) 4.775882048386114e-5 + , CurveVector 2 7.5 (0.01, 1.0, 0.008) 0.005708255750329728 + , CurveVector 2 7.5 (0.01, 5.0, 0.008) 0.006626604852363778 + , CurveVector 2 7.5 (0.01, 10.0, 0.008) 0.007670129248913579 + , CurveVector 2 7.5 (0.5, 1.0, 0.4) 0.13906910749847123 + , CurveVector 2 7.5 (0.5, 5.0, 0.4) 0.16134272115754933 + , CurveVector 2 7.5 (0.5, 10.0, 0.4) 0.18923388510382727 + , CurveVector 2 7.5 (1.0, 1.0, 0.8) 0.2286715753538474 + , CurveVector 2 7.5 (1.0, 5.0, 0.8) 0.2606433931299252 + , CurveVector 2 7.5 (1.0, 10.0, 0.8) 0.2986864762920948 + , CurveVector 2 7.5 (3.9221, 1.0, 3.13768) 0.5088705317514521 + , CurveVector 2 7.5 (3.9221, 5.0, 3.13768) 0.5503180540673742 + , CurveVector 2 7.5 (3.9221, 10.0, 3.13768) 0.59105320756731 + , CurveVector 2 7.5 (15.0, 1.0, 12.0) 0.7853774683958099 + , CurveVector 2 7.5 (15.0, 5.0, 12.0) 0.8079024970966162 + , CurveVector 2 7.5 (15.0, 10.0, 12.0) 0.8230822955274959 + , CurveVector 2 7.5 (100.0, 1.0, 80.0) 0.9533974364575405 + , CurveVector 2 7.5 (100.0, 5.0, 80.0) 0.9547986987526896 + , CurveVector 2 7.5 (100.0, 10.0, 80.0) 0.9507340887217234 + , CurveVector 2 7.5 (1000.0, 1.0, 800.0) 0.9913299029320517 + , CurveVector 2 7.5 (1000.0, 5.0, 800.0) 0.9894488055563875 + , CurveVector 2 7.5 (1000.0, 10.0, 800.0) 0.9849034685648734 + , CurveVector 2 7.5 (36500.0, 1.0, 29200.0) 0.99824051437321 + , CurveVector 2 7.5 (36500.0, 5.0, 29200.0) 0.9973713826554285 + , CurveVector 2 7.5 (36500.0, 10.0, 29200.0) 0.9955816304801578 + , CurveVector 2 7.5 (0.5, 2.5, 0.025) 0.12418583700436632 + , CurveVector 2 7.5 (0.5, 2.5, 0.5) 0.14887550293016052 + , CurveVector 2 7.5 (0.5, 2.5, 10.0) 0.15993872112226143 + , CurveVector 2 7.5 (0.5, 7.0, 0.025) 0.1359177160254534 + , CurveVector 2 7.5 (0.5, 7.0, 0.5) 0.17526799304220755 + , CurveVector 2 7.5 (0.5, 7.0, 10.0) 0.19480252825078292 + , CurveVector 2 7.5 (3.9221, 2.5, 0.196105) 0.49470921562680537 + , CurveVector 2 7.5 (3.9221, 2.5, 3.9221) 0.5266053890974843 + , CurveVector 2 7.5 (3.9221, 2.5, 78.442) 0.537354913434569 + , CurveVector 2 7.5 (3.9221, 7.0, 0.196105) 0.5189549945743637 + , CurveVector 2 7.5 (3.9221, 7.0, 3.9221) 0.5710122843830848 + , CurveVector 2 7.5 (3.9221, 7.0, 78.442) 0.5901824939022676 + , CurveVector 2 7.5 (100.0, 2.5, 5.0) 0.9400929993145268 + , CurveVector 2 7.5 (100.0, 2.5, 100.0) 0.9550132273839339 + , CurveVector 2 7.5 (100.0, 2.5, 2000.0) 0.9605371143131649 + , CurveVector 2 7.5 (100.0, 7.0, 5.0) 0.9314004386467777 + , CurveVector 2 7.5 (100.0, 7.0, 100.0) 0.95509914972221 + , CurveVector 2 7.5 (100.0, 7.0, 2000.0) 0.9640322559509401 + , CurveVector 2 30.0 (0.0001, 1.0, 0.0001) 2.2753506871997313e-5 + , CurveVector 2 30.0 (0.0001, 5.0, 0.0001) 2.2147255843209133e-5 + , CurveVector 2 30.0 (0.0001, 10.0, 0.0001) 2.0957603579750426e-5 + , CurveVector 2 30.0 (0.01, 1.0, 0.008) 0.002025851646589126 + , CurveVector 2 30.0 (0.01, 5.0, 0.008) 0.00241016004453687 + , CurveVector 2 30.0 (0.01, 10.0, 0.008) 0.002878270401894584 + , CurveVector 2 30.0 (0.5, 1.0, 0.4) 0.04981255586402158 + , CurveVector 2 30.0 (0.5, 5.0, 0.4) 0.06012317734619036 + , CurveVector 2 30.0 (0.5, 10.0, 0.4) 0.0747254461119086 + , CurveVector 2 30.0 (1.0, 1.0, 0.8) 0.0836731508096704 + , CurveVector 2 30.0 (1.0, 5.0, 0.8) 0.0995896816192388 + , CurveVector 2 30.0 (1.0, 10.0, 0.8) 0.12161558681799543 + , CurveVector 2 30.0 (3.9221, 1.0, 3.13768) 0.22764963798643387 + , CurveVector 2 30.0 (3.9221, 5.0, 3.13768) 0.2617374781853212 + , CurveVector 2 30.0 (3.9221, 10.0, 3.13768) 0.3049583206318022 + , CurveVector 2 30.0 (15.0, 1.0, 12.0) 0.5026692184925919 + , CurveVector 2 30.0 (15.0, 5.0, 12.0) 0.5477286856432816 + , CurveVector 2 30.0 (15.0, 10.0, 12.0) 0.5960442654819842 + , CurveVector 2 30.0 (100.0, 1.0, 80.0) 0.8595434852547091 + , CurveVector 2 30.0 (100.0, 5.0, 80.0) 0.8763756562595285 + , CurveVector 2 30.0 (100.0, 10.0, 80.0) 0.8882053179650696 + , CurveVector 2 30.0 (1000.0, 1.0, 800.0) 0.9797661804171302 + , CurveVector 2 30.0 (1000.0, 5.0, 800.0) 0.9797945310575209 + , CurveVector 2 30.0 (1000.0, 10.0, 800.0) 0.9768932785565566 + , CurveVector 2 30.0 (36500.0, 1.0, 29200.0) 0.9978469590880075 + , CurveVector 2 30.0 (36500.0, 5.0, 29200.0) 0.9969946185608363 + , CurveVector 2 30.0 (36500.0, 10.0, 29200.0) 0.9951750403858741 + , CurveVector 2 30.0 (0.5, 2.5, 0.025) 0.04088579368120055 + , CurveVector 2 30.0 (0.5, 2.5, 0.5) 0.05453403645598735 + , CurveVector 2 30.0 (0.5, 2.5, 10.0) 0.06227039532975829 + , CurveVector 2 30.0 (0.5, 7.0, 0.025) 0.04589126641649157 + , CurveVector 2 30.0 (0.5, 7.0, 0.5) 0.06743388476713384 + , CurveVector 2 30.0 (0.5, 7.0, 10.0) 0.08063750273132556 + , CurveVector 2 30.0 (3.9221, 2.5, 0.196105) 0.22305180349983778 + , CurveVector 2 30.0 (3.9221, 2.5, 3.9221) 0.24110326737569038 + , CurveVector 2 30.0 (3.9221, 2.5, 78.442) 0.2460625360568548 + , CurveVector 2 30.0 (3.9221, 7.0, 0.196105) 0.25013850871197163 + , CurveVector 2 30.0 (3.9221, 7.0, 3.9221) 0.28068048568817405 + , CurveVector 2 30.0 (3.9221, 7.0, 78.442) 0.29038832105078954 + , CurveVector 2 30.0 (100.0, 2.5, 5.0) 0.8523767986602097 + , CurveVector 2 30.0 (100.0, 2.5, 100.0) 0.8672404007218758 + , CurveVector 2 30.0 (100.0, 2.5, 2000.0) 0.8727903426695016 + , CurveVector 2 30.0 (100.0, 7.0, 5.0) 0.8594297312715142 + , CurveVector 2 30.0 (100.0, 7.0, 100.0) 0.8835299094736583 + , CurveVector 2 30.0 (100.0, 7.0, 2000.0) 0.8927811045057018 + , CurveVector 2 365.0 (0.0001, 1.0, 0.0001) 1.1400202101800752e-5 + , CurveVector 2 365.0 (0.0001, 5.0, 0.0001) 1.1325308880053122e-5 + , CurveVector 2 365.0 (0.0001, 10.0, 0.0001) 1.1184377573375479e-5 + , CurveVector 2 365.0 (0.01, 1.0, 0.008) 0.0003540314991635756 + , CurveVector 2 365.0 (0.01, 5.0, 0.008) 0.00043802301680623024 + , CurveVector 2 365.0 (0.01, 10.0, 0.008) 0.0005485632266402005 + , CurveVector 2 365.0 (0.5, 1.0, 0.4) 0.009577586891717338 + , CurveVector 2 365.0 (0.5, 5.0, 0.4) 0.0125770375842484 + , CurveVector 2 365.0 (0.5, 10.0, 0.4) 0.017459346842731052 + , CurveVector 2 365.0 (1.0, 1.0, 0.8) 0.014633012014014249 + , CurveVector 2 365.0 (1.0, 5.0, 0.8) 0.01889160470679945 + , CurveVector 2 365.0 (1.0, 10.0, 0.8) 0.02581201390989589 + , CurveVector 2 365.0 (3.9221, 1.0, 3.13768) 0.03603351631027348 + , CurveVector 2 365.0 (3.9221, 5.0, 3.13768) 0.04459058562860817 + , CurveVector 2 365.0 (3.9221, 10.0, 3.13768) 0.057937675729558866 + , CurveVector 2 365.0 (15.0, 1.0, 12.0) 0.09735397688447144 + , CurveVector 2 365.0 (15.0, 5.0, 12.0) 0.11632130315770434 + , CurveVector 2 365.0 (15.0, 10.0, 12.0) 0.14395497016634798 + , CurveVector 2 365.0 (100.0, 1.0, 80.0) 0.3685953635897845 + , CurveVector 2 365.0 (100.0, 5.0, 80.0) 0.415030120712426 + , CurveVector 2 365.0 (100.0, 10.0, 80.0) 0.4727539533673303 + , CurveVector 2 365.0 (1000.0, 1.0, 800.0) 0.8406511356552404 + , CurveVector 2 365.0 (1000.0, 5.0, 800.0) 0.8637008084958262 + , CurveVector 2 365.0 (1000.0, 10.0, 800.0) 0.8849196016054459 + , CurveVector 2 365.0 (36500.0, 1.0, 29200.0) 0.9930909858686856 + , CurveVector 2 365.0 (36500.0, 5.0, 29200.0) 0.9930632484222065 + , CurveVector 2 365.0 (36500.0, 10.0, 29200.0) 0.9919796164962521 + , CurveVector 2 365.0 (0.5, 2.5, 0.025) 0.005222412367127948 + , CurveVector 2 365.0 (0.5, 2.5, 0.5) 0.011210286253951809 + , CurveVector 2 365.0 (0.5, 2.5, 10.0) 0.017269523662625342 + , CurveVector 2 365.0 (0.5, 7.0, 0.025) 0.0060575336057090805 + , CurveVector 2 365.0 (0.5, 7.0, 0.5) 0.015315869490976507 + , CurveVector 2 365.0 (0.5, 7.0, 10.0) 0.025164229521336755 + , CurveVector 2 365.0 (3.9221, 2.5, 0.196105) 0.03226773999564753 + , CurveVector 2 365.0 (3.9221, 2.5, 3.9221) 0.03943125588678332 + , CurveVector 2 365.0 (3.9221, 2.5, 78.442) 0.04113928811696532 + , CurveVector 2 365.0 (3.9221, 7.0, 0.196105) 0.03847703393394597 + , CurveVector 2 365.0 (3.9221, 7.0, 3.9221) 0.050230266377797025 + , CurveVector 2 365.0 (3.9221, 7.0, 78.442) 0.053445639815885126 + , CurveVector 2 365.0 (100.0, 2.5, 5.0) 0.3787175968276551 + , CurveVector 2 365.0 (100.0, 2.5, 100.0) 0.38618980751385373 + , CurveVector 2 365.0 (100.0, 2.5, 2000.0) 0.3880068996887712 + , CurveVector 2 365.0 (100.0, 7.0, 5.0) 0.42546115340138324 + , CurveVector 2 365.0 (100.0, 7.0, 100.0) 0.43892778160196777 + , CurveVector 2 365.0 (100.0, 7.0, 2000.0) 0.44276403113708734 + , CurveVector 2 3650.0 (0.0001, 1.0, 0.0001) 1.0183515040016187e-5 + , CurveVector 2 3650.0 (0.0001, 5.0, 0.0001) 1.0172820566235828e-5 + , CurveVector 2 3650.0 (0.0001, 10.0, 0.0001) 1.0153261435042202e-5 + , CurveVector 2 3650.0 (0.01, 1.0, 0.008) 8.539756014106344e-5 + , CurveVector 2 3650.0 (0.01, 5.0, 0.008) 0.00010686667698510345 + , CurveVector 2 3650.0 (0.01, 10.0, 0.008) 0.00013619167551386118 + , CurveVector 2 3650.0 (0.5, 1.0, 0.4) 0.0032155909289725703 + , CurveVector 2 3650.0 (0.5, 5.0, 0.4) 0.004514731337312922 + , CurveVector 2 3650.0 (0.5, 10.0, 0.4) 0.006751625012038792 + , CurveVector 2 3650.0 (1.0, 1.0, 0.8) 0.004575199446967804 + , CurveVector 2 3650.0 (1.0, 5.0, 0.8) 0.006395606971449417 + , CurveVector 2 3650.0 (1.0, 10.0, 0.8) 0.00958314720037796 + , CurveVector 2 3650.0 (3.9221, 1.0, 3.13768) 0.008636824330200443 + , CurveVector 2 3650.0 (3.9221, 5.0, 3.13768) 0.011681161854313605 + , CurveVector 2 3650.0 (3.9221, 10.0, 3.13768) 0.017035774624588426 + , CurveVector 2 3650.0 (15.0, 1.0, 12.0) 0.017964548078554115 + , CurveVector 2 3650.0 (15.0, 5.0, 12.0) 0.022987717136320654 + , CurveVector 2 3650.0 (15.0, 10.0, 12.0) 0.031446262100137345 + , CurveVector 2 3650.0 (100.0, 1.0, 80.0) 0.07003548052903615 + , CurveVector 2 3650.0 (100.0, 5.0, 80.0) 0.08447245295344952 + , CurveVector 2 3650.0 (100.0, 10.0, 80.0) 0.10638194300860046 + , CurveVector 2 3650.0 (1000.0, 1.0, 800.0) 0.3694510138100528 + , CurveVector 2 3650.0 (1000.0, 5.0, 800.0) 0.41708278117436703 + , CurveVector 2 3650.0 (1000.0, 10.0, 800.0) 0.4778101802119574 + , CurveVector 2 3650.0 (36500.0, 1.0, 29200.0) 0.9499975606993506 + , CurveVector 2 3650.0 (36500.0, 5.0, 29200.0) 0.957920723025976 + , CurveVector 2 3650.0 (36500.0, 10.0, 29200.0) 0.9647747327745895 + , CurveVector 2 3650.0 (0.5, 2.5, 0.025) 0.0008688926111881486 + , CurveVector 2 3650.0 (0.5, 2.5, 0.5) 0.004042778388781684 + , CurveVector 2 3650.0 (0.5, 2.5, 10.0) 0.00910815284390743 + , CurveVector 2 3650.0 (0.5, 7.0, 0.025) 0.0010548502442169153 + , CurveVector 2 3650.0 (0.5, 7.0, 0.5) 0.005925842632400022 + , CurveVector 2 3650.0 (0.5, 7.0, 10.0) 0.014031519871995113 + , CurveVector 2 3650.0 (3.9221, 2.5, 0.196105) 0.005528831902427268 + , CurveVector 2 3650.0 (3.9221, 2.5, 3.9221) 0.009979957822829323 + , CurveVector 2 3650.0 (3.9221, 2.5, 78.442) 0.011911651819387262 + , CurveVector 2 3650.0 (3.9221, 7.0, 0.196105) 0.0069899388145079535 + , CurveVector 2 3650.0 (3.9221, 7.0, 3.9221) 0.014099148238070692 + , CurveVector 2 3650.0 (3.9221, 7.0, 78.442) 0.017369370103370106 + , CurveVector 2 3650.0 (100.0, 2.5, 5.0) 0.07283785746109507 + , CurveVector 2 3650.0 (100.0, 2.5, 100.0) 0.07519509048679449 + , CurveVector 2 3650.0 (100.0, 2.5, 2000.0) 0.07462576077041552 + , CurveVector 2 3650.0 (100.0, 7.0, 5.0) 0.08851892641324664 + , CurveVector 2 3650.0 (100.0, 7.0, 100.0) 0.09279644141246947 + , CurveVector 2 3650.0 (100.0, 7.0, 2000.0) 0.09217565013387817 + ] + +-- | The fast trace's own recall probability, which drives its own +-- stability update. This is the piece that replaced the draft's +-- long-\/short-term transition function. +data FastRecallVector = FastRecallVector + { frParams :: !Int + , frElapsedDays :: !Double + , frStabilityFast :: !Double + , frRecall :: !Double + } + deriving stock (Eq, Show) + +goldenFastRecallVectors :: [FastRecallVector] +goldenFastRecallVectors = + [ FastRecallVector 0 0.0 0.0001 1.0 + , FastRecallVector 0 0.0 0.01 1.0 + , FastRecallVector 0 0.0 1.0 1.0 + , FastRecallVector 0 0.0 3.9221 1.0 + , FastRecallVector 0 0.0 100.0 1.0 + , FastRecallVector 0 0.0 36500.0 1.0 + , FastRecallVector 0 1.1574074074074073e-5 0.0001 0.33447315507944103 + , FastRecallVector 0 1.1574074074074073e-5 0.01 0.6742218448481596 + , FastRecallVector 0 1.1574074074074073e-5 1.0 0.9853510946325674 + , FastRecallVector 0 1.1574074074074073e-5 3.9221 0.9963073832168102 + , FastRecallVector 0 1.1574074074074073e-5 100.0 0.9998702648108787 + , FastRecallVector 0 1.1574074074074073e-5 36500.0 0.9999997143170597 + , FastRecallVector 0 0.0006944444444444445 0.0001 0.18105815685681764 + , FastRecallVector 0 0.0006944444444444445 0.01 0.36429777448663436 + , FastRecallVector 0 0.0006944444444444445 1.0 0.738422429619944 + , FastRecallVector 0 0.0006944444444444445 3.9221 0.8696620894444018 + , FastRecallVector 0 0.0006944444444444445 100.0 0.9924244414092437 + , FastRecallVector 0 0.0006944444444444445 36500.0 0.9999828600445108 + , FastRecallVector 0 0.006944444444444444 0.0001 0.12820220623313675 + , FastRecallVector 0 0.006944444444444444 0.01 0.2560146788102081 + , FastRecallVector 0 0.006944444444444444 1.0 0.5261131886683705 + , FastRecallVector 0 0.006944444444444444 3.9221 0.6507461382457376 + , FastRecallVector 0 0.006944444444444444 100.0 0.9385048591885684 + , FastRecallVector 0 0.006944444444444444 36500.0 0.9998286938158902 + , FastRecallVector 0 0.25 0.0001 0.07491514710272403 + , FastRecallVector 0 0.25 0.01 0.14781986481561618 + , FastRecallVector 0 0.25 1.0 0.3008248222009966 + , FastRecallVector 0 0.25 3.9221 0.3736370867703619 + , FastRecallVector 0 0.25 100.0 0.6266063092964018 + , FastRecallVector 0 0.25 36500.0 0.9939602758467697 + , FastRecallVector 0 1.0 0.0001 0.06085648239832377 + , FastRecallVector 0 1.0 0.01 0.11952334572467405 + , FastRecallVector 0 1.0 1.0 0.2421 + , FastRecallVector 0 1.0 3.9221 0.3003214671815383 + , FastRecallVector 0 1.0 100.0 0.5051526493264178 + , FastRecallVector 0 1.0 36500.0 0.97726184261423 + , FastRecallVector 0 3.0 0.0001 0.05161492203323463 + , FastRecallVector 0 3.0 0.01 0.1010002423200838 + , FastRecallVector 0 3.0 1.0 0.20381456007017393 + , FastRecallVector 0 3.0 3.9221 0.2525525082990618 + , FastRecallVector 0 3.0 100.0 0.42427068857558714 + , FastRecallVector 0 3.0 36500.0 0.9406751481206361 + , FastRecallVector 0 7.5 0.0001 0.044989877972066245 + , FastRecallVector 0 7.5 0.01 0.08776644361481144 + , FastRecallVector 0 7.5 1.0 0.17655482944262638 + , FastRecallVector 0 7.5 3.9221 0.21857011053674494 + , FastRecallVector 0 7.5 100.0 0.3665136968745924 + , FastRecallVector 0 7.5 36500.0 0.8832985916047102 + , FastRecallVector 0 30.0 0.0001 0.036547024380649766 + , FastRecallVector 0 30.0 0.01 0.0709656617018256 + , FastRecallVector 0 30.0 1.0 0.142081521323464 + , FastRecallVector 0 30.0 3.9221 0.17564282227680497 + , FastRecallVector 0 30.0 100.0 0.29358781797004063 + , FastRecallVector 0 30.0 36500.0 0.7552213904410912 + , FastRecallVector 0 365.0 0.0001 0.025128095000834794 + , FastRecallVector 0 365.0 0.01 0.048385972222715914 + , FastRecallVector 0 365.0 1.0 0.09604869120835895 + , FastRecallVector 0 365.0 3.9221 0.11843113704465046 + , FastRecallVector 0 365.0 100.0 0.19675299089688422 + , FastRecallVector 0 365.0 36500.0 0.5156067987676493 + , FastRecallVector 0 3650.0 0.0001 0.017792472876827583 + , FastRecallVector 0 3650.0 0.01 0.03399736779914001 + , FastRecallVector 0 3650.0 1.0 0.06695630377639386 + , FastRecallVector 0 3650.0 3.9221 0.08236347849391541 + , FastRecallVector 0 3650.0 100.0 0.1360571600290321 + , FastRecallVector 0 3650.0 36500.0 0.35373755521015193 + , FastRecallVector 1 0.0 0.0001 1.0 + , FastRecallVector 1 0.0 0.01 1.0 + , FastRecallVector 1 0.0 1.0 1.0 + , FastRecallVector 1 0.0 3.9221 1.0 + , FastRecallVector 1 0.0 100.0 1.0 + , FastRecallVector 1 0.0 36500.0 1.0 + , FastRecallVector 1 1.1574074074074073e-5 0.0001 0.8844004657781895 + , FastRecallVector 1 1.1574074074074073e-5 0.01 0.9983410883786962 + , FastRecallVector 1 1.1574074074074073e-5 1.0 0.9999863320148057 + , FastRecallVector 1 1.1574074074074073e-5 3.9221 0.9999966968900681 + , FastRecallVector 1 1.1574074074074073e-5 100.0 0.9999998848012994 + , FastRecallVector 1 1.1574074074074073e-5 36500.0 0.9999999997372572 + , FastRecallVector 1 0.0006944444444444445 0.0001 0.5655214367799205 + , FastRecallVector 1 0.0006944444444444445 0.01 0.9272347754571629 + , FastRecallVector 1 0.0006944444444444445 1.0 0.9991823199427969 + , FastRecallVector 1 0.0006944444444444445 3.9221 0.9998019493084167 + , FastRecallVector 1 0.0006944444444444445 100.0 0.9999930882309652 + , FastRecallVector 1 0.0006944444444444445 36500.0 0.9999999842354295 + , FastRecallVector 1 0.006944444444444444 0.0001 0.42685044489659973 + , FastRecallVector 1 0.006944444444444444 0.01 0.745636395742636 + , FastRecallVector 1 0.006944444444444444 1.0 0.9920349655798718 + , FastRecallVector 1 0.006944444444444444 3.9221 0.9980318254414419 + , FastRecallVector 1 0.006944444444444444 100.0 0.9999308963091021 + , FastRecallVector 1 0.006944444444444444 36500.0 0.9999998423543586 + , FastRecallVector 1 0.25 0.0001 0.275086534818235 + , FastRecallVector 1 0.25 0.01 0.4600086052404927 + , FastRecallVector 1 0.25 1.0 0.846215573159978 + , FastRecallVector 1 0.25 3.9221 0.9424039837152947 + , FastRecallVector 1 0.25 100.0 0.9975316734870963 + , FastRecallVector 1 0.25 36500.0 0.9999943248456091 + , FastRecallVector 1 1.0 0.0001 0.2320796415793974 + , FastRecallVector 1 1.0 0.01 0.379159469837454 + , FastRecallVector 1 1.0 1.0 0.712382 + , FastRecallVector 1 1.0 3.9221 0.8471632913574345 + , FastRecallVector 1 1.0 100.0 0.9903571366342847 + , FastRecallVector 1 1.0 36500.0 0.9999773004771466 + , FastRecallVector 1 3.0 0.0001 0.2028269824123318 + , FastRecallVector 1 3.0 0.01 0.3252352602214052 + , FastRecallVector 1 3.0 1.0 0.6059898723769258 + , FastRecallVector 1 3.0 3.9221 0.7399173433814594 + , FastRecallVector 1 3.0 100.0 0.9727367044865721 + , FastRecallVector 1 3.0 36500.0 0.9999319101872398 + , FastRecallVector 1 7.5 0.0001 0.18126944452711868 + , FastRecallVector 1 7.5 0.01 0.28616015046150234 + , FastRecallVector 1 7.5 1.0 0.5259275192148761 + , FastRecallVector 1 7.5 3.9221 0.6466706129261264 + , FastRecallVector 1 7.5 100.0 0.9393942428488806 + , FastRecallVector 1 7.5 36500.0 0.9998298246944654 + , FastRecallVector 1 30.0 0.0001 0.15292950358545299 + , FastRecallVector 1 30.0 0.01 0.23577358736201828 + , FastRecallVector 1 30.0 1.0 0.4226763069795214 + , FastRecallVector 1 30.0 3.9221 0.5188438930624684 + , FastRecallVector 1 30.0 100.0 0.838196690202147 + , FastRecallVector 1 30.0 36500.0 0.999320281232652 + , FastRecallVector 1 365.0 0.0001 0.11256717032197745 + , FastRecallVector 1 365.0 0.01 0.16629403422367212 + , FastRecallVector 1 365.0 1.0 0.28415033817320634 + , FastRecallVector 1 365.0 3.9221 0.34414115593651684 + , FastRecallVector 1 365.0 100.0 0.5755470142498635 + , FastRecallVector 1 365.0 36500.0 0.9919032354685755 + , FastRecallVector 1 3650.0 0.0001 0.08487449279718141 + , FastRecallVector 1 3650.0 0.01 0.12054708690261254 + , FastRecallVector 1 3650.0 1.0 0.19696322659569285 + , FastRecallVector 1 3650.0 3.9221 0.23516400470435175 + , FastRecallVector 1 3650.0 100.0 0.382086610632168 + , FastRecallVector 1 3650.0 36500.0 0.9323428123521598 + , FastRecallVector 2 0.0 0.0001 1.0 + , FastRecallVector 2 0.0 0.01 1.0 + , FastRecallVector 2 0.0 1.0 1.0 + , FastRecallVector 2 0.0 3.9221 1.0 + , FastRecallVector 2 0.0 100.0 1.0 + , FastRecallVector 2 0.0 36500.0 1.0 + , FastRecallVector 2 1.1574074074074073e-5 0.0001 0.8242423333800115 + , FastRecallVector 2 1.1574074074074073e-5 0.01 0.9965472580837926 + , FastRecallVector 2 1.1574074074074073e-5 1.0 0.9998062799932467 + , FastRecallVector 2 1.1574074074074073e-5 3.9221 0.9998726518720278 + , FastRecallVector 2 1.1574074074074073e-5 100.0 0.9997964400662621 + , FastRecallVector 2 1.1574074074074073e-5 36500.0 0.797837681586641 + , FastRecallVector 2 0.0006944444444444445 0.0001 0.07863351328998766 + , FastRecallVector 2 0.0006944444444444445 0.01 0.838071986580995 + , FastRecallVector 2 0.0006944444444444445 1.0 0.9887064516724984 + , FastRecallVector 2 0.0006944444444444445 3.9221 0.9925345458323506 + , FastRecallVector 2 0.0006944444444444445 100.0 0.9884969433994782 + , FastRecallVector 2 0.0006944444444444445 36500.0 0.686693304140361 + , FastRecallVector 2 0.006944444444444444 0.0001 0.009375039560579244 + , FastRecallVector 2 0.006944444444444444 0.01 0.42199783981577405 + , FastRecallVector 2 0.006944444444444444 1.0 0.9094312148050276 + , FastRecallVector 2 0.006944444444444444 3.9221 0.9378223077885313 + , FastRecallVector 2 0.006944444444444444 100.0 0.9219699132303174 + , FastRecallVector 2 0.006944444444444444 36500.0 0.6311092800785385 + , FastRecallVector 2 0.25 0.0001 0.0003136442688646113 + , FastRecallVector 2 0.25 0.01 0.066147703763706 + , FastRecallVector 2 0.25 1.0 0.4952416030137906 + , FastRecallVector 2 0.25 3.9221 0.5952061073025883 + , FastRecallVector 2 0.25 100.0 0.6725319313419971 + , FastRecallVector 2 0.25 36500.0 0.5534170235601299 + , FastRecallVector 2 1.0 0.0001 8.405118585714037e-5 + , FastRecallVector 2 1.0 0.01 0.030856507802529604 + , FastRecallVector 2 1.0 1.0 0.35787700000000006 + , FastRecallVector 2 1.0 3.9221 0.46227678913869563 + , FastRecallVector 2 1.0 100.0 0.5819469322679293 + , FastRecallVector 2 1.0 36500.0 0.5259951598653689 + , FastRecallVector 2 3.0 0.0001 2.9600071583764095e-5 + , FastRecallVector 2 3.0 0.01 0.016832588369560884 + , FastRecallVector 2 3.0 1.0 0.275076143605072 + , FastRecallVector 2 3.0 3.9221 0.3763824445221876 + , FastRecallVector 2 3.0 100.0 0.5183576730835542 + , FastRecallVector 2 3.0 36500.0 0.5052322662412635 + , FastRecallVector 2 7.5 0.0001 1.2395212758468752e-5 + , FastRecallVector 2 7.5 0.01 0.01015025571223255 + , FastRecallVector 2 7.5 1.0 0.22060007032572151 + , FastRecallVector 2 7.5 3.9221 0.316721587123548 + , FastRecallVector 2 7.5 100.0 0.47056325904847857 + , FastRecallVector 2 7.5 36500.0 0.48854333733999644 + , FastRecallVector 2 30.0 0.0001 3.321231208342476e-6 + , FastRecallVector 2 30.0 0.01 0.004720996863201854 + , FastRecallVector 2 30.0 1.0 0.15786612140479306 + , FastRecallVector 2 30.0 3.9221 0.24377880360808532 + , FastRecallVector 2 30.0 100.0 0.40644454947367104 + , FastRecallVector 2 30.0 36500.0 0.464335969471123 + , FastRecallVector 2 365.0 0.0001 3.093048488862336e-7 + , FastRecallVector 2 365.0 0.01 0.001187849814795759 + , FastRecallVector 2 365.0 1.0 0.0863255467691219 + , FastRecallVector 2 365.0 3.9221 0.1520133706986155 + , FastRecallVector 2 365.0 100.0 0.312101131535636 + , FastRecallVector 2 365.0 36500.0 0.42369300203013316 + , FastRecallVector 2 3650.0 0.0001 3.4704579015469925e-8 + , FastRecallVector 2 3650.0 0.01 0.0003330526740963906 + , FastRecallVector 2 3650.0 1.0 0.049490981971068854 + , FastRecallVector 2 3650.0 3.9221 0.09836262621163125 + , FastRecallVector 2 3650.0 100.0 0.24467251813551136 + , FastRecallVector 2 3650.0 36500.0 0.3893969446308483 + ] + +-- | Initial and subsequent difficulty. The retrievability only +-- matters on a lapse, where it weights the step. +data DifficultyVector = DifficultyVector + { dvParams :: !Int + , dvDifficulty :: !(Maybe Double) + -- ^ 'Nothing' for the initial difficulty of a brand-new card. + , dvRetrievability :: !Double + , dvRating :: !Int + , dvNextDifficulty :: !Double + } + deriving stock (Eq, Show) + +goldenDifficultyVectors :: [DifficultyVector] +goldenDifficultyVectors = + [ DifficultyVector 0 Nothing 1.0 1 6.1686 + , DifficultyVector 0 Nothing 1.0 2 5.261278312731786 + , DifficultyVector 0 Nothing 1.0 3 3.5307239812763354 + , DifficultyVector 0 Nothing 1.0 4 1.0 + , DifficultyVector 0 (Just 1.0) 0.05 1 2.0854679017389546 + , DifficultyVector 0 (Just 1.0) 0.05 2 4.636193001738953 + , DifficultyVector 0 (Just 1.0) 0.05 3 1.0 + , DifficultyVector 0 (Just 1.0) 0.05 4 1.0 + , DifficultyVector 0 (Just 1.0) 0.5 1 5.3649716017389535 + , DifficultyVector 0 (Just 1.0) 0.5 2 4.636193001738953 + , DifficultyVector 0 (Just 1.0) 0.5 3 1.0 + , DifficultyVector 0 (Just 1.0) 0.5 4 1.0 + , DifficultyVector 0 (Just 1.0) 0.95 1 8.644475301738954 + , DifficultyVector 0 (Just 1.0) 0.95 2 4.636193001738953 + , DifficultyVector 0 (Just 1.0) 0.95 3 1.0 + , DifficultyVector 0 (Just 1.0) 0.95 4 1.0 + , DifficultyVector 0 (Just 2.5) 0.05 1 3.3882732517389544 + , DifficultyVector 0 (Just 2.5) 0.05 2 5.513877501738953 + , DifficultyVector 0 (Just 2.5) 0.05 3 2.4773000017389544 + , DifficultyVector 0 (Just 2.5) 0.05 4 1.0 + , DifficultyVector 0 (Just 2.5) 0.5 1 6.121193001738954 + , DifficultyVector 0 (Just 2.5) 0.5 2 5.513877501738953 + , DifficultyVector 0 (Just 2.5) 0.5 3 2.4773000017389544 + , DifficultyVector 0 (Just 2.5) 0.5 4 1.0 + , DifficultyVector 0 (Just 2.5) 0.95 1 8.854112751738953 + , DifficultyVector 0 (Just 2.5) 0.95 2 5.513877501738953 + , DifficultyVector 0 (Just 2.5) 0.95 3 2.4773000017389544 + , DifficultyVector 0 (Just 2.5) 0.95 4 1.0 + , DifficultyVector 0 (Just 3.5307239812763354) 0.05 1 4.28349506319236 + , DifficultyVector 0 (Just 3.5307239812763354) 0.05 2 6.116977809835307 + , DifficultyVector 0 (Just 3.5307239812763354) 0.05 3 3.4977167432025262 + , DifficultyVector 0 (Just 3.5307239812763354) 0.05 4 1.0 + , DifficultyVector 0 (Just 3.5307239812763354) 0.5 1 6.640830023161864 + , DifficultyVector 0 (Just 3.5307239812763354) 0.5 2 6.116977809835307 + , DifficultyVector 0 (Just 3.5307239812763354) 0.5 3 3.4977167432025262 + , DifficultyVector 0 (Just 3.5307239812763354) 0.5 4 1.0 + , DifficultyVector 0 (Just 3.5307239812763354) 0.95 1 8.998164983131367 + , DifficultyVector 0 (Just 3.5307239812763354) 0.95 2 6.116977809835307 + , DifficultyVector 0 (Just 3.5307239812763354) 0.95 3 3.4977167432025262 + , DifficultyVector 0 (Just 3.5307239812763354) 0.95 4 1.0 + , DifficultyVector 0 (Just 7.0) 0.05 1 7.2966893017389545 + , DifficultyVector 0 (Just 7.0) 0.05 2 8.146931001738954 + , DifficultyVector 0 (Just 7.0) 0.05 3 6.9323000017389536 + , DifficultyVector 0 (Just 7.0) 0.05 4 5.717669001738954 + , DifficultyVector 0 (Just 7.0) 0.5 1 8.389857201738954 + , DifficultyVector 0 (Just 7.0) 0.5 2 8.146931001738954 + , DifficultyVector 0 (Just 7.0) 0.5 3 6.9323000017389536 + , DifficultyVector 0 (Just 7.0) 0.5 4 5.717669001738954 + , DifficultyVector 0 (Just 7.0) 0.95 1 9.483025101738953 + , DifficultyVector 0 (Just 7.0) 0.95 2 8.146931001738954 + , DifficultyVector 0 (Just 7.0) 0.95 3 6.9323000017389536 + , DifficultyVector 0 (Just 7.0) 0.95 4 5.717669001738954 + , DifficultyVector 0 (Just 10.0) 0.05 1 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.05 2 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.05 3 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.05 4 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.5 1 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.5 2 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.5 3 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.5 4 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.95 1 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.95 2 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.95 3 9.902300001738954 + , DifficultyVector 0 (Just 10.0) 0.95 4 9.902300001738954 + , DifficultyVector 1 Nothing 1.0 1 8.15903 + , DifficultyVector 1 Nothing 1.0 2 1.7511448034338732 + , DifficultyVector 1 Nothing 1.0 3 1.0 + , DifficultyVector 1 Nothing 1.0 4 1.0 + , DifficultyVector 1 (Just 1.0) 0.05 1 1.0 + , DifficultyVector 1 (Just 1.0) 0.05 2 1.0 + , DifficultyVector 1 (Just 1.0) 0.05 3 1.0 + , DifficultyVector 1 (Just 1.0) 0.05 4 1.0 + , DifficultyVector 1 (Just 1.0) 0.5 1 1.0 + , DifficultyVector 1 (Just 1.0) 0.5 2 1.0 + , DifficultyVector 1 (Just 1.0) 0.5 3 1.0 + , DifficultyVector 1 (Just 1.0) 0.5 4 1.0 + , DifficultyVector 1 (Just 1.0) 0.95 1 1.7156461830343153 + , DifficultyVector 1 (Just 1.0) 0.95 2 1.0 + , DifficultyVector 1 (Just 1.0) 0.95 3 1.0 + , DifficultyVector 1 (Just 1.0) 0.95 4 1.0 + , DifficultyVector 1 (Just 2.5) 0.05 1 1.0 + , DifficultyVector 1 (Just 2.5) 0.05 2 1.0 + , DifficultyVector 1 (Just 2.5) 0.05 3 1.0 + , DifficultyVector 1 (Just 2.5) 0.05 4 1.0 + , DifficultyVector 1 (Just 2.5) 0.5 1 1.0 + , DifficultyVector 1 (Just 2.5) 0.5 2 1.0 + , DifficultyVector 1 (Just 2.5) 0.5 3 1.0 + , DifficultyVector 1 (Just 2.5) 0.5 4 1.0 + , DifficultyVector 1 (Just 2.5) 0.95 1 2.417435601034316 + , DifficultyVector 1 (Just 2.5) 0.95 2 1.0 + , DifficultyVector 1 (Just 2.5) 0.95 3 1.0 + , DifficultyVector 1 (Just 2.5) 0.95 4 1.0 + , DifficultyVector 1 (Just 3.5307239812763354) 0.05 1 1.0 + , DifficultyVector 1 (Just 3.5307239812763354) 0.05 2 1.1303090946385872 + , DifficultyVector 1 (Just 3.5307239812763354) 0.05 3 1.0 + , DifficultyVector 1 (Just 3.5307239812763354) 0.05 4 1.0 + , DifficultyVector 1 (Just 3.5307239812763354) 0.5 1 1.4520110270667272 + , DifficultyVector 1 (Just 3.5307239812763354) 0.5 2 1.1303090946385872 + , DifficultyVector 1 (Just 3.5307239812763354) 0.5 3 1.0 + , DifficultyVector 1 (Just 3.5307239812763354) 0.5 4 1.0 + , DifficultyVector 1 (Just 3.5307239812763354) 0.95 1 2.899669722993357 + , DifficultyVector 1 (Just 3.5307239812763354) 0.95 2 1.1303090946385872 + , DifficultyVector 1 (Just 3.5307239812763354) 0.95 3 1.0 + , DifficultyVector 1 (Just 3.5307239812763354) 0.95 4 1.0 + , DifficultyVector 1 (Just 7.0) 0.05 1 3.1801571430343145 + , DifficultyVector 1 (Just 7.0) 0.05 2 3.702297531034315 + , DifficultyVector 1 (Just 7.0) 0.05 3 2.9563826910343147 + , DifficultyVector 1 (Just 7.0) 0.05 4 2.2104678510343154 + , DifficultyVector 1 (Just 7.0) 0.5 1 3.8514804990343148 + , DifficultyVector 1 (Just 7.0) 0.5 2 3.702297531034315 + , DifficultyVector 1 (Just 7.0) 0.5 3 2.9563826910343147 + , DifficultyVector 1 (Just 7.0) 0.5 4 2.2104678510343154 + , DifficultyVector 1 (Just 7.0) 0.95 1 4.522803855034314 + , DifficultyVector 1 (Just 7.0) 0.95 2 3.702297531034315 + , DifficultyVector 1 (Just 7.0) 0.95 3 2.9563826910343147 + , DifficultyVector 1 (Just 7.0) 0.95 4 2.2104678510343154 + , DifficultyVector 1 (Just 10.0) 0.05 1 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.05 2 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.05 3 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.05 4 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.5 1 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.5 2 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.5 3 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.5 4 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.95 1 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.95 2 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.95 3 5.926382691034315 + , DifficultyVector 1 (Just 10.0) 0.95 4 5.926382691034315 + , DifficultyVector 2 Nothing 1.0 1 7.614116 + , DifficultyVector 2 Nothing 1.0 2 5.356124178155698 + , DifficultyVector 2 Nothing 1.0 3 1.0 + , DifficultyVector 2 Nothing 1.0 4 1.0 + , DifficultyVector 2 (Just 1.0) 0.05 1 1.0 + , DifficultyVector 2 (Just 1.0) 0.05 2 1.1172835591001746 + , DifficultyVector 2 (Just 1.0) 0.05 3 1.0 + , DifficultyVector 2 (Just 1.0) 0.05 4 1.0 + , DifficultyVector 2 (Just 1.0) 0.5 1 1.1946760171001747 + , DifficultyVector 2 (Just 1.0) 0.5 2 1.1172835591001746 + , DifficultyVector 2 (Just 1.0) 0.5 3 1.0 + , DifficultyVector 2 (Just 1.0) 0.5 4 1.0 + , DifficultyVector 2 (Just 1.0) 0.95 1 1.5429420781001746 + , DifficultyVector 2 (Just 1.0) 0.95 2 1.1172835591001746 + , DifficultyVector 2 (Just 1.0) 0.95 3 1.0 + , DifficultyVector 2 (Just 1.0) 0.95 4 1.0 + , DifficultyVector 2 (Just 2.5) 0.05 1 2.312061841600175 + , DifficultyVector 2 (Just 2.5) 0.05 2 2.5377898441001747 + , DifficultyVector 2 (Just 2.5) 0.05 3 2.215321269100175 + , DifficultyVector 2 (Just 2.5) 0.05 4 1.8928526941001744 + , DifficultyVector 2 (Just 2.5) 0.5 1 2.6022835591001745 + , DifficultyVector 2 (Just 2.5) 0.5 2 2.5377898441001747 + , DifficultyVector 2 (Just 2.5) 0.5 3 2.215321269100175 + , DifficultyVector 2 (Just 2.5) 0.5 4 1.8928526941001744 + , DifficultyVector 2 (Just 2.5) 0.95 1 2.892505276600175 + , DifficultyVector 2 (Just 2.5) 0.95 2 2.5377898441001747 + , DifficultyVector 2 (Just 2.5) 0.95 3 2.215321269100175 + , DifficultyVector 2 (Just 2.5) 0.95 4 1.8928526941001744 + , DifficultyVector 2 (Just 3.5307239812763354) 0.05 1 3.319183539325327 + , DifficultyVector 2 (Just 3.5307239812763354) 0.05 2 3.513889773102346 + , DifficultyVector 2 (Just 3.5307239812763354) 0.05 3 3.2357380105637468 + , DifficultyVector 2 (Just 3.5307239812763354) 0.05 4 2.9575862480251476 + , DifficultyVector 2 (Just 3.5307239812763354) 0.5 1 3.5695201256100657 + , DifficultyVector 2 (Just 3.5307239812763354) 0.5 2 3.513889773102346 + , DifficultyVector 2 (Just 3.5307239812763354) 0.5 3 3.2357380105637468 + , DifficultyVector 2 (Just 3.5307239812763354) 0.5 4 2.9575862480251476 + , DifficultyVector 2 (Just 3.5307239812763354) 0.95 1 3.819856711894805 + , DifficultyVector 2 (Just 3.5307239812763354) 0.95 2 3.513889773102346 + , DifficultyVector 2 (Just 3.5307239812763354) 0.95 3 3.2357380105637468 + , DifficultyVector 2 (Just 3.5307239812763354) 0.95 4 2.9575862480251476 + , DifficultyVector 2 (Just 7.0) 0.05 1 6.709017498100175 + , DifficultyVector 2 (Just 7.0) 0.05 2 6.799308699100174 + , DifficultyVector 2 (Just 7.0) 0.05 3 6.6703212691001745 + , DifficultyVector 2 (Just 7.0) 0.05 4 6.541333839100175 + , DifficultyVector 2 (Just 7.0) 0.5 1 6.825106185100174 + , DifficultyVector 2 (Just 7.0) 0.5 2 6.799308699100174 + , DifficultyVector 2 (Just 7.0) 0.5 3 6.6703212691001745 + , DifficultyVector 2 (Just 7.0) 0.5 4 6.541333839100175 + , DifficultyVector 2 (Just 7.0) 0.95 1 6.941194872100175 + , DifficultyVector 2 (Just 7.0) 0.95 2 6.799308699100174 + , DifficultyVector 2 (Just 7.0) 0.95 3 6.6703212691001745 + , DifficultyVector 2 (Just 7.0) 0.95 4 6.541333839100175 + , DifficultyVector 2 (Just 10.0) 0.05 1 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.05 2 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.05 3 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.05 4 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.5 1 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.5 2 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.5 3 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.5 4 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.95 1 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.95 2 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.95 3 9.640321269100175 + , DifficultyVector 2 (Just 10.0) 0.95 4 9.640321269100175 + ] + +-- | One trace's stability update, before the lapse cap is applied. +data HalfStabilityVector = HalfStabilityVector + { hsParams :: !Int + , hsSlowTrace :: !Bool + -- ^ 'True' for the slow trace's block, 'False' for the fast one's. + , hsStability :: !Double + , hsDifficulty :: !Double + , hsRetrievability :: !Double + , hsRating :: !Int + , hsNextStability :: !Double + } + deriving stock (Eq, Show) + +goldenHalfStabilityVectors :: [HalfStabilityVector] +goldenHalfStabilityVectors = + [ HalfStabilityVector 0 True 0.01 1.0 0.05 1 0.009117697887342275 + , HalfStabilityVector 0 False 0.01 1.0 0.05 1 0.0024104195051093086 + , HalfStabilityVector 0 True 0.01 1.0 0.05 2 0.29100022497763484 + , HalfStabilityVector 0 False 0.01 1.0 0.05 2 43.40579452226374 + , HalfStabilityVector 0 True 0.01 1.0 0.05 3 0.4492001015592917 + , HalfStabilityVector 0 False 0.01 1.0 0.05 3 70.43485316823067 + , HalfStabilityVector 0 True 0.01 1.0 0.05 4 0.4492001015592917 + , HalfStabilityVector 0 False 0.01 1.0 0.05 4 76.55477290854992 + , HalfStabilityVector 0 True 0.01 1.0 0.5 1 0.006319545857512049 + , HalfStabilityVector 0 False 0.01 1.0 0.5 1 0.001042274975825335 + , HalfStabilityVector 0 True 0.01 1.0 0.5 2 0.1129633145130704 + , HalfStabilityVector 0 False 0.01 1.0 0.5 2 6.694342509256355 + , HalfStabilityVector 0 True 0.01 1.0 0.5 3 0.17093046969845324 + , HalfStabilityVector 0 False 0.01 1.0 0.5 3 10.857683397040498 + , HalfStabilityVector 0 True 0.01 1.0 0.5 4 0.17093046969845324 + , HalfStabilityVector 0 False 0.01 1.0 0.5 4 11.800347084243317 + , HalfStabilityVector 0 True 0.01 1.0 0.95 1 0.00438012537140983 + , HalfStabilityVector 0 False 0.01 1.0 0.95 1 0.00045068384276223284 + , HalfStabilityVector 0 True 0.01 1.0 0.95 2 0.01739695301562896 + , HalfStabilityVector 0 False 0.01 1.0 0.95 2 0.2511203496292514 + , HalfStabilityVector 0 True 0.01 1.0 0.95 3 0.021561352009423197 + , HalfStabilityVector 0 False 0.01 1.0 0.95 3 0.4013020928744749 + , HalfStabilityVector 0 True 0.01 1.0 0.95 4 0.021561352009423197 + , HalfStabilityVector 0 False 0.01 1.0 0.95 4 0.4353062447452667 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.05 1 0.009117697887342275 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.05 1 0.0024104195051093086 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.05 2 0.21988682416814023 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.05 2 32.42351673386043 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.05 3 0.33805067859978155 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.05 3 52.61226668916007 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.05 4 0.33805067859978155 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.05 4 57.18340366444808 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.5 1 0.006319545857512049 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.5 1 0.001042274975825335 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.5 2 0.08690614159007791 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.5 2 5.002719920532366 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.5 3 0.13020340980005923 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.5 3 8.112434145622146 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.5 4 0.13020340980005923 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.5 4 8.816535672876709 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.95 1 0.00438012537140983 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.95 1 0.00045068384276223284 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.95 2 0.015524988377126308 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.95 2 0.19009944451120325 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.95 3 0.01863549293080073 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.95 3 0.3022743338383695 + , HalfStabilityVector 0 True 0.01 3.5307239812763354 0.95 4 0.01863549293080073 + , HalfStabilityVector 0 False 0.01 3.5307239812763354 0.95 4 0.3276729734489238 + , HalfStabilityVector 0 True 0.01 10.0 0.05 1 0.009117697887342275 + , HalfStabilityVector 0 False 0.01 10.0 0.05 1 0.0024104195051093086 + , HalfStabilityVector 0 True 0.01 10.0 0.05 2 0.03810002249776349 + , HalfStabilityVector 0 False 0.01 10.0 0.05 2 4.349579452226375 + , HalfStabilityVector 0 True 0.01 10.0 0.05 3 0.05392001015592917 + , HalfStabilityVector 0 False 0.01 10.0 0.05 3 7.052485316823069 + , HalfStabilityVector 0 True 0.01 10.0 0.05 4 0.05392001015592917 + , HalfStabilityVector 0 False 0.01 10.0 0.05 4 7.664477290854993 + , HalfStabilityVector 0 True 0.01 10.0 0.5 1 0.006319545857512049 + , HalfStabilityVector 0 False 0.01 10.0 0.5 1 0.001042274975825335 + , HalfStabilityVector 0 True 0.01 10.0 0.5 2 0.02029633145130704 + , HalfStabilityVector 0 False 0.01 10.0 0.5 2 0.6784342509256355 + , HalfStabilityVector 0 True 0.01 10.0 0.5 3 0.026093046969845324 + , HalfStabilityVector 0 False 0.01 10.0 0.5 3 1.0947683397040497 + , HalfStabilityVector 0 True 0.01 10.0 0.5 4 0.026093046969845324 + , HalfStabilityVector 0 False 0.01 10.0 0.5 4 1.1890347084243318 + , HalfStabilityVector 0 True 0.01 10.0 0.95 1 0.00438012537140983 + , HalfStabilityVector 0 False 0.01 10.0 0.95 1 0.00045068384276223284 + , HalfStabilityVector 0 True 0.01 10.0 0.95 2 0.010739695301562895 + , HalfStabilityVector 0 False 0.01 10.0 0.95 2 0.03411203496292514 + , HalfStabilityVector 0 True 0.01 10.0 0.95 3 0.01115613520094232 + , HalfStabilityVector 0 False 0.01 10.0 0.95 3 0.049130209287447484 + , HalfStabilityVector 0 True 0.01 10.0 0.95 4 0.01115613520094232 + , HalfStabilityVector 0 False 0.01 10.0 0.95 4 0.052530624474526666 + , HalfStabilityVector 0 True 1.0 1.0 0.05 1 0.7852258277795375 + , HalfStabilityVector 0 False 1.0 1.0 0.05 1 0.17338546611409061 + , HalfStabilityVector 0 True 1.0 1.0 0.05 2 29.100022497763483 + , HalfStabilityVector 0 False 1.0 1.0 0.05 2 198.7186534937513 + , HalfStabilityVector 0 True 1.0 1.0 0.05 3 44.92001015592917 + , HalfStabilityVector 0 False 1.0 1.0 0.05 3 321.86766227483173 + , HalfStabilityVector 0 True 1.0 1.0 0.05 4 44.92001015592917 + , HalfStabilityVector 0 False 1.0 1.0 0.05 4 349.7510621265146 + , HalfStabilityVector 0 True 1.0 1.0 0.5 1 0.5442460024963717 + , HalfStabilityVector 0 False 1.0 1.0 0.5 1 0.07497256478362802 + , HalfStabilityVector 0 True 1.0 1.0 0.5 2 11.29633145130704 + , HalfStabilityVector 0 False 1.0 1.0 0.5 2 31.45500641181179 + , HalfStabilityVector 0 True 1.0 1.0 0.5 3 17.093046969845325 + , HalfStabilityVector 0 False 1.0 1.0 0.5 3 50.42389875334598 + , HalfStabilityVector 0 True 1.0 1.0 0.5 4 17.093046969845325 + , HalfStabilityVector 0 False 1.0 1.0 0.5 4 54.718835555011744 + , HalfStabilityVector 0 True 1.0 1.0 0.95 1 0.37722104998874756 + , HalfStabilityVector 0 False 1.0 1.0 0.95 1 0.032418435040781686 + , HalfStabilityVector 0 True 1.0 1.0 0.95 2 1.739695301562896 + , HalfStabilityVector 0 False 1.0 1.0 0.95 2 2.0985855054267875 + , HalfStabilityVector 0 True 1.0 1.0 0.95 3 2.1561352009423196 + , HalfStabilityVector 0 False 1.0 1.0 0.95 3 2.7828391843992004 + , HalfStabilityVector 0 True 1.0 1.0 0.95 4 2.1561352009423196 + , HalfStabilityVector 0 False 1.0 1.0 0.95 4 2.937767909523491 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.05 1 0.7852258277795375 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.05 1 0.17338546611409061 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.05 2 21.988682416814022 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.05 2 148.68151969952106 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.05 3 33.80506785997815 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.05 3 240.66491350133248 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.05 4 33.80506785997815 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.05 4 261.49179448459824 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.5 1 0.5442460024963717 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.5 1 0.07497256478362802 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.5 2 8.69061415900779 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.5 2 23.74768490418213 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.5 3 13.020340980005923 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.5 3 37.91607417101936 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.5 4 13.020340980005923 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.5 4 41.12408101648094 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.95 1 0.37722104998874756 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.95 1 0.032418435040781686 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.95 2 1.5524988377126308 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.95 2 1.8205638370201718 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.95 3 1.863549293080073 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.95 3 2.331651796527381 + , HalfStabilityVector 0 True 1.0 3.5307239812763354 0.95 4 1.863549293080073 + , HalfStabilityVector 0 False 1.0 3.5307239812763354 0.95 4 2.44737233764561 + , HalfStabilityVector 0 True 1.0 10.0 0.05 1 0.7852258277795375 + , HalfStabilityVector 0 False 1.0 10.0 0.05 1 0.17338546611409061 + , HalfStabilityVector 0 True 1.0 10.0 0.05 2 3.8100022497763484 + , HalfStabilityVector 0 False 1.0 10.0 0.05 2 20.77186534937513 + , HalfStabilityVector 0 True 1.0 10.0 0.05 3 5.392001015592917 + , HalfStabilityVector 0 False 1.0 10.0 0.05 3 33.086766227483174 + , HalfStabilityVector 0 True 1.0 10.0 0.05 4 5.392001015592917 + , HalfStabilityVector 0 False 1.0 10.0 0.05 4 35.87510621265146 + , HalfStabilityVector 0 True 1.0 10.0 0.5 1 0.5442460024963717 + , HalfStabilityVector 0 False 1.0 10.0 0.5 1 0.07497256478362802 + , HalfStabilityVector 0 True 1.0 10.0 0.5 2 2.029633145130704 + , HalfStabilityVector 0 False 1.0 10.0 0.5 2 4.04550064118118 + , HalfStabilityVector 0 True 1.0 10.0 0.5 3 2.609304696984532 + , HalfStabilityVector 0 False 1.0 10.0 0.5 3 5.942389875334598 + , HalfStabilityVector 0 True 1.0 10.0 0.5 4 2.609304696984532 + , HalfStabilityVector 0 False 1.0 10.0 0.5 4 6.371883555501174 + , HalfStabilityVector 0 True 1.0 10.0 0.95 1 0.37722104998874756 + , HalfStabilityVector 0 False 1.0 10.0 0.95 1 0.032418435040781686 + , HalfStabilityVector 0 True 1.0 10.0 0.95 2 1.0739695301562895 + , HalfStabilityVector 0 False 1.0 10.0 0.95 2 1.1098585505426788 + , HalfStabilityVector 0 True 1.0 10.0 0.95 3 1.1156135200942319 + , HalfStabilityVector 0 False 1.0 10.0 0.95 3 1.17828391843992 + , HalfStabilityVector 0 True 1.0 10.0 0.95 4 1.1156135200942319 + , HalfStabilityVector 0 False 1.0 10.0 0.95 4 1.1937767909523491 + , HalfStabilityVector 0 True 3.9221 1.0 0.05 1 2.4389022348225784 + , HalfStabilityVector 0 False 3.9221 1.0 0.05 1 0.41609622979421645 + , HalfStabilityVector 0 True 3.9221 1.0 0.05 2 114.13319823847816 + , HalfStabilityVector 0 False 3.9221 1.0 0.05 2 314.01608325549387 + , HalfStabilityVector 0 True 3.9221 1.0 0.05 3 176.1807718325698 + , HalfStabilityVector 0 False 3.9221 1.0 0.05 3 507.15803517606923 + , HalfStabilityVector 0 True 3.9221 1.0 0.05 4 176.1807718325698 + , HalfStabilityVector 0 False 3.9221 1.0 0.05 4 550.8892379428696 + , HalfStabilityVector 0 True 3.9221 1.0 0.5 1 1.6904217166864894 + , HalfStabilityVector 0 False 3.9221 1.0 0.5 1 0.1799216638143297 + , HalfStabilityVector 0 True 3.9221 1.0 0.5 2 44.30534158517134 + , HalfStabilityVector 0 False 3.9221 1.0 0.5 2 51.68650705736846 + , HalfStabilityVector 0 True 3.9221 1.0 0.5 3 67.04063952043035 + , HalfStabilityVector 0 False 3.9221 1.0 0.5 3 81.43655481559308 + , HalfStabilityVector 0 True 3.9221 1.0 0.5 4 67.04063952043035 + , HalfStabilityVector 0 False 3.9221 1.0 0.5 4 88.17256093906812 + , HalfStabilityVector 0 True 3.9221 1.0 0.95 1 1.1716441682022456 + , HalfStabilityVector 0 False 3.9221 1.0 0.95 1 0.07779884265167795 + , HalfStabilityVector 0 True 3.9221 1.0 0.95 2 6.823258942259834 + , HalfStabilityVector 0 False 3.9221 1.0 0.95 2 5.645077318047074 + , HalfStabilityVector 0 True 3.9221 1.0 0.95 3 8.456577871615872 + , HalfStabilityVector 0 False 3.9221 1.0 0.95 3 6.718233265250039 + , HalfStabilityVector 0 True 3.9221 1.0 0.95 4 8.456577871615872 + , HalfStabilityVector 0 False 3.9221 1.0 0.95 4 6.961217246000268 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.05 1 2.4389022348225784 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.05 1 0.41609622979421645 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.05 2 86.24181130698628 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.05 2 235.53985526807577 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.05 3 132.58685665362032 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.05 3 379.80291023705905 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.05 4 132.58685665362032 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.05 4 412.4669526466595 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.5 1 1.6904217166864894 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.5 1 0.1799216638143297 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.5 2 34.085457793044455 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.5 2 39.59865401821576 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.5 3 51.06707935768123 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.5 3 61.81978584585485 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.5 4 51.06707935768123 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.5 4 66.85109474585964 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.95 1 1.1716441682022456 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.95 1 0.07779884265167795 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.95 2 6.0890556913927085 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.95 2 5.209039316249383 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.95 3 7.309026682389354 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.95 3 6.010609114328761 + , HalfStabilityVector 0 True 3.9221 3.5307239812763354 0.95 4 7.309026682389354 + , HalfStabilityVector 0 False 3.9221 3.5307239812763354 0.95 4 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1.0 0.5 1 1.1992764415774615 + , HalfStabilityVector 2 True 3.9221 1.0 0.5 2 33.20918871173612 + , HalfStabilityVector 2 False 3.9221 1.0 0.5 2 96.93214762285132 + , HalfStabilityVector 2 True 3.9221 1.0 0.5 3 102.57666928818188 + , HalfStabilityVector 2 False 3.9221 1.0 0.5 3 134.51072095461387 + , HalfStabilityVector 2 True 3.9221 1.0 0.5 4 454.80662958227197 + , HalfStabilityVector 2 False 3.9221 1.0 0.5 4 674.2325772396862 + , HalfStabilityVector 2 True 3.9221 1.0 0.95 1 2.6264423142794957 + , HalfStabilityVector 2 False 3.9221 1.0 0.95 1 0.8307942231065403 + , HalfStabilityVector 2 True 3.9221 1.0 0.95 2 5.601415931491084 + , HalfStabilityVector 2 False 3.9221 1.0 0.95 2 8.70931836828358 + , HalfStabilityVector 2 True 3.9221 1.0 0.95 3 9.57893368363089 + , HalfStabilityVector 2 False 3.9221 1.0 0.95 3 10.643483989154706 + , HalfStabilityVector 2 True 3.9221 1.0 0.95 4 29.77573063031087 + , HalfStabilityVector 2 False 3.9221 1.0 0.95 4 38.422916966643186 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.05 1 3.9221 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.05 1 1.731191603553383 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.05 2 82.39239794714516 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.05 2 289.33055851278755 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.05 3 268.2520073556841 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.05 3 404.643290436312 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.05 4 1211.9985914643476 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.05 4 2060.8211654612564 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.5 1 3.875023387257474 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.5 1 1.1992764415774615 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.5 2 25.797434937280308 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.5 2 73.39387182097096 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.5 3 77.6099208521729 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.5 3 101.46234548144922 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.5 4 340.70020040223653 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.5 4 504.59549727456044 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.95 1 2.6264423142794957 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.95 1 0.8307942231065403 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.95 2 5.1764274214946955 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.95 2 7.497805535461398 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.95 3 8.147345217505247 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.95 3 8.942487224282644 + , HalfStabilityVector 2 True 3.9221 3.5307239812763354 0.95 4 23.23289032639206 + , HalfStabilityVector 2 False 3.9221 3.5307239812763354 0.95 4 29.69171247953225 + , HalfStabilityVector 2 True 3.9221 10.0 0.05 1 3.9221 + , HalfStabilityVector 2 False 3.9221 10.0 0.05 1 1.731191603553383 + , HalfStabilityVector 2 True 3.9221 10.0 0.05 2 14.427843495144524 + , HalfStabilityVector 2 False 3.9221 10.0 0.05 2 42.13309364882724 + , HalfStabilityVector 2 True 3.9221 10.0 0.05 3 39.311059611757955 + , HalfStabilityVector 2 False 3.9221 10.0 0.05 3 57.5713679386598 + , HalfStabilityVector 2 True 3.9221 10.0 0.05 4 165.6615361161634 + , HalfStabilityVector 2 False 3.9221 10.0 0.05 4 279.30341678426515 + , HalfStabilityVector 2 True 3.9221 10.0 0.5 1 3.875023387257474 + , HalfStabilityVector 2 False 3.9221 10.0 0.5 1 1.1992764415774615 + , HalfStabilityVector 2 True 3.9221 10.0 0.5 2 6.85080887117361 + , HalfStabilityVector 2 False 3.9221 10.0 0.5 2 13.223104762285132 + , HalfStabilityVector 2 True 3.9221 10.0 0.5 3 13.787556928818187 + , HalfStabilityVector 2 False 3.9221 10.0 0.5 3 16.98096209546139 + , HalfStabilityVector 2 True 3.9221 10.0 0.5 4 49.0105529582272 + , HalfStabilityVector 2 False 3.9221 10.0 0.5 4 70.95314772396864 + , HalfStabilityVector 2 True 3.9221 10.0 0.95 1 2.6264423142794957 + , HalfStabilityVector 2 False 3.9221 10.0 0.95 1 0.8307942231065403 + , HalfStabilityVector 2 True 3.9221 10.0 0.95 2 4.090031593149108 + , HalfStabilityVector 2 False 3.9221 10.0 0.95 2 4.400821836828357 + , HalfStabilityVector 2 True 3.9221 10.0 0.95 3 4.487783368363089 + , HalfStabilityVector 2 False 3.9221 10.0 0.95 3 4.59423839891547 + , HalfStabilityVector 2 True 3.9221 10.0 0.95 4 6.507463063031087 + , HalfStabilityVector 2 False 3.9221 10.0 0.95 4 7.3721816966643186 + , HalfStabilityVector 2 True 1000.0 1.0 0.05 1 1000.0 + , HalfStabilityVector 2 False 1000.0 1.0 0.05 1 66.18935453973037 + , HalfStabilityVector 2 True 1000.0 1.0 0.05 2 1411.1052608428026 + , HalfStabilityVector 2 False 1000.0 1.0 0.05 2 1009.6980940525461 + , HalfStabilityVector 2 True 1000.0 1.0 0.05 3 2384.822262115112 + , HalfStabilityVector 2 False 1000.0 1.0 0.05 3 1013.6163861924418 + , HalfStabilityVector 2 True 1000.0 1.0 0.05 4 7329.103038146133 + , HalfStabilityVector 2 False 1000.0 1.0 0.05 4 1069.8928150111012 + , HalfStabilityVector 2 True 1000.0 1.0 0.5 1 721.9841200909241 + , HalfStabilityVector 2 False 1000.0 1.0 0.5 1 45.85242524269734 + , HalfStabilityVector 2 True 1000.0 1.0 0.5 2 1114.604704081431 + , HalfStabilityVector 2 False 1000.0 1.0 0.5 2 1002.360630026971 + , HalfStabilityVector 2 True 1000.0 1.0 0.5 3 1386.049901744669 + , HalfStabilityVector 2 False 1000.0 1.0 0.5 3 1003.3143883664721 + , HalfStabilityVector 2 True 1000.0 1.0 0.5 4 2764.377763740122 + , HalfStabilityVector 2 False 1000.0 1.0 0.5 4 1017.0127322843831 + , HalfStabilityVector 2 True 1000.0 1.0 0.95 1 489.3517931995533 + , HalfStabilityVector 2 False 1000.0 1.0 0.95 1 31.76409432086469 + , HalfStabilityVector 2 True 1000.0 1.0 0.95 2 1006.5714112891886 + , HalfStabilityVector 2 False 1000.0 1.0 0.95 2 1000.121501404576 + , HalfStabilityVector 2 True 1000.0 1.0 0.95 3 1022.1360257665555 + , HalfStabilityVector 2 False 1000.0 1.0 0.95 3 1000.1705912562473 + , HalfStabilityVector 2 True 1000.0 1.0 0.95 4 1101.1690754578165 + , HalfStabilityVector 2 False 1000.0 1.0 0.95 4 1000.8756437241784 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.05 1 1000.0 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.05 1 66.18935453973037 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.05 2 1307.0658665984283 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.05 2 1007.2437741334011 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.05 3 2034.3619712611062 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.05 3 1010.1704546848887 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.05 4 5727.3817542855995 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.05 4 1052.2048727043507 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.5 1 721.9841200909241 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.5 1 45.85242524269734 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.5 2 1085.6014167828357 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.5 2 1001.7632197249533 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.5 3 1288.351327313208 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.5 3 1002.4756081542428 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.5 4 2317.862451867338 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.5 4 1012.7072793264708 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.95 1 489.3517931995533 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.95 1 31.76409432086469 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.95 2 1004.9083684751505 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.95 2 1000.0907527527438 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.95 3 1016.5340086407983 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.95 3 1000.1274193179293 + , HalfStabilityVector 2 True 1000.0 3.5307239812763354 0.95 4 1075.5659749153515 + , HalfStabilityVector 2 False 1000.0 3.5307239812763354 0.95 4 1000.6540424669952 + , HalfStabilityVector 2 True 1000.0 10.0 0.05 1 1000.0 + , HalfStabilityVector 2 False 1000.0 10.0 0.05 1 66.18935453973037 + , HalfStabilityVector 2 True 1000.0 10.0 0.05 2 1041.1105260842803 + , HalfStabilityVector 2 False 1000.0 10.0 0.05 2 1000.9698094052546 + , HalfStabilityVector 2 True 1000.0 10.0 0.05 3 1138.482226211511 + , HalfStabilityVector 2 False 1000.0 10.0 0.05 3 1001.3616386192441 + , HalfStabilityVector 2 True 1000.0 10.0 0.05 4 1632.9103038146134 + , HalfStabilityVector 2 False 1000.0 10.0 0.05 4 1006.9892815011101 + , HalfStabilityVector 2 True 1000.0 10.0 0.5 1 721.9841200909241 + , HalfStabilityVector 2 False 1000.0 10.0 0.5 1 45.85242524269734 + , HalfStabilityVector 2 True 1000.0 10.0 0.5 2 1011.4604704081431 + , HalfStabilityVector 2 False 1000.0 10.0 0.5 2 1000.2360630026972 + , HalfStabilityVector 2 True 1000.0 10.0 0.5 3 1038.604990174467 + , HalfStabilityVector 2 False 1000.0 10.0 0.5 3 1000.3314388366473 + , HalfStabilityVector 2 True 1000.0 10.0 0.5 4 1176.4377763740122 + , HalfStabilityVector 2 False 1000.0 10.0 0.5 4 1001.7012732284383 + , HalfStabilityVector 2 True 1000.0 10.0 0.95 1 489.3517931995533 + , HalfStabilityVector 2 False 1000.0 10.0 0.95 1 31.76409432086469 + , HalfStabilityVector 2 True 1000.0 10.0 0.95 2 1000.6571411289189 + , HalfStabilityVector 2 False 1000.0 10.0 0.95 2 1000.0121501404575 + , HalfStabilityVector 2 True 1000.0 10.0 0.95 3 1002.2136025766555 + , HalfStabilityVector 2 False 1000.0 10.0 0.95 3 1000.0170591256248 + , HalfStabilityVector 2 True 1000.0 10.0 0.95 4 1010.1169075457816 + , HalfStabilityVector 2 False 1000.0 10.0 0.95 4 1000.0875643724179 + ] + +-- | A full memory-state transition. +data StepVector = StepVector + { svParams :: !Int + , svState :: !(Maybe (Double, Double, Double)) + -- ^ @(stability, difficulty, fast stability)@; 'Nothing' for the + -- first review. + , svElapsedDays :: !Double + , svRating :: !Int + , svNextState :: !(Double, Double, Double) + } + deriving stock (Eq, Show) + +goldenStepVectors :: [StepVector] +goldenStepVectors = + [ StepVector 0 Nothing 0.0 1 (0.1104, 6.1686, 0.08832000000000001) + , StepVector 0 Nothing 0.0 2 (2.2395, 5.261278312731786, 1.7916) + , StepVector 0 Nothing 0.0 3 (3.9221, 3.5307239812763354, 3.13768) + , StepVector 0 Nothing 0.0 4 (11.7841, 1.0, 9.427280000000001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.0 1 (0.0001, 9.008791723878954, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.0 2 (0.00010001428854459669, 4.636193001738953, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.0 3 (0.00010002233282994169, 1.0, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.0 4 (0.00010002233282994169, 1.0, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.006944444444444444 1 (0.0001, 2.8544796237435115, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.006944444444444444 2 (0.0023882552225345235, 4.636193001738953, 6.974505924724382) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.006944444444444444 3 (0.0036765164465997553, 1.0, 11.318512730808798) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.006944444444444444 4 (0.0036765164465997553, 1.0, 12.302082797116082) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.5 1 (0.0001, 2.362349180046658, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.5 2 (0.0027133226717944207, 4.636193001738953, 8.884549191761216) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.5 3 (0.004184593110025665, 1.0, 14.418225919768284) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 0.5 4 (0.004184593110025665, 1.0, 15.671161062196148) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 1.0 1 (0.0001, 2.306672599266798, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 1.0 2 (0.0027520464362506135, 4.636193001738953, 9.122953844839316) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 1.0 3 (0.004245117905987205, 1.0, 14.805120845243941) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 1.0 4 (0.004245117905987205, 1.0, 16.09167715669564) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 45.0 1 (0.0001, 2.079752401416066, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 45.0 2 (0.0029141720177064197, 4.636193001738953, 10.132713494987769) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 45.0 3 (0.004498518314639605, 1.0, 16.44380901491037) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 45.0 4 (0.004498518314639605, 1.0, 17.872767328306082) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 400.0 1 (0.0001, 1.9936885015055066, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 400.0 2 (0.0029775100258990486, 4.636193001738953, 10.525553697562268) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 400.0 3 (0.0045975148888700345, 1.0, 17.08132962927989) + , StepVector 0 (Just (0.0001, 1.0, 0.0001)) 400.0 4 (0.0045975148888700345, 1.0, 18.56568848406431) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.0 1 (0.0001, 9.008791723878954, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.0 2 (0.00010001428854459669, 4.636193001738953, 0.0005) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.0 3 (0.00010002233282994169, 1.0, 0.0005) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.0 4 (0.00010002233282994169, 1.0, 0.0005) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.006944444444444444 1 (0.0001, 3.0950415201682877, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.006944444444444444 2 (0.002240066195782809, 4.636193001738953, 10.317495895758277) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.006944444444444444 3 (0.003444898711758063, 1.0, 16.74343394313255) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.006944444444444444 4 (0.003444898711758063, 1.0, 18.19839490279077) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.5 1 (0.0001, 2.486082995419939, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.5 2 (0.0026287148769216498, 4.636193001738953, 14.0658493307264) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.5 3 (0.00405235210522296, 1.0, 22.826448280958132) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 0.5 4 (0.00405235210522296, 1.0, 24.810023186573392) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 1.0 1 (0.0001, 2.417761880350123, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 1.0 2 (0.002675186431778802, 4.636193001738953, 14.548589568353835) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 1.0 3 (0.004124986607969367, 1.0, 23.609863142411285) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 1.0 4 (0.004124986607969367, 1.0, 25.66151679948683) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 45.0 1 (0.0001, 2.1411951349220995, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 45.0 2 (0.002869582286215389, 4.636193001738953, 16.624341267255343) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 45.0 3 (0.00442882508004906, 1.0, 26.978496214305974) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 45.0 4 (0.00442882508004906, 1.0, 29.322884085329164) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 400.0 1 (0.0001, 2.0374184150759755, 0.0001) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 400.0 2 (0.002945198132148376, 4.636193001738953, 17.44395123971817) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 400.0 3 (0.004547011772660793, 1.0, 28.30860003199963) + , StepVector 0 (Just (0.0001, 1.0, 0.0005)) 400.0 4 (0.004547011772660793, 1.0, 30.768573924780398) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.0 1 (0.0001, 9.260038704573313, 0.0001) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.0 2 (0.00010001067250834986, 6.116977809835307, 0.0001) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.0 3 (0.00010001668100711137, 3.4977167432025262, 0.0001) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.0 4 (0.00010001668100711137, 1.0, 0.0001) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.006944444444444444 1 (0.0001, 4.792605905037189, 0.0001) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.006944444444444444 2 (0.0018379169678157817, 6.116977809835307, 5.209476291838806) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.006944444444444444 3 (0.0028163441197495806, 3.4977167432025262, 8.454134878024677) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.006944444444444444 4 (0.0028163441197495806, 1.0, 9.188790508925022) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.5 1 (0.0001, 4.4499089882779845, 0.0001) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.5 2 (0.002075508166823859, 6.116977809835307, 6.63614032875909) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.5 3 (0.003187696415792215, 3.4977167432025262, 10.769396216746335) + , StepVector 0 (Just (0.0001, 3.5307239812763354, 0.0001)) 0.5 4 (0.003187696415792215, 1.0, 11.705248057981592) + , StepVector 0 (Just (0.0001, 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(5.909552440513434, 3.513889773102346, 36500.0) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 0.006944444444444444 3 (19.906294534597997, 3.2357380105637468, 36500.0) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 0.006944444444444444 4 (90.97809750447648, 2.9575862480251476, 36500.0) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 0.5 1 (0.0001, 3.2918710884095126, 0.0001) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 0.5 2 (6.570314774371488, 3.513889773102346, 36500.0) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 0.5 3 (22.132095265091838, 3.2357380105637468, 36500.0) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 0.5 4 (101.15075471187878, 2.9575862480251476, 36500.0) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 1.0 1 (0.0001, 3.291638800173569, 0.0001) + , StepVector 2 (Just (0.0001, 3.5307239812763354, 0.0005)) 1.0 2 (6.577205176391799, 3.513889773102346, 36500.0) + , StepVector 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(24.914079068858864, 9.640321269100175, 27.87688581390956) + , StepVector 2 (Just (3.9221, 10.0, 19.6105)) 45.0 4 (99.86249764965214, 9.640321269100175, 62.04180051809707) + , StepVector 2 (Just (3.9221, 10.0, 19.6105)) 400.0 1 (3.9221, 9.640321269100175, 3.13768) + , StepVector 2 (Just (3.9221, 10.0, 19.6105)) 400.0 2 (14.166552240903771, 9.640321269100175, 27.26356030946093) + , StepVector 2 (Just (3.9221, 10.0, 19.6105)) 400.0 3 (38.43089100232015, 9.640321269100175, 30.355603539216485) + , StepVector 2 (Just (3.9221, 10.0, 19.6105)) 400.0 4 (161.63886983437988, 9.640321269100175, 74.76504125107346) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.0 1 (468.6596382727856, 1.5816305678543745, 26.63407073444681) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.0 2 (1000.0012419568192, 1.1172835591001746, 800.0) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.0 3 (1000.0041835744164, 1.0, 800.0) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.0 4 (1000.0191203407643, 1.0, 800.0) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.006944444444444444 1 (469.33715246647114, 1.5803369788406272, 30.574695296047533) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.006944444444444444 2 (1000.2092229352963, 1.1172835591001746, 800.5618777994351) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.006944444444444444 3 (1000.704774679724, 1.0, 800.7888916181483) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.006944444444444444 4 (1003.2210570906315, 1.0, 804.0493751537143) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.5 1 (470.31335581875624, 1.5784763776461148, 36.544994610784194) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.5 2 (1000.5097381280299, 1.1172835591001746, 801.7799225979489) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.5 3 (1001.7170704799482, 1.0, 802.4990594394126) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 0.5 4 (1007.8475890290455, 1.0, 812.8276546090891) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 1.0 1 (470.53615498711827, 1.5780522734126903, 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800.0)) 400.0 3 (1087.4783143057027, 1.0, 805.8648722137867) + , StepVector 2 (Just (1000.0, 1.0, 800.0)) 400.0 4 (1399.805289090668, 1.0, 830.1043480192616) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.0 1 (468.6596382727856, 1.5816305678543745, 80.4482986922301) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.0 2 (1000.0012419568192, 1.1172835591001746, 5000.0) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.0 3 (1000.0041835744164, 1.0, 5000.0) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.0 4 (1000.0191203407643, 1.0, 5000.0) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.006944444444444444 1 (469.4129391374792, 1.5801923942409661, 100.66082195754248) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.006944444444444444 2 (1000.2325174901796, 1.1172835591001746, 5000.315525262071) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.006944444444444444 3 (1000.7832431919543, 1.0, 5000.4430059967) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.006944444444444444 4 (1003.579684556944, 1.0, 5002.273946680019) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.5 1 (469.9125074105885, 1.579239909559075, 113.34467714690412) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.5 2 (1000.3862200571965, 1.1172835591001746, 5000.601789195075) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.5 3 (1001.3009955946184, 1.0, 5000.844928296444) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 0.5 4 (1005.9459870019253, 1.0, 5004.337011031149) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 1.0 1 (470.07156138950904, 1.578936867263926, 115.27210488132408) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 1.0 2 (1000.4352110904695, 1.1172835591001746, 5000.652123632614) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 1.0 3 (1001.466023581323, 1.0, 5000.915599207307) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 1.0 4 (1006.7002203505699, 1.0, 5004.699764321912) + , StepVector 2 (Just (1000.0, 1.0, 5000.0)) 45.0 1 (479.2343286005937, 1.5616501247878574, 125.17820109112498) + , StepVector 2 (Just 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411.85242154787056) + , StepVector 2 (Just (36500.0, 3.5307239812763354, 36500.0)) 45.0 2 (36500.0, 3.513889773102346, 36500.0) + , StepVector 2 (Just (36500.0, 3.5307239812763354, 36500.0)) 45.0 3 (36500.0, 3.2357380105637468, 36500.0) + , StepVector 2 (Just (36500.0, 3.5307239812763354, 36500.0)) 45.0 4 (36500.0, 2.9575862480251476, 36500.0) + , StepVector 2 (Just (36500.0, 3.5307239812763354, 36500.0)) 400.0 1 (13673.363880874544, 3.8436868452926305, 423.854237949416) + , StepVector 2 (Just (36500.0, 3.5307239812763354, 36500.0)) 400.0 2 (36500.0, 3.513889773102346, 36500.0) + , StepVector 2 (Just (36500.0, 3.5307239812763354, 36500.0)) 400.0 3 (36500.0, 3.2357380105637468, 36500.0) + , StepVector 2 (Just (36500.0, 3.5307239812763354, 36500.0)) 400.0 4 (36500.0, 2.9575862480251476, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.0 1 (13589.089128669066, 9.640321269100175, 231.52233554269924) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.0 2 (36500.0, 9.640321269100175, 29200.0) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.0 3 (36500.0, 9.640321269100175, 29200.0) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.0 4 (36500.0, 9.640321269100175, 29200.0) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.006944444444444444 1 (13625.155437836656, 9.640321269100175, 310.44113340992357) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.006944444444444444 2 (36500.0, 9.640321269100175, 29200.014553824436) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.006944444444444444 3 (36500.0, 9.640321269100175, 29200.020433962894) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.006944444444444444 4 (36500.0, 9.640321269100175, 29200.10488738851) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.5 1 (13634.893053561857, 9.640321269100175, 335.8470179263028) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.5 2 (36500.0, 9.640321269100175, 29200.021433696278) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.5 3 (36500.0, 9.640321269100175, 29200.03009348893) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 0.5 4 (36500.0, 9.640321269100175, 29200.154469668036) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 1.0 1 (13636.370339415538, 9.640321269100175, 339.7598828425326) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 1.0 2 (36500.0, 9.640321269100175, 29200.0226028457) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 1.0 3 (36500.0, 9.640321269100175, 29200.03173500633) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 1.0 4 (36500.0, 9.640321269100175, 29200.162895565343) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 45.0 1 (13647.976920062796, 9.640321269100175, 360.2036807441739) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 45.0 2 (36500.0, 9.640321269100175, 29200.02921664214) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 45.0 3 (36500.0, 9.640321269100175, 29200.041020955294) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 45.0 4 (36500.0, 9.640321269100175, 29200.210560276384) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 400.0 1 (13687.134322782369, 9.640321269100175, 371.1347897110286) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 400.0 2 (36500.0, 9.640321269100175, 29200.033115668088) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 400.0 3 (36500.0, 9.640321269100175, 29200.046495293125) + , StepVector 2 (Just (36500.0, 10.0, 29200.0)) 400.0 4 (36500.0, 9.640321269100175, 29200.238660014144) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.0 1 (13589.089128669066, 9.640321269100175, 264.5694395118582) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.0 2 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.0 3 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.0 4 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.006944444444444444 1 (13624.42138932558, 9.640321269100175, 357.4622180851439) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.006944444444444444 2 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.006944444444444444 3 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.006944444444444444 4 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.5 1 (13633.256052529967, 9.640321269100175, 385.1892381325808) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.5 2 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.5 3 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 0.5 4 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 1.0 1 (13634.605213814782, 9.640321269100175, 389.4663475443259) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 1.0 2 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 1.0 3 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 1.0 4 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 45.0 1 (13645.587677560383, 9.640321269100175, 411.85242154787056) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 45.0 2 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 45.0 3 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 45.0 4 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 400.0 1 (13684.447005110704, 9.640321269100175, 423.854237949416) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 400.0 2 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 400.0 3 (36500.0, 9.640321269100175, 36500.0) + , StepVector 2 (Just (36500.0, 10.0, 36500.0)) 400.0 4 (36500.0, 9.640321269100175, 36500.0) + ] + +-- | The interval that lands exactly on the desired retention. +data IntervalVector = IntervalVector + { ivParams :: !Int + , ivDesiredRetention :: !Double + , ivState :: !(Double, Double, Double) + , ivInterval :: !Double + } + deriving stock (Eq, Show) + +goldenIntervalVectors :: [IntervalVector] +goldenIntervalVectors = + [ IntervalVector 0 0.7 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.7 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.7 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.7 (0.01, 1.0, 0.008) 5.522869936320109e-5 + , IntervalVector 0 0.7 (0.01, 5.0, 0.008) 2.3022474404303497e-5 + , IntervalVector 0 0.7 (0.01, 10.0, 0.008) 1.2996044561251682e-5 + , IntervalVector 0 0.7 (0.5, 1.0, 0.4) 19.03800904279629 + , IntervalVector 0 0.7 (0.5, 5.0, 0.4) 3.039791333404169 + , IntervalVector 0 0.7 (0.5, 10.0, 0.4) 0.1872813242019531 + , IntervalVector 0 0.7 (1.0, 1.0, 0.8) 64.69131051324193 + , IntervalVector 0 0.7 (1.0, 5.0, 0.8) 13.220820725860593 + , IntervalVector 0 0.7 (1.0, 10.0, 0.8) 1.2561372506520427 + , IntervalVector 0 0.7 (3.9221, 1.0, 3.13768) 477.8604830336278 + , IntervalVector 0 0.7 (3.9221, 5.0, 3.13768) 134.43247903444777 + , IntervalVector 0 0.7 (3.9221, 10.0, 3.13768) 21.88160787721904 + , IntervalVector 0 0.7 (15.0, 1.0, 12.0) 2478.7432740212735 + , IntervalVector 0 0.7 (15.0, 5.0, 12.0) 826.2714301256167 + , IntervalVector 0 0.7 (15.0, 10.0, 12.0) 184.07781865532874 + , IntervalVector 0 0.7 (100.0, 1.0, 80.0) 19817.803605842637 + , IntervalVector 0 0.7 (100.0, 5.0, 80.0) 7352.325422392295 + , IntervalVector 0 0.7 (100.0, 10.0, 80.0) 2027.426867196434 + , IntervalVector 0 0.7 (1000.0, 1.0, 800.0) 36500.0 + , IntervalVector 0 0.7 (1000.0, 5.0, 800.0) 36500.0 + , IntervalVector 0 0.7 (1000.0, 10.0, 800.0) 24761.522635404242 + , IntervalVector 0 0.7 (36500.0, 1.0, 29200.0) 36500.0 + , IntervalVector 0 0.7 (36500.0, 5.0, 29200.0) 36500.0 + , IntervalVector 0 0.7 (36500.0, 10.0, 29200.0) 36500.0 + , IntervalVector 0 0.7 (3.9221, 5.0, 0.196105) 125.17800505393978 + , IntervalVector 0 0.7 (3.9221, 5.0, 3.9221) 135.4027343625504 + , IntervalVector 0 0.7 (3.9221, 5.0, 78.442) 153.45603286101988 + , IntervalVector 0 0.8 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.8 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.8 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.8 (0.01, 1.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.8 (0.01, 5.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.8 (0.01, 10.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.8 (0.5, 1.0, 0.4) 2.8149394808118666 + , IntervalVector 0 0.8 (0.5, 5.0, 0.4) 0.3069393640341582 + , IntervalVector 0 0.8 (0.5, 10.0, 0.4) 0.007564091957912695 + , IntervalVector 0 0.8 (1.0, 1.0, 0.8) 10.626348789772006 + , IntervalVector 0 0.8 (1.0, 5.0, 0.8) 1.9252711547909516 + , IntervalVector 0 0.8 (1.0, 10.0, 0.8) 0.10683587035122498 + , IntervalVector 0 0.8 (3.9221, 1.0, 3.13768) 83.50921535224911 + , IntervalVector 0 0.8 (3.9221, 5.0, 3.13768) 23.01389166377201 + , IntervalVector 0 0.8 (3.9221, 10.0, 3.13768) 3.5045728556557623 + , IntervalVector 0 0.8 (15.0, 1.0, 12.0) 440.1083644352774 + , IntervalVector 0 0.8 (15.0, 5.0, 12.0) 145.93757769106412 + , IntervalVector 0 0.8 (15.0, 10.0, 12.0) 32.12157579592958 + , IntervalVector 0 0.8 (100.0, 1.0, 80.0) 3542.1833352348235 + , IntervalVector 0 0.8 (100.0, 5.0, 80.0) 1312.6785159753792 + , IntervalVector 0 0.8 (100.0, 10.0, 80.0) 361.4207804999397 + , IntervalVector 0 0.8 (1000.0, 1.0, 800.0) 36500.0 + , IntervalVector 0 0.8 (1000.0, 5.0, 800.0) 14726.945997467577 + , IntervalVector 0 0.8 (1000.0, 10.0, 800.0) 4433.225664707421 + , IntervalVector 0 0.8 (36500.0, 1.0, 29200.0) 36500.0 + , IntervalVector 0 0.8 (36500.0, 5.0, 29200.0) 36500.0 + , IntervalVector 0 0.8 (36500.0, 10.0, 29200.0) 36500.0 + , IntervalVector 0 0.8 (3.9221, 5.0, 0.196105) 20.93590555398564 + , IntervalVector 0 0.8 (3.9221, 5.0, 3.9221) 23.23272887175912 + , IntervalVector 0 0.8 (3.9221, 5.0, 78.442) 27.333642659742278 + , IntervalVector 0 0.85 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.85 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.85 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.85 (0.01, 1.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.85 (0.01, 5.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.85 (0.01, 10.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.85 (0.5, 1.0, 0.4) 0.7710192916487589 + , IntervalVector 0 0.85 (0.5, 5.0, 0.4) 0.0308473556868 + , IntervalVector 0 0.85 (0.5, 10.0, 0.4) 0.0013838319537463545 + , IntervalVector 0 0.85 (1.0, 1.0, 0.8) 3.8047706474501384 + , IntervalVector 0 0.85 (1.0, 5.0, 0.8) 0.5014734449850002 + , IntervalVector 0 0.85 (1.0, 10.0, 0.8) 0.012904953660551204 + , IntervalVector 0 0.85 (3.9221, 1.0, 3.13768) 34.265138474776144 + , IntervalVector 0 0.85 (3.9221, 5.0, 3.13768) 8.971593947607886 + , IntervalVector 0 0.85 (3.9221, 10.0, 3.13768) 1.150492339959377 + , IntervalVector 0 0.85 (15.0, 1.0, 12.0) 186.95798532936604 + , IntervalVector 0 0.85 (15.0, 5.0, 12.0) 61.06486943343903 + , IntervalVector 0 0.85 (15.0, 10.0, 12.0) 12.94031638791068 + , IntervalVector 0 0.85 (100.0, 1.0, 80.0) 1527.7953747567321 + , IntervalVector 0 0.85 (100.0, 5.0, 80.0) 563.966890963036 + , IntervalVector 0 0.85 (100.0, 10.0, 80.0) 154.01769822120775 + , IntervalVector 0 0.85 (1000.0, 1.0, 800.0) 16497.91363277772 + , IntervalVector 0 0.85 (1000.0, 5.0, 800.0) 6377.648144411187 + , IntervalVector 0 0.85 (1000.0, 10.0, 800.0) 1916.3618070935595 + , IntervalVector 0 0.85 (36500.0, 1.0, 29200.0) 36500.0 + , IntervalVector 0 0.85 (36500.0, 5.0, 29200.0) 36500.0 + , IntervalVector 0 0.85 (36500.0, 10.0, 29200.0) 36500.0 + , IntervalVector 0 0.85 (3.9221, 5.0, 0.196105) 7.892789279155961 + , IntervalVector 0 0.85 (3.9221, 5.0, 3.9221) 9.085228643663998 + , IntervalVector 0 0.85 (3.9221, 5.0, 78.442) 11.215869635176261 + , IntervalVector 0 0.9 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.9 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.9 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.9 (0.01, 1.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.9 (0.01, 5.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.9 (0.01, 10.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.9 (0.5, 1.0, 0.4) 0.03526181023369375 + , IntervalVector 0 0.9 (0.5, 5.0, 0.4) 0.0017184119364847734 + , IntervalVector 0 0.9 (0.5, 10.0, 0.4) 0.000319798140118296 + , IntervalVector 0 0.9 (1.0, 1.0, 0.8) 0.7657780801013794 + , IntervalVector 0 0.9 (1.0, 5.0, 0.8) 0.0267562174446808 + , IntervalVector 0 0.9 (1.0, 10.0, 0.8) 0.0015743299752396995 + , IntervalVector 0 0.9 (3.9221, 1.0, 3.13768) 11.970108216223352 + , IntervalVector 0 0.9 (3.9221, 5.0, 3.13768) 2.619446985553184 + , IntervalVector 0 0.9 (3.9221, 10.0, 3.13768) 0.16767274495528917 + , IntervalVector 0 0.9 (15.0, 1.0, 12.0) 72.55337012121673 + , IntervalVector 0 0.9 (15.0, 5.0, 12.0) 22.63473507198234 + , IntervalVector 0 0.9 (15.0, 10.0, 12.0) 4.233789982119944 + , IntervalVector 0 0.9 (100.0, 1.0, 80.0) 618.8884014081879 + , IntervalVector 0 0.9 (100.0, 5.0, 80.0) 225.86623331098025 + , IntervalVector 0 0.9 (100.0, 10.0, 80.0) 60.16725855282242 + , IntervalVector 0 0.9 (1000.0, 1.0, 800.0) 6775.304945582538 + , IntervalVector 0 0.9 (1000.0, 5.0, 800.0) 2611.9682322401554 + , IntervalVector 0 0.9 (1000.0, 10.0, 800.0) 780.5147600380255 + , IntervalVector 0 0.9 (36500.0, 1.0, 29200.0) 36500.0 + , IntervalVector 0 0.9 (36500.0, 5.0, 29200.0) 36500.0 + , IntervalVector 0 0.9 (36500.0, 10.0, 29200.0) 30939.37702108297 + , IntervalVector 0 0.9 (3.9221, 5.0, 0.196105) 2.014163263105267 + , IntervalVector 0 0.9 (3.9221, 5.0, 3.9221) 2.682765558679898 + , IntervalVector 0 0.9 (3.9221, 5.0, 78.442) 3.861040268787109 + , IntervalVector 0 0.95 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.95 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.95 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.95 (0.01, 1.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.95 (0.01, 5.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.95 (0.01, 10.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.95 (0.5, 1.0, 0.4) 0.0005364223344337926 + , IntervalVector 0 0.95 (0.5, 5.0, 0.4) 0.00017315187172096914 + , IntervalVector 0 0.95 (0.5, 10.0, 0.4) 7.276901150881206e-5 + , IntervalVector 0 0.95 (1.0, 1.0, 0.8) 0.004799335871906806 + , IntervalVector 0 0.95 (1.0, 5.0, 0.8) 0.0008049118450892202 + , IntervalVector 0 0.95 (1.0, 10.0, 0.8) 0.00024273058434702682 + , IntervalVector 0 0.95 (3.9221, 1.0, 3.13768) 1.6400439289120672 + , IntervalVector 0 0.95 (3.9221, 5.0, 3.13768) 0.08456884803791671 + , IntervalVector 0 0.95 (3.9221, 10.0, 3.13768) 0.004777905638285502 + , IntervalVector 0 0.95 (15.0, 1.0, 12.0) 18.658891839510765 + , IntervalVector 0 0.95 (15.0, 5.0, 12.0) 4.624908782985952 + , IntervalVector 0 0.95 (15.0, 10.0, 12.0) 0.39795074006707243 + , IntervalVector 0 0.95 (100.0, 1.0, 80.0) 190.3270085604805 + , IntervalVector 0 0.95 (100.0, 5.0, 80.0) 66.43881296589308 + , IntervalVector 0 0.95 (100.0, 10.0, 80.0) 15.953872037232383 + , IntervalVector 0 0.95 (1000.0, 1.0, 800.0) 2191.8275353960594 + , IntervalVector 0 0.95 (1000.0, 5.0, 800.0) 836.5610900883948 + , IntervalVector 0 0.95 (1000.0, 10.0, 800.0) 244.88255505399007 + , IntervalVector 0 0.95 (36500.0, 1.0, 29200.0) 36500.0 + , IntervalVector 0 0.95 (36500.0, 5.0, 29200.0) 32753.50258839635 + , IntervalVector 0 0.95 (36500.0, 10.0, 29200.0) 10122.148404427307 + , IntervalVector 0 0.95 (3.9221, 5.0, 0.196105) 0.006530282470891567 + , IntervalVector 0 0.95 (3.9221, 5.0, 3.9221) 0.10080543783779433 + , IntervalVector 0 0.95 (3.9221, 5.0, 78.442) 0.5872153601577011 + , IntervalVector 0 0.97 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.97 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.97 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 0 0.97 (0.01, 1.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.97 (0.01, 5.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.97 (0.01, 10.0, 0.008) 1.1574074074074073e-5 + , IntervalVector 0 0.97 (0.5, 1.0, 0.4) 0.00013946742999969874 + , IntervalVector 0 0.97 (0.5, 5.0, 0.4) 6.568268136004309e-5 + , IntervalVector 0 0.97 (0.5, 10.0, 0.4) 3.376612017828218e-5 + , IntervalVector 0 0.97 (1.0, 1.0, 0.8) 0.0006507422720658678 + , IntervalVector 0 0.97 (1.0, 5.0, 0.8) 0.00023560936778980234 + , IntervalVector 0 0.97 (1.0, 10.0, 0.8) 0.00010169232935142352 + , IntervalVector 0 0.97 (3.9221, 1.0, 3.13768) 0.06888096781582646 + , IntervalVector 0 0.97 (3.9221, 5.0, 3.13768) 0.005748367549859383 + , IntervalVector 0 0.97 (3.9221, 10.0, 3.13768) 0.0012290606943829287 + , IntervalVector 0 0.97 (15.0, 1.0, 12.0) 6.12319547230958 + , IntervalVector 0 0.97 (15.0, 5.0, 12.0) 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IntervalVector 2 0.95 (36500.0, 1.0, 29200.0) 3649.804691878699 + , IntervalVector 2 0.95 (36500.0, 5.0, 29200.0) 4428.893665333159 + , IntervalVector 2 0.95 (36500.0, 10.0, 29200.0) 5532.728110595564 + , IntervalVector 2 0.95 (3.9221, 5.0, 0.196105) 0.024903082525702055 + , IntervalVector 2 0.95 (3.9221, 5.0, 3.9221) 0.21540544032947656 + , IntervalVector 2 0.95 (3.9221, 5.0, 78.442) 0.36435668971934176 + , IntervalVector 2 0.97 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 2 0.97 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 2 0.97 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 2 0.97 (0.01, 1.0, 0.008) 0.0002464752295411534 + , IntervalVector 2 0.97 (0.01, 5.0, 0.008) 0.00021080392688973887 + , IntervalVector 2 0.97 (0.01, 10.0, 0.008) 0.00016871170246583172 + , IntervalVector 2 0.97 (0.5, 1.0, 0.4) 0.01253731434185335 + , IntervalVector 2 0.97 (0.5, 5.0, 0.4) 0.00975349966550954 + , IntervalVector 2 0.97 (0.5, 10.0, 0.4) 0.0064308148195433 + , IntervalVector 2 0.97 (1.0, 1.0, 0.8) 0.025276751083574495 + , IntervalVector 2 0.97 (1.0, 5.0, 0.8) 0.019120126823181063 + , IntervalVector 2 0.97 (1.0, 10.0, 0.8) 0.011843819037548603 + , IntervalVector 2 0.97 (3.9221, 1.0, 3.13768) 0.10625081663718366 + , IntervalVector 2 0.97 (3.9221, 5.0, 3.13768) 0.07647573088068495 + , IntervalVector 2 0.97 (3.9221, 10.0, 3.13768) 0.03945354586787302 + , IntervalVector 2 0.97 (15.0, 1.0, 12.0) 0.47570036820632505 + , IntervalVector 2 0.97 (15.0, 5.0, 12.0) 0.35610463181598406 + , IntervalVector 2 0.97 (15.0, 10.0, 12.0) 0.14803848484030374 + , IntervalVector 2 0.97 (100.0, 1.0, 80.0) 4.08803573809441 + , IntervalVector 2 0.97 (100.0, 5.0, 80.0) 3.772524802093857 + , IntervalVector 2 0.97 (100.0, 10.0, 80.0) 2.0610586015609678 + , IntervalVector 2 0.97 (1000.0, 1.0, 800.0) 49.934916643225925 + , IntervalVector 2 0.97 (1000.0, 5.0, 800.0) 54.450383021231865 + , IntervalVector 2 0.97 (1000.0, 10.0, 800.0) 51.72178548245827 + , IntervalVector 2 0.97 (36500.0, 1.0, 29200.0) 2084.319346218482 + , IntervalVector 2 0.97 (36500.0, 5.0, 29200.0) 2489.0659130695617 + , IntervalVector 2 0.97 (36500.0, 10.0, 29200.0) 2999.664683692157 + , IntervalVector 2 0.97 (3.9221, 5.0, 0.196105) 0.009705712401078998 + , IntervalVector 2 0.97 (3.9221, 5.0, 3.9221) 0.08506427680302324 + , IntervalVector 2 0.97 (3.9221, 5.0, 78.442) 0.17569982513853688 + , IntervalVector 2 0.99 (0.0001, 1.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 2 0.99 (0.0001, 5.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 2 0.99 (0.0001, 10.0, 0.0001) 1.1574074074074073e-5 + , IntervalVector 2 0.99 (0.01, 1.0, 0.008) 7.763144704865068e-5 + , IntervalVector 2 0.99 (0.01, 5.0, 0.008) 6.646872321547714e-5 + , IntervalVector 2 0.99 (0.01, 10.0, 0.008) 5.352629677126989e-5 + , IntervalVector 2 0.99 (0.5, 1.0, 0.4) 0.003338414368076456 + , IntervalVector 2 0.99 (0.5, 5.0, 0.4) 0.002590057723127188 + , IntervalVector 2 0.99 (0.5, 10.0, 0.4) 0.001779690048393649 + , IntervalVector 2 0.99 (1.0, 1.0, 0.8) 0.006195039188676159 + , IntervalVector 2 0.99 (1.0, 5.0, 0.8) 0.004648826773860824 + , IntervalVector 2 0.99 (1.0, 10.0, 0.8) 0.0030631180816817075 + , IntervalVector 2 0.99 (3.9221, 1.0, 3.13768) 0.020023819971737293 + , IntervalVector 2 0.99 (3.9221, 5.0, 3.13768) 0.013574979601023374 + , IntervalVector 2 0.99 (3.9221, 10.0, 3.13768) 0.007968671777467391 + , IntervalVector 2 0.99 (15.0, 1.0, 12.0) 0.06375231963643287 + , IntervalVector 2 0.99 (15.0, 5.0, 12.0) 0.035793071125005425 + , IntervalVector 2 0.99 (15.0, 10.0, 12.0) 0.017168574277007437 + , IntervalVector 2 0.99 (100.0, 1.0, 80.0) 0.49879516630933024 + , IntervalVector 2 0.99 (100.0, 5.0, 80.0) 0.18087256692573578 + , IntervalVector 2 0.99 (100.0, 10.0, 80.0) 0.04167879628912574 + , IntervalVector 2 0.99 (1000.0, 1.0, 800.0) 9.965943783790568 + , IntervalVector 2 0.99 (1000.0, 5.0, 800.0) 6.354866247500458 + , IntervalVector 2 0.99 (1000.0, 10.0, 800.0) 0.4450840914454956 + , IntervalVector 2 0.99 (36500.0, 1.0, 29200.0) 589.2249784152581 + , IntervalVector 2 0.99 (36500.0, 5.0, 29200.0) 638.7831438729796 + , IntervalVector 2 0.99 (36500.0, 10.0, 29200.0) 592.3263176231044 + , IntervalVector 2 0.99 (3.9221, 5.0, 0.196105) 0.002263027882333082 + , IntervalVector 2 0.99 (3.9221, 5.0, 3.9221) 0.014996831551057166 + , IntervalVector 2 0.99 (3.9221, 5.0, 78.442) 0.029697257220141427 + ] + +-- | A whole review history folded into a final memory state. +data ReplayVector = ReplayVector + { rvParams :: !Int + , rvReviews :: ![(Double, Int)] + -- ^ @(days since the previous review, rating)@. + , rvFinalState :: !(Double, Double, Double) + } + deriving stock (Eq, Show) + +goldenReplayVectors :: [ReplayVector] +goldenReplayVectors = + [ ReplayVector 0 [(0.0, 3)] (3.9221, 3.5307239812763354, 3.13768) + , ReplayVector 0 [(0.0, 1)] (0.1104, 6.1686, 0.08832000000000001) + , ReplayVector 0 [(0.0, 4)] (11.7841, 1.0, 9.427280000000001) + , ReplayVector 0 [(0.0, 3), (0.006944444444444444, 3)] (5.691489456757392, 3.4977167432025262, 32.238155986503116) + , ReplayVector 0 [(0.0, 1), (0.0006944444444444445, 3), (0.006944444444444444, 3), (1.0, 3)] (2.5166528900813034, 5.992217646564867, 132.45285833658133) + , ReplayVector 0 [(0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (47.290437623478276, 3.400662293377536, 1149.3080142246497) + , ReplayVector 0 [(0.0, 1), (0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (25.985713355194175, 5.877549518858744, 700.5588554145093) + , ReplayVector 0 [(0.0, 2), (1.0, 2), (2.0, 2), (3.0, 2)] (9.920572300295085, 8.86238572359253, 179.27328013950893) + , ReplayVector 0 [(0.0, 4), (15.0, 4), (90.0, 4), (365.0, 4)] (230.48928248956594, 1.0, 2600.831126687825) + , ReplayVector 0 [(0.0, 3), (5.0, 1), (0.006944444444444444, 3), (1.0, 3), (4.0, 4)] (7.957627163126913, 7.891815754342685, 146.16937957559588) + , ReplayVector 0 [(0.0, 1), (0.0, 1), (0.0, 1), (0.0, 3)] (0.019019389972869345, 9.75858882916552, 0.0001443217311120975) + , ReplayVector 0 [(0.0, 3), (100.0, 1), (0.5, 2), (2.0, 3), (6.0, 4), (30.0, 1)] (2.64927464433167, 9.397730054311058, 0.9731637673620137) + , ReplayVector 0 [(0.0, 2), (0.25, 3), (0.75, 4), (2.5, 1), (0.01, 3), (7.0, 3)] (6.650266248266943, 8.846450033642256, 73.0846915217098) + , ReplayVector 0 [(0.0, 3), (1.0, 3), (2.0, 3), (4.0, 3), (8.0, 3), (16.0, 3), (32.0, 3), (64.0, 3), (128.0, 3), (256.0, 3), (512.0, 3)] (827.9827603597868, 3.2151156198455344, 5492.495374527894) + , ReplayVector 0 [(0.0, 4), (1.0, 4), (1.0, 3), (1.0, 2), (1.0, 1), (1.0, 3), (1.0, 4), (1.0, 2), (1.0, 1)] (2.522469988723747, 9.788112823199821, 0.5953527493883451) + , ReplayVector 1 [(0.0, 3)] (64.835975, 1.0, 51.86878000000001) + , ReplayVector 1 [(0.0, 1)] (21.160516, 8.15903, 16.9284128) + , ReplayVector 1 [(0.0, 4)] (64.835975, 1.0, 51.86878000000001) + , ReplayVector 1 [(0.0, 3), (0.006944444444444444, 3)] (64.83612651782667, 1.0, 51.909194191961326) + , ReplayVector 1 [(0.0, 1), (0.0006944444444444445, 3), (0.006944444444444444, 3), (1.0, 3)] (21.216065157195295, 1.0, 31.29467317840364) + , ReplayVector 1 [(0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (65.35836653641853, 1.0, 155.97777657441551) + , ReplayVector 1 [(0.0, 1), (0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (22.417256679832132, 1.0, 149.13587643912234) + , ReplayVector 1 [(0.0, 2), (1.0, 2), (2.0, 2), (3.0, 2)] (50.98302456542983, 1.0, 73.02994362506014) + , ReplayVector 1 [(0.0, 4), (15.0, 4), (90.0, 4), (365.0, 4)] (71.59614033617626, 1.0, 1301.4547482642834) + , ReplayVector 1 [(0.0, 3), (5.0, 1), (0.006944444444444444, 3), (1.0, 3), (4.0, 4)] (13.801554217282716, 1.0, 140.78084274472752) + , ReplayVector 1 [(0.0, 1), (0.0, 1), (0.0, 1), (0.0, 3)] (2.2683628003123015, 1.0, 0.11292343589450687) + , ReplayVector 1 [(0.0, 3), (100.0, 1), (0.5, 2), (2.0, 3), (6.0, 4), (30.0, 1)] (15.2869354425651, 1.0, 2.8367938378344424) + , ReplayVector 1 [(0.0, 2), (0.25, 3), (0.75, 4), (2.5, 1), (0.01, 3), (7.0, 3)] (11.306692190136417, 1.0, 160.46408936344827) + , ReplayVector 1 [(0.0, 3), (1.0, 3), (2.0, 3), (4.0, 3), (8.0, 3), (16.0, 3), (32.0, 3), (64.0, 3), (128.0, 3), (256.0, 3), (512.0, 3)] (70.78571586823713, 1.0, 759.5749941044895) + , ReplayVector 1 [(0.0, 4), (1.0, 4), (1.0, 3), (1.0, 2), (1.0, 1), (1.0, 3), (1.0, 4), (1.0, 2), (1.0, 1)] (4.380219891824702, 1.7676883002379586, 1.4739349071405754) + , ReplayVector 2 [(0.0, 3)] (79.640406, 1.0, 63.712324800000005) + , ReplayVector 2 [(0.0, 1)] (2.462798, 7.614116, 1.9702384) + , ReplayVector 2 [(0.0, 4)] (79.640406, 1.0, 63.712324800000005) + , ReplayVector 2 [(0.0, 3), (0.006944444444444444, 3)] (79.98163766636087, 1.0, 65.19326163019883) + , ReplayVector 2 [(0.0, 1), (0.0006944444444444445, 3), (0.006944444444444444, 3), (1.0, 3)] (9.819166892198902, 6.61669734203843, 42.74604192601035) + , ReplayVector 2 [(0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (130.06910767768903, 1.0, 131.92705057768674) + , ReplayVector 2 [(0.0, 1), (0.0, 3), (1.0, 3), (3.0, 3), (8.0, 3), (21.0, 3)] (54.069208442608165, 5.968264390441213, 126.4505201756272) + , ReplayVector 2 [(0.0, 2), (1.0, 2), (2.0, 2), (3.0, 2)] (18.09911726016345, 5.033143534988341, 58.82722290134258) + , ReplayVector 2 [(0.0, 4), (15.0, 4), (90.0, 4), (365.0, 4)] (1102.2116657016993, 1.0, 341.5315500994411) + , ReplayVector 2 [(0.0, 3), (5.0, 1), (0.006944444444444444, 3), (1.0, 3), (4.0, 4)] (98.16500626333594, 1.0, 172.13803089520258) + , ReplayVector 2 [(0.0, 1), (0.0, 1), (0.0, 1), (0.0, 3)] (1.059361809955083, 7.0716245439612075, 0.12705618196362403) + , ReplayVector 2 [(0.0, 3), (100.0, 1), (0.5, 2), (2.0, 3), (6.0, 4), (30.0, 1)] (72.68115037324422, 1.4908772725977828, 16.97229087188503) + , ReplayVector 2 [(0.0, 2), (0.25, 3), (0.75, 4), (2.5, 1), (0.01, 3), (7.0, 3)] (38.34481864536556, 4.100575639911832, 66.07988882976876) + , ReplayVector 2 [(0.0, 3), (1.0, 3), (2.0, 3), (4.0, 3), (8.0, 3), (16.0, 3), (32.0, 3), (64.0, 3), (128.0, 3), (256.0, 3), (512.0, 3)] (634.5922261077083, 1.0, 224.70493752141786) + , ReplayVector 2 [(0.0, 4), (1.0, 4), (1.0, 3), (1.0, 2), (1.0, 1), (1.0, 3), (1.0, 4), (1.0, 2), (1.0, 1)] (42.83652178194841, 1.6759310653229147, 13.141314727879033) ] diff --git a/test/Test/FSRS/Properties.hs b/test/Test/FSRS/Properties.hs --- a/test/Test/FSRS/Properties.hs +++ b/test/Test/FSRS/Properties.hs @@ -1,12 +1,19 @@ -- | Properties of the FSRS-7 model. -- -- Most of these hold for every parameter vector inside the valid box, and are --- generated that way. A few — the ones about how retrievability and intervals --- respond to /stability/ — only hold for well-behaved parameters: the two --- power laws of the FSRS-7 forgetting curve are re-weighted by stability, and --- for adversarial weights the second component can pull retrievability --- /down/ as stability grows. Those properties are therefore stated for --- 'defaultParameters', and say so. +-- generated that way. The ones about how retrievability and intervals respond +-- to /stability/ or /difficulty/ are narrower, for two reasons, and each such +-- property says which apply to it: +-- +-- * The FSRS-7 forgetting curve re-weights its two components by stability, so +-- for adversarial-but-in-bounds weights the slow component can pull +-- retrievability /down/ as stability grows. Those properties are stated for +-- 'defaultParameters'. +-- * Difficulty pulls the curve two ways — it speeds the slow component up, but +-- also shifts mixture weight onto the fast one. At the trace ratio the model +-- itself maintains the first effect wins; for an arbitrarily lopsided pair of +-- traces neither does. Those properties are stated over +-- 'genNaturalMemoryState' / 'genGrowableState'. module Test.FSRS.Properties (tests) where import Test.Tasty (TestTree, testGroup) @@ -29,13 +36,28 @@ "properties" [ parameterProperties , curveProperties + , fastTraceProperties , intervalProperties , difficultyProperties , stabilityProperties - , transitionProperties , stateProperties ] +-- | Grow both memory traces by the same factor, keeping their ratio — the +-- meaningful way to ask what "more stable" does now that a card has two +-- stabilities. The factor comes from 'genGrowableState', which guarantees +-- neither trace saturates. +scaleTraces :: Double -> MemoryState -> MemoryState +scaleTraces k st = + st + { memoryStability = memoryStability st * k + , memoryStabilityFast = memoryStabilityFast st * k + } + +-- | The largest value 'retrievability' can take. +retrievabilityCeiling :: Retrievability +retrievabilityCeiling = 1 - retrievabilityFloor + -- --------------------------------------------------------------------------- parameterProperties :: TestTree @@ -46,6 +68,8 @@ validateParameters (parametersToList defaultParameters) === [] , testProperty "there are exactly parameterCount defaults" $ length (parametersToList defaultParameters) === parameterCount + , testProperty "there is a bound for every weight" $ + length parameterBounds === parameterCount , testProperty "mkParameters . parametersToList is the identity" $ forAll genParameters $ \p -> mkParameters (parametersToList p) === Right p @@ -69,6 +93,14 @@ , testProperty "clampParameters keeps valid weights untouched" $ forAll genParameters $ \p -> clampParameters (parametersToList p) === Right p + , testProperty "clampParameters settles the ordering constraints" $ + forAll (vectorOf parameterCount (QC.choose (-1000, 1000))) $ \ws -> + case clampParameters ws of + Left errs -> counterexample (show errs) False + Right p -> + let at = parameterAt p + in counterexample (show p) $ + and [at i <= at j | (i, j) <- orderingConstraints] ] -- --------------------------------------------------------------------------- @@ -77,52 +109,143 @@ curveProperties = testGroup "forgetting curve" - [ testProperty "a card just reviewed is certain to be recalled" $ + [ testProperty "a card just reviewed is as recallable as it gets" $ + -- FSRS-7 rescales retrievability away from 1, so "certain" is the + -- ceiling rather than exactly 1. forAll genParameters $ \p -> - forAll genStability $ \s -> - retrievability p 0 s === 1 - , testProperty "retrievability is a probability" $ + forAll genMemoryState $ \st -> + counterexample (show (retrievability p 0 st)) $ + approxEqual 1.0e-15 1.0e-15 (retrievability p 0 st) retrievabilityCeiling + , testProperty "retrievability stays inside the rescaled range" $ forAll genParameters $ \p -> forAll genElapsedDays $ \t -> - forAll genStability $ \s -> - let r = retrievability p t s - in counterexample (show r) (r > 0 && r <= 1) + forAll genMemoryState $ \st -> + let r = retrievability p t st + in counterexample (show r) $ + r >= retrievabilityFloor && r <= retrievabilityCeiling , testProperty "retrievability decreases as time passes" $ forAll genParameters $ \p -> forAll genElapsedDays $ \t1 -> forAll (QC.choose (1.0e-6, 5)) $ \gap -> - forAll genStability $ \s -> - let t2 = t1 + gap - r1 = retrievability p t1 s - r2 = retrievability p t2 s - in counterexample (show (t1, t2, r1, r2)) (r2 <= r1 + 1.0e-15) + forAll genMemoryState $ \st -> + let r1 = retrievability p t1 st + r2 = retrievability p (t1 + gap) st + in counterexample (show (t1, r1, r2)) (r2 <= r1 + 1.0e-15) + , testProperty "a negative elapsed time reads as no time at all" $ + forAll genParameters $ \p -> + forAll genMemoryState $ \st -> + forAll (QC.choose (-1000, -1.0e-9)) $ \t -> + retrievability p t st === retrievability p 0 st , testProperty "the derivative is never positive" $ forAll genParameters $ \p -> forAll genElapsedDays $ \t -> - forAll genStability $ \s -> - let d = retrievabilityDerivative p t s + forAll genMemoryState $ \st -> + let d = retrievabilityDerivative p t st in counterexample (show d) (d <= 0) , testProperty "the derivative matches a finite difference" $ forAll genParameters $ \p -> forAll (QC.choose (0.5, 50)) $ \t -> - forAll (QC.choose (1, 500)) $ \s -> + forAll genMemoryState $ \st -> let h = 1.0e-6 * t - numeric = (retrievability p (t + h) s - retrievability p (t - h) s) / (2 * h) - exact = retrievabilityDerivative p t s + numeric = + (retrievability p (t + h) st - retrievability p (t - h) st) / (2 * h) + exact = retrievabilityDerivative p t st in counterexample (show (numeric, exact)) $ approxEqual 1.0e-7 1.0e-5 numeric exact + , testProperty "with the default weights, difficulty never helps recall" $ + -- Difficulty pulls two ways: it speeds the slow component up (good for + -- this property) but also shifts mixture weight onto the fast one + -- (bad). At the trace ratio the model maintains the first wins; for an + -- arbitrarily lopsided pair of traces neither does, which is why this + -- is stated over 'genNaturalMemoryState'. + forAll genElapsedDays $ \t -> + forAll genNaturalMemoryState $ \st -> + forAll (QC.choose (difficultyMin, difficultyMax)) $ \d1 -> + forAll (QC.choose (difficultyMin, difficultyMax)) $ \d2 -> + let r1 = retrievability defaultParameters t st {memoryDifficulty = min d1 d2} + r2 = retrievability defaultParameters t st {memoryDifficulty = max d1 d2} + in counterexample (show (d1, d2, r1, r2)) (r2 <= r1 + 1.0e-15) , testProperty "with the default weights, more stability means more recall" $ forAll genElapsedDays $ \t -> - forAll genStability $ \s1 -> - forAll (QC.choose (1.0e-6, 5)) $ \growth -> - let s2 = min stabilityMax (s1 * exp growth) - r1 = retrievability defaultParameters t s1 - r2 = retrievability defaultParameters t s2 - in counterexample (show (s1, s2, r1, r2)) (r2 >= r1) + forAll genGrowableState $ \(st, growth) -> + let st' = scaleTraces growth st + r1 = retrievability defaultParameters t st + r2 = retrievability defaultParameters t st' + in counterexample (show (st, st', r1, r2)) (r2 >= r1 - 1.0e-15) ] -- --------------------------------------------------------------------------- +fastTraceProperties :: TestTree +fastTraceProperties = + testGroup + "fast trace" + [ testProperty "the fast trace's own recall is a probability" $ + forAll genParameters $ \p -> + forAll genElapsedDays $ \t -> + forAll genStability $ \s -> + let r = fastTraceRetrievability p t s + in counterexample (show r) (r > 0 && r <= 1) + , testProperty "it is exactly 1 at no elapsed time" $ + -- Unlike the mixture, this component is not rescaled. + forAll genParameters $ \p -> + forAll genStability $ \s -> + fastTraceRetrievability p 0 s === 1 + , testProperty "it decreases as time passes" $ + forAll genParameters $ \p -> + forAll genElapsedDays $ \t1 -> + forAll (QC.choose (1.0e-6, 5)) $ \gap -> + forAll genStability $ \s -> + let r1 = fastTraceRetrievability p t1 s + r2 = fastTraceRetrievability p (t1 + gap) s + in counterexample (show (r1, r2)) (r2 <= r1 + 1.0e-15) + , testProperty "a lapse leaves the fast trace below the slow one" $ + -- The post-lapse cap is what stops a forgotten card from keeping a + -- large short-term boost. It is applied before the final clamp, so at + -- the very bottom of the range the floor wins — as it does upstream. + forAll genParameters $ \p -> + forAll genMemoryState $ \st -> + forAll genElapsedDays $ \t -> + let after = nextMemoryState p (Just st) t Again + cap = max stabilityMin (fastTraceRatio * memoryStability after) + in counterexample (show (after, cap)) $ + memoryStabilityFast after <= cap + 1.0e-12 + , testProperty "the slow trace is the slow block applied to itself" $ + forAll genParameters $ \p -> + forAll genMemoryState $ \st -> + forAll genElapsedDays $ \t -> + forAll genRating $ \rating -> + let r = retrievability p t st + expected = + stabilityAfterReview + (slowTraceWeights p) + (memoryStability st) + (memoryDifficulty st) + r + rating + (slow, _) = nextStability p st t rating + in counterexample (show (expected, slow)) $ + approxEqual 1.0e-12 1.0e-12 slow expected + , testProperty "the fast trace reads its own recall, not the mixture" $ + forAll genParameters $ \p -> + forAll genMemoryState $ \st -> + forAll genElapsedDays $ \t -> + forAll (QC.elements [Hard, Good, Easy]) $ \rating -> + let rFast = fastTraceRetrievability p t (memoryStabilityFast st) + expected = + stabilityAfterReview + (fastTraceWeights p) + (memoryStabilityFast st) + (memoryDifficulty st) + rFast + rating + (_, fast) = nextStability p st t rating + in counterexample (show (expected, fast)) $ + approxEqual 1.0e-12 1.0e-12 fast expected + ] + +-- --------------------------------------------------------------------------- + intervalProperties :: TestTree intervalProperties = testGroup @@ -130,40 +253,41 @@ [ testProperty "the answer is always a legal interval" $ forAll genParameters $ \p -> forAll genDesiredRetention $ \dr -> - forAll genStability $ \s -> - let t = nextIntervalDays p dr s + forAll genMemoryState $ \st -> + let t = nextIntervalDays p dr st in counterexample (show t) (t >= minimumIntervalDays && t <= maximumIntervalDays) , testProperty "waiting that long really does land on the desired retention" $ forAll genParameters $ \p -> forAll genDesiredRetention $ \dr -> - forAll genStability $ \s -> - let t = nextIntervalDays p dr s - r = retrievability p t s + forAll genMemoryState $ \st -> + let t = nextIntervalDays p dr st + r = retrievability p t st in -- Saturated answers cannot hit the target and do not claim to. t > minimumIntervalDays && t < maximumIntervalDays ==> counterexample (show (t, r, dr)) (approxEqual 1.0e-9 1.0e-9 r dr) , testProperty "asking for more retention never buys a longer interval" $ forAll genParameters $ \p -> - forAll genStability $ \s -> + forAll genMemoryState $ \st -> forAll genDesiredRetention $ \dr1 -> forAll (QC.choose (1.0e-6, 0.2)) $ \bump -> let dr2 = min 0.999 (dr1 + bump) - t1 = nextIntervalDays p dr1 s - t2 = nextIntervalDays p dr2 s + t1 = nextIntervalDays p dr1 st + t2 = nextIntervalDays p dr2 st in counterexample (show (dr1, dr2, t1, t2)) (t2 <= t1 * (1 + 1.0e-9)) , testProperty "with the default weights, more stability means a longer interval" $ + -- Stated over 'genGrowableState' for the same reason as the curve's + -- monotonicity above. forAll genDesiredRetention $ \dr -> - forAll genStability $ \s1 -> - forAll (QC.choose (1.0e-6, 5)) $ \growth -> - let s2 = min stabilityMax (s1 * exp growth) - t1 = nextIntervalDays defaultParameters dr s1 - t2 = nextIntervalDays defaultParameters dr s2 - in counterexample (show (s1, s2, t1, t2)) (t2 >= t1 * (1 - 1.0e-9)) + forAll genGrowableState $ \(st, growth) -> + let st' = scaleTraces growth st + t1 = nextIntervalDays defaultParameters dr st + t2 = nextIntervalDays defaultParameters dr st' + in counterexample (show (st, st', t1, t2)) (t2 >= t1 * (1 - 1.0e-9)) , testProperty "an impossible retention saturates instead of diverging" $ forAll genParameters $ \p -> - forAll genStability $ \s -> - counterexample "retention 1" (nextIntervalDays p 1 s == minimumIntervalDays) - QC..&&. counterexample "retention 0" (nextIntervalDays p 0 s == maximumIntervalDays) + forAll genMemoryState $ \st -> + counterexample "retention 1" (nextIntervalDays p 1 st == minimumIntervalDays) + QC..&&. counterexample "retention 0" (nextIntervalDays p 0 st == maximumIntervalDays) ] -- --------------------------------------------------------------------------- @@ -180,14 +304,33 @@ , testProperty "difficulty stays in range" $ forAll genParameters $ \p -> forAll genDifficulty $ \d -> - forAll genRating $ \rating -> - let d' = nextDifficulty p d rating - in counterexample (show d') (d' >= difficultyMin && d' <= difficultyMax) - , testProperty "a better rating never makes a card harder" $ + forAll genRetrievability $ \r -> + forAll genRating $ \rating -> + let d' = nextDifficulty p d r rating + in counterexample (show d') (d' >= difficultyMin && d' <= difficultyMax) + , testProperty "among the passing grades, a better rating never makes a card harder" $ forAll genParameters $ \p -> forAll genDifficulty $ \d -> - let ds = map (nextDifficulty p d) allRatings - in counterexample (show ds) (nonIncreasing ds) + forAll genRetrievability $ \r -> + let ds = map (nextDifficulty p d r) [Hard, Good, Easy] + in counterexample (show ds) (nonIncreasing ds) + , testProperty "a surprising lapse is the harshest answer of all" $ + -- FSRS-7 weights a lapse's step by `r + 0.1`, so a lapse only + -- outweighs a Hard once the model expected the card to be recalled. + -- Below that the weighting deliberately softens it. + forAll genParameters $ \p -> + forAll genDifficulty $ \d -> + forAll (QC.choose (0.4, 1.0)) $ \r -> + let ds = map (nextDifficulty p d r) allRatings + in counterexample (show ds) (nonIncreasing ds) + , testProperty "a less surprising lapse is a gentler lapse" $ + forAll genParameters $ \p -> + forAll genDifficulty $ \d -> + forAll genRetrievability $ \r1 -> + forAll genRetrievability $ \r2 -> + let lo = nextDifficulty p d (min r1 r2) Again + hi = nextDifficulty p d (max r1 r2) Again + in counterexample (show (r1, r2, lo, hi)) (hi >= lo - 1.0e-12) , testProperty "an easier first answer means an easier card" $ forAll genParameters $ \p -> counterexample @@ -195,8 +338,8 @@ (nonIncreasing (map (initialDifficulty p) allRatings)) , testProperty "difficulty stays in range over a long history" $ forAll genParameters $ \p -> - forAll (vectorOf 200 genRating) $ \ratings -> - let ds = scanl (nextDifficulty p) 5 ratings + forAll (vectorOf 200 ((,) <$> genRetrievability <*> genRating)) $ \steps -> + let ds = scanl (\d (r, rating) -> nextDifficulty p d r rating) 5 steps in counterexample (show (minimum ds, maximum ds)) $ all (\d -> d >= difficultyMin && d <= difficultyMax) ds ] @@ -207,13 +350,15 @@ stabilityProperties = testGroup "stability" - [ testProperty "stability stays in range" $ + [ testProperty "both traces stay in range" $ forAll genParameters $ \p -> forAll genMemoryState $ \st -> forAll genElapsedDays $ \t -> forAll genRating $ \rating -> - let s = memoryStability (nextMemoryState p (Just st) t rating) - in counterexample (show s) (s >= stabilityMin && s <= stabilityMax) + let after = nextMemoryState p (Just st) t rating + in counterexample (show after) $ + inStabilityRange (memoryStability after) + && inStabilityRange (memoryStabilityFast after) , testProperty "a better rating never means less stability" $ forAll genParameters $ \p -> forAll genMemoryState $ \st -> @@ -235,60 +380,24 @@ let before = memoryStability st after = memoryStability (nextMemoryState p (Just st) t Again) in counterexample (show (before, after)) (after <= before * (1 + 1.0e-12)) - , testProperty "the two blocks bracket the blended result" $ + , testProperty "post-lapse stability does not depend on difficulty" $ + -- The finished model ablated the d ** -fail_d_exp factor, so a lapse's + -- stability is difficulty-free. Only the sinc branch reads difficulty, + -- and Again never takes it. forAll genParameters $ \p -> - forAll genMemoryState $ \st -> - forAll genElapsedDays $ \t -> - forAll genRating $ \rating -> - let r = retrievability p t (memoryStability st) - long = stabilityAfterReview (longTermWeights p) st r rating - short = stabilityAfterReview (shortTermWeights p) st r rating - blended = nextStability p st t rating - in counterexample (show (short, blended, long)) $ - blended >= min short long - 1.0e-9 - && blended <= max short long + 1.0e-9 - , testProperty "at zero elapsed time the blend is the short-term block" $ - -- Only when the transition amplitude is exactly 1 — which is the - -- default, and the upper bound of w26. - forAll (withFullAmplitude <$> genParameters) $ \p -> - forAll genMemoryState $ \st -> - forAll genRating $ \rating -> - let r = retrievability p 0 (memoryStability st) - short = stabilityAfterReview (shortTermWeights p) st r rating - in counterexample (show (short, nextStability p st 0 rating)) $ - approxEqual 1.0e-12 1.0e-12 (nextStability p st 0 rating) short + forAll genStability $ \s -> + forAll genRetrievability $ \r -> + forAll genDifficulty $ \d1 -> + forAll genDifficulty $ \d2 -> + let f d = stabilityAfterReview (slowTraceWeights p) s d r Again + in counterexample (show (f d1, f d2)) (f d1 === f d2) , testProperty "the initial stability is the matching weight" $ forAll genParameters $ \p -> forAll genRating $ \rating -> initialStability p rating === parameterAt p (ratingToInt rating - 1) ] - --- --------------------------------------------------------------------------- - -transitionProperties :: TestTree -transitionProperties = - testGroup - "long-/short-term transition" - [ testProperty "the coefficient is a weight in [0, 1]" $ - forAll genParameters $ \p -> - forAll genElapsedDays $ \t -> - let c = transitionCoefficient p t - in counterexample (show c) (c >= 0 && c <= 1) - , testProperty "the coefficient grows with the gap" $ - forAll genParameters $ \p -> - forAll genElapsedDays $ \t1 -> - forAll (QC.choose (1.0e-6, 10)) $ \gap -> - let c1 = transitionCoefficient p t1 - c2 = transitionCoefficient p (t1 + gap) - in counterexample (show (c1, c2)) (c2 >= c1 - 1.0e-15) - , testProperty "a same-instant review is purely short-term" $ - forAll genParameters $ \p -> - transitionCoefficient p 0 === 1 - transitionAmplitude p - , testProperty "a distant review is purely long-term" $ - forAll genParameters $ \p -> - counterexample (show (transitionCoefficient p 3650)) $ - approxEqual 1.0e-9 0 (transitionCoefficient p 3650) 1 - ] + where + inStabilityRange s = s >= stabilityMin && s <= stabilityMax -- --------------------------------------------------------------------------- @@ -300,8 +409,15 @@ forAll genParameters $ \p -> forAll genElapsedDays $ \t -> forAll genRating $ \rating -> - nextMemoryState p Nothing t rating - === MemoryState (initialStability p rating) (initialDifficulty p rating) + nextMemoryState p Nothing t rating === initialMemoryState p rating + , testProperty "a new card's fast trace is a fraction of its slow one" $ + forAll genParameters $ \p -> + forAll genRating $ \rating -> + let st = initialMemoryState p rating + in counterexample (show st) $ + approxEqual 1.0e-12 1.0e-12 + (memoryStabilityFast st) + (fastTraceRatio * memoryStability st) , testProperty "the elapsed time of a first review is ignored" $ forAll genParameters $ \p -> forAll genElapsedDays $ \t1 -> @@ -323,10 +439,12 @@ forAll genReviewHistory $ \history -> case replayReviews p history of Nothing -> QC.property (null history) - Just (MemoryState s d) -> - counterexample (show (s, d)) $ + Just (MemoryState s d sFast) -> + counterexample (show (s, d, sFast)) $ s >= stabilityMin && s <= stabilityMax + && sFast >= stabilityMin + && sFast <= stabilityMax && d >= difficultyMin && d <= difficultyMax , testProperty "the state is finite, however long the history" $ @@ -334,22 +452,13 @@ forAll (vectorOf 100 ((,) <$> genElapsedDays <*> genRating)) $ \history -> case replayReviews p history of Nothing -> counterexample "unexpected Nothing" False - Just (MemoryState s d) -> - counterexample (show (s, d)) $ - not (isNaN s) && not (isInfinite s) && not (isNaN d) && not (isInfinite d) + Just (MemoryState s d sFast) -> + counterexample (show (s, d, sFast)) (all finite [s, d, sFast]) ] + where + finite x = not (isNaN x) && not (isInfinite x) -- --------------------------------------------------------------------------- - --- | Pin @w26@ to its upper bound, so a same-instant review is purely --- short-term. -withFullAmplitude :: Parameters -> Parameters -withFullAmplitude p = - case clampParameters (setAt 26 1 (parametersToList p)) of - Right p' -> p' - Left errs -> error (show errs) - where - setAt i x xs = take i xs <> [x] <> drop (i + 1) xs nonDecreasing :: [Double] -> Bool nonDecreasing xs = and (zipWith (<=) xs (drop 1 xs)) diff --git a/test/Test/FSRS/SchedulerSpec.hs b/test/Test/FSRS/SchedulerSpec.hs --- a/test/Test/FSRS/SchedulerSpec.hs +++ b/test/Test/FSRS/SchedulerSpec.hs @@ -90,7 +90,7 @@ cardState card @?= Review cardStep card @?= Nothing , testCase "a card scheduled by a longer-stepped scheduler still graduates" $ do - let stale = (newCard t0) {cardStep = Just 5, cardMemory = Just (MemoryState 10 5)} + let stale = (newCard t0) {cardStep = Just 5, cardMemory = Just (MemoryState 10 5 8)} (card, _) = reviewCard defaultScheduler stale Good t0 cardState card @?= Review , testCase "retrievability is unknown until the first review" $ @@ -173,8 +173,8 @@ _ -> cardStep card' /= Nothing , testProperty "a graduated interval respects the scheduler's bounds" $ forAll genScheduler $ \sched -> - forAll genStability $ \s -> - let ivl = nextReviewInterval sched s + forAll genMemoryState $ \memory -> + let ivl = nextReviewInterval sched memory in counterexample (show ivl) $ ivl >= schedulerMinimumInterval sched && ivl <= schedulerMaximumInterval sched @@ -259,9 +259,11 @@ ] in counterexample (show states) $ all - ( \(MemoryState s d) -> + ( \(MemoryState s d sFast) -> s >= stabilityMin && s <= stabilityMax + && sFast >= stabilityMin + && sFast <= stabilityMax && d >= difficultyMin && d <= difficultyMax ) diff --git a/test/Test/FSRS/Unit.hs b/test/Test/FSRS/Unit.hs --- a/test/Test/FSRS/Unit.hs +++ b/test/Test/FSRS/Unit.hs @@ -1,8 +1,9 @@ -- | Hand-written checks of specific values and edge cases. -- -- The numbers here were derived independently of the Haskell implementation: --- the default weights come from the upstream model file, and the worked --- examples were computed from the published formulas. +-- the default weights come from the reference model file, the worked examples +-- were computed from the published formulas, and 'referenceFixtures' reproduces +-- the two numeric assertions the reference implementation makes about itself. module Test.FSRS.Unit (tests) where import Test.Tasty (TestTree, testGroup) @@ -19,10 +20,14 @@ , curveTests , stateTests , intervalTests + , referenceFixtures ] close :: String -> Double -> Double -> Assertion -close label expected actual = +close = closeWith 1.0e-12 + +closeWith :: Double -> String -> Double -> Double -> Assertion +closeWith t label expected actual = assertBool ( label <> ": expected " @@ -33,7 +38,7 @@ <> show (relativeError actual expected) <> ")" ) - (approxEqual 1.0e-12 1.0e-12 actual expected) + (approxEqual t t actual expected) -- --------------------------------------------------------------------------- @@ -41,45 +46,44 @@ parameterTests = testGroup "parameters" - [ testCase "FSRS-7 has 35 weights" $ - parameterCount @?= 35 + [ testCase "FSRS-7 has 34 weights" $ + parameterCount @?= 34 , testCase "the default weights are the published ones" $ parametersToList defaultParameters - @?= [ 0.041 - , 2.4175 - , 4.1283 - , 11.9709 - , 5.6385 - , 0.4468 - , 3.262 - , 2.3054 - , 0.1688 - , 1.3325 - , 0.3524 - , 0.0049 - , 0.7503 - , 0.0896 - , 0.6625 - , 1.3 - , 0.882 - , 0.3072 - , 3.5875 - , 0.303 - , 0.0107 - , 0.2279 - , 2.6413 - , 0.5594 - , 1.3 - , 2.5 + @?= [ 0.1104 + , 2.2395 + , 3.9221 + , 11.7841 + , 6.1686 + , 0.6457 + , 3.6807 + , 1.9795 + , 0.0 + , 1.3826 + , 0.7024 + , 0.5999 + , 0.8146 + , 0.6398 , 1.0 - , 0.0723 - , 0.1634 - , 0.5 - , 0.9555 - , 0.2245 - , 0.6232 - , 0.1362 - , 0.3862 + , 1.3207 + , 0.6707 + , 3.8668 + , 0.4416 + , 0.0934 + , 1.8631 + , 0.6162 + , 1.0869 + , 0.1567 + , 0.0801 + , 0.2421 + , 0.9464 + , 0.1433 + , 0.7145 + , 0.0 + , 0.5667 + , 0.3734 + , 0.5333 + , 0.3048 ] , testCase "there is a bound for every weight" $ length parameterBounds @?= parameterCount @@ -90,13 +94,19 @@ Left errs -> errs @?= [ParameterOutOfBounds 5 99 0.001 4.0] Right _ -> assertFailure "expected a rejection" , testCase "several bad weights are all reported" $ - case mkParameters (setAt 4 0 (setAt 26 7 (parametersToList defaultParameters))) of + case mkParameters (setAt 4 0 (setAt 24 7 (parametersToList defaultParameters))) of Left errs -> length errs @?= 2 Right _ -> assertFailure "expected a rejection" , testCase "the initial-stability weights must be ordered" $ case mkParameters (setAt 0 5 (parametersToList defaultParameters)) of - Left errs -> errs @?= [ParameterOutOfOrder 0 1 5 2.4175] + Left errs -> errs @?= [ParameterOutOfOrder 0 1 5 2.2395] Right _ -> assertFailure "expected a rejection" + , testCase "the curve's two bases must be ordered" $ + -- The bounds of w25 and w26 overlap, so only a base1 above base2 is a + -- violation. + case mkParameters (setAt 26 0.5 (setAt 25 0.85 (parametersToList defaultParameters))) of + Right _ -> assertFailure "expected a rejection" + Left errs -> errs @?= [ParameterOutOfOrder 25 26 0.85 0.5] , testCase "a NaN weight is rejected" $ case mkParameters (setAt 6 (0 / 0) (parametersToList defaultParameters)) of Left [ParameterNotFinite 6 _] -> pure () @@ -108,20 +118,21 @@ , testCase "clamping fixes the ordering constraints too" $ case clampParameters (setAt 1 0.0001 (parametersToList defaultParameters)) of Right p -> do - parameterAt p 0 @?= 0.041 + parameterAt p 0 @?= 0.1104 -- w1 is pulled up to w0, not left below it. - parameterAt p 1 @?= 0.041 + parameterAt p 1 @?= 0.1104 validateParameters (parametersToList p) @?= [] Left errs -> assertFailure (show errs) , testCase "the weight blocks read the right indices" $ do let p = defaultParameters - swIncreaseBase (longTermWeights p) @?= parameterAt p 7 - swEasyBonus (longTermWeights p) @?= parameterAt p 15 - swIncreaseBase (shortTermWeights p) @?= parameterAt p 16 - swEasyBonus (shortTermWeights p) @?= parameterAt p 24 - cwDecay1 (curveWeights p) @?= negate (parameterAt p 27) - cwDecay2 (curveWeights p) @?= negate (parameterAt p 28) - cwStabilityPower2 (curveWeights p) @?= parameterAt p 34 + swIncreaseBase (slowTraceWeights p) @?= parameterAt p 7 + swEasyBonus (slowTraceWeights p) @?= parameterAt p 14 + swIncreaseBase (fastTraceWeights p) @?= parameterAt p 15 + swEasyBonus (fastTraceWeights p) @?= parameterAt p 22 + cwDecayBase1 (curveWeights p) @?= parameterAt p 23 + cwDecay2 (curveWeights p) @?= parameterAt p 24 + cwStabilityPower2 (curveWeights p) @?= parameterAt p 30 + cwStabilityDecay1 (curveWeights p) @?= parameterAt p 33 , testCase "ratings number from one" $ map ratingToInt allRatings @?= [1, 2, 3, 4] , testCase "rating numbers round-trip" $ do @@ -139,28 +150,34 @@ curveTests = testGroup "forgetting curve" - [ testCase "no time has passed, nothing is forgotten" $ - retrievability defaultParameters 0 10 @?= 1 - , testCase "w29 and w30 are the recall probability at t == s" $ do - -- Both components carry the same base, so their mixture is that base - -- at t == s whatever the stability-dependent weighting does. + [ testCase "no time has passed, almost nothing is forgotten" $ + -- FSRS-7 rescales retrievability into [1e-5, 1 - 1e-5], so a card + -- reviewed a moment ago stops just short of certainty. + close "R(0)" (1 - retrievabilityFloor) (retrievability defaultParameters 0 (MemoryState 10 5 8)) + , testCase "w25 and w26 are the recall probability at t == s" $ do + -- Both components carry the same base, and at an average difficulty + -- with the two traces level the mixture is that base at t == s, + -- whatever the stability-dependent weighting does. mapM_ ( \(base, s) -> close ("R(s, s) with both bases at " <> show base) - base - (retrievability (tweak [(29, base), (30, base)]) s s) + (base * (1 - 2 * retrievabilityFloor) + retrievabilityFloor) + (retrievability (tweak [(25, base), (26, base)]) s (MemoryState s 5 s)) ) - [(b, s) | b <- [0.5, 0.85], s <- [0.5, 1, 37, 1000]] - , testCase "a worked value of the default curve" $ - -- R(1, 1) with the default weights, computed from the published - -- formulas: weights 0.2245 and 0.6232, components 0.5 and 0.9555. - close - "R(1, 1)" - ((0.2245 * 0.5 + 0.6232 * 0.9555) / (0.2245 + 0.6232)) - (retrievability defaultParameters 1 1) - , testCase "retrievability at a century is still positive" $ - assertBool "positive" (retrievability defaultParameters 36500 0.5 > 0) + [(b, s) | b <- [0.5, 0.7, 0.85], s <- [0.5, 1, 37, 1000]] + , testCase "the fast component alone is not rescaled" $ + -- fastTraceRetrievability is a bare power law, so it hits 1 exactly. + mapM_ + (\s -> fastTraceRetrievability defaultParameters 0 s @?= 1) + [0.01, 1, 37, 1000] + , testCase "a harder card is forgotten faster" $ do + let r d = retrievability defaultParameters 7 (MemoryState 10 d 8) + assertBool "monotone in difficulty" (and (zipWith (>=) (map r [1, 3, 5, 7, 10]) (drop 1 (map r [1, 3, 5, 7, 10])))) + , testCase "retrievability at a century is still above the floor" $ + assertBool + "above the floor" + (retrievability defaultParameters 36500 (MemoryState 0.5 5 0.4) > retrievabilityFloor) ] where tweak overrides = @@ -178,52 +195,60 @@ "state transitions" [ testCase "a first review reads stability straight off the weights" $ map (memoryStability . firstReview) allRatings - @?= [0.041, 2.4175, 4.1283, 11.9709] + @?= [0.1104, 2.2395, 3.9221, 11.7841] + , testCase "a new card's fast trace starts below its slow one" $ + mapM_ + ( \rating -> + close + ("initial fast stability for " <> show rating) + (fastTraceRatio * memoryStability (firstReview rating)) + (memoryStabilityFast (firstReview rating)) + ) + allRatings , testCase "a first review's difficulty follows the published formula" $ mapM_ ( \rating -> close ("initial difficulty for " <> show rating) ( min 10 . max 1 $ - 5.6385 - exp (0.4468 * fromIntegral (ratingToInt rating - 1)) + 1 + 6.1686 - exp (0.6457 * fromIntegral (ratingToInt rating - 1)) + 1 ) (memoryDifficulty (firstReview rating)) ) allRatings , testCase "Again on a brand-new card gives the smallest stability" $ - memoryStability (firstReview Again) @?= 0.041 - , testCase "a same-instant review is handled by the short-term block" $ do - -- w26 is 1 by default, so the transition coefficient is 0 at dt == 0. - let before = MemoryState 10 5 - r = retrievability defaultParameters 0 10 - expected = stabilityAfterReview (shortTermWeights defaultParameters) before r Good - close - "same-instant stability" - expected - (memoryStability (nextMemoryState defaultParameters (Just before) 0 Good)) - , testCase "a review after ten years is handled by the long-term block" $ do - let before = MemoryState 10 5 - r = retrievability defaultParameters 3650 10 - expected = stabilityAfterReview (longTermWeights defaultParameters) before r Good - close - "long-term stability" - expected - (memoryStability (nextMemoryState defaultParameters (Just before) 3650 Good)) - , testCase "stability is clamped at the century mark" $ - memoryStability (nextMemoryState defaultParameters (Just (MemoryState 36500 1)) 36500 Easy) - @?= stabilityMax - , testCase "repeated Good reviews converge on the Easy anchor" $ - -- A Good review zeroes the rating delta, leaving only the 1% pull - -- towards the difficulty an Easy first review would have produced. - -- Iterating it therefore pins down which rating that anchor comes from. + memoryStability (firstReview Again) @?= 0.1104 + , testCase "a Good review reverts difficulty 1% towards the Easy anchor" $ do + -- A Good review zeroes the rating delta, leaving only the mean + -- reversion. The anchor is the *unclamped* initial difficulty of an + -- Easy first review, which is what makes this pin down the anchor. + let anchor = 6.1686 - exp (0.6457 * 3) + 1 mapM_ - ( \start -> + ( \d -> close - ("limit from " <> show start) - (initialDifficulty defaultParameters Easy) - (iterate (\d -> nextDifficulty defaultParameters d Good) start !! 3000) + ("mean reversion from " <> show d) + (min 10 (max 1 (0.01 * anchor + 0.99 * d))) + (nextDifficulty defaultParameters d 0.9 Good) ) - [difficultyMin, 5, difficultyMax] + [2, 5, 7.5] + , testCase "a lapse's difficulty step is weighted by how surprising it was" $ do + -- Forgetting a card you were expected to recall (high R) is harsher + -- than forgetting one that was long overdue. + let d = 5 + harsh = nextDifficulty defaultParameters d 0.95 Again + gentle = nextDifficulty defaultParameters d 0.05 Again + assertBool + ("expected " <> show harsh <> " > " <> show gentle) + (harsh > gentle) + , testCase "a lapse pulls the fast trace under the slow one" $ do + let after = nextMemoryState defaultParameters (Just (MemoryState 100 5 400)) 30 Again + assertBool + (show after) + (memoryStabilityFast after <= fastTraceRatio * memoryStability after + 1.0e-12) + , testCase "stability is clamped at the century mark" $ + memoryStability + (nextMemoryState defaultParameters (Just (MemoryState 36500 1 36500)) 36500 Easy) + @?= stabilityMax , testCase "an empty history has no state" $ replayReviews defaultParameters [] @?= Nothing , testCase "a one-review history is a first review" $ @@ -241,33 +266,79 @@ "interval inversion" [ testCase "the interval really does land on the target" $ mapM_ - ( \(dr, s) -> + ( \(dr, st) -> close - ("R after the scheduled interval for " <> show (dr, s)) + ("R after the scheduled interval for " <> show (dr, st)) dr - (retrievability defaultParameters (nextIntervalDays defaultParameters dr s) s) + (retrievability defaultParameters (nextIntervalDays defaultParameters dr st) st) ) - [(0.9, 10), (0.8, 1), (0.95, 100), (0.7, 0.5), (0.99, 1000)] + [ (0.9, MemoryState 10 5 8) + , (0.8, MemoryState 1 5 0.8) + , (0.95, MemoryState 100 2 80) + , (0.7, MemoryState 0.5 8 0.4) + , (0.99, MemoryState 1000 5 800) + ] , testCase "an unreachable target saturates at the shortest interval" $ - nextIntervalDays defaultParameters 1 10 @?= minimumIntervalDays + nextIntervalDays defaultParameters 1 (MemoryState 10 5 8) @?= minimumIntervalDays , testCase "a target of zero saturates at the longest interval" $ - nextIntervalDays defaultParameters 0 10 @?= maximumIntervalDays + nextIntervalDays defaultParameters 0 (MemoryState 10 5 8) @?= maximumIntervalDays , testCase "a nonsensical target does not diverge" $ do - nextIntervalDays defaultParameters (0 / 0) 10 @?= maximumIntervalDays - nextIntervalDays defaultParameters (-1) 10 @?= maximumIntervalDays - nextIntervalDays defaultParameters 2 10 @?= minimumIntervalDays - , testCase "a fresh Good card comes back in about three days" $ + let st = MemoryState 10 5 8 + nextIntervalDays defaultParameters (0 / 0) st @?= maximumIntervalDays + nextIntervalDays defaultParameters (-1) st @?= maximumIntervalDays + nextIntervalDays defaultParameters 2 st @?= minimumIntervalDays + , testCase "a fresh Good card comes back in about five days" $ close "interval after one Good" - 2.9669271623721456 + 4.777721806896744 ( nextIntervalDays defaultParameters 0.9 $ - memoryStability (nextMemoryState defaultParameters Nothing 0 Good) + nextMemoryState defaultParameters Nothing 0 Good ) - , testCase "a fresh Easy card comes back in about seventeen days" $ + , testCase "a fresh Easy card comes back in about two months" $ close "interval after one Easy" - 16.9366155257869 + 53.86951316227529 ( nextIntervalDays defaultParameters 0.9 $ - memoryStability (nextMemoryState defaultParameters Nothing 0 Easy) + nextMemoryState defaultParameters Nothing 0 Easy ) ] + +-- --------------------------------------------------------------------------- + +-- | The two numeric assertions the reference implementation makes about +-- FSRS-7 in its own test suite, reproduced here. These are the only fixtures +-- in the package that were not produced by our own transcription of the model, +-- so they are what pins the port to upstream rather than to itself. +-- +-- Both come from @src\/inference.rs@ of +-- : +-- @test_memory_state_fsrs7@ and @test_next_interval_fsrs7@. The tolerances are +-- loose because upstream computes in single precision. +referenceFixtures :: TestTree +referenceFixtures = + testGroup + "reference fixtures" + [ testCase "test_memory_state_fsrs7" $ do + let history = + [ (0, Again) + , (0, Good) + , (1, Good) + , (3, Good) + , (8, Good) + , (21, Good) + ] + case replayReviews defaultParameters history of + Nothing -> assertFailure "replayReviews returned Nothing" + Just st -> do + closeWith 1.0e-6 "stability" 25.985723 (memoryStability st) + closeWith 1.0e-6 "difficulty" 5.877549 (memoryDifficulty st) + , testCase "test_next_interval_fsrs7" $ + -- Upstream rounds to whole days and floors at one. + map (wholeDays . (/ 10) . fromIntegral) [1 .. 10 :: Int] + @?= [36500, 36500, 36500, 12813, 843, 92, 13, 2, 1, 1] + ] + where + wholeDays :: Retrievability -> Integer + wholeDays dr = + max 1 . round $ + nextIntervalDays defaultParameters dr (MemoryState 1 5 1)