hydra-kernel-0.16.0: src/main/haskell/Hydra/Differentiation.hs
-- Note: this is an automatically generated file. Do not edit.
-- | Source-to-source automatic differentiation for Float64 terms.
module Hydra.Differentiation where
import qualified Hydra.Ast as Ast
import qualified Hydra.Coders as Coders
import qualified Hydra.Core as Core
import qualified Hydra.Error.Checking as Checking
import qualified Hydra.Error.Core as ErrorCore
import qualified Hydra.Error.Packaging as ErrorPackaging
import qualified Hydra.Errors as Errors
import qualified Hydra.Graph as Graph
import qualified Hydra.Json.Model as Model
import qualified Hydra.Haskell.Lib.Equality as Equality
import qualified Hydra.Haskell.Lib.Lists as Lists
import qualified Hydra.Haskell.Lib.Logic as Logic
import qualified Hydra.Haskell.Lib.Optionals as Optionals
import qualified Hydra.Haskell.Lib.Pairs as Pairs
import qualified Hydra.Packaging as Packaging
import qualified Hydra.Parsing as Parsing
import qualified Hydra.Paths as Paths
import qualified Hydra.Query as Query
import qualified Hydra.Relational as Relational
import qualified Hydra.Strip as Strip
import qualified Hydra.Tabular as Tabular
import qualified Hydra.Testing as Testing
import qualified Hydra.Topology as Topology
import qualified Hydra.Typed as Typed
import qualified Hydra.Typing as Typing
import qualified Hydra.Util as Util
import qualified Hydra.Validation as Validation
import qualified Hydra.Variables as Variables
import qualified Hydra.Variants as Variants
import Prelude hiding (Enum, Ordering, decodeFloat, encodeFloat, fail, map, pure, sum)
import qualified Data.Scientific as Sci
-- | Differentiate a binary primitive application given both arguments and their derivatives
differentiateBinary :: Core.Name -> Core.Term -> Core.Term -> Core.Term -> Core.Term -> Core.Term
differentiateBinary bfname a b da db =
Logic.ifElse (Logic.or (Equality.equal bfname (Core.Name "hydra.lib.math.add")) (Equality.equal bfname (Core.Name "hydra.lib.math.addFloat64"))) (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.addFloat64")),
Core.applicationArgument = da})),
Core.applicationArgument = db})) (Logic.ifElse (Logic.or (Equality.equal bfname (Core.Name "hydra.lib.math.sub")) (Equality.equal bfname (Core.Name "hydra.lib.math.subFloat64"))) (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.subFloat64")),
Core.applicationArgument = da})),
Core.applicationArgument = db})) (Logic.ifElse (Logic.or (Equality.equal bfname (Core.Name "hydra.lib.math.mul")) (Equality.equal bfname (Core.Name "hydra.lib.math.mulFloat64"))) (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.addFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = a})),
Core.applicationArgument = db}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = b})),
Core.applicationArgument = da}))})) (Logic.ifElse (Equality.equal bfname (Core.Name "hydra.lib.math.pow")) (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = a})),
Core.applicationArgument = b}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.addFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = db})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.log")),
Core.applicationArgument = a}))}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = b})),
Core.applicationArgument = da}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = a})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))}))})) (Logic.ifElse (Equality.equal bfname (Core.Name "hydra.lib.math.atan2")) (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.subFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = b})),
Core.applicationArgument = da}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = a})),
Core.applicationArgument = db}))}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.addFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = a})),
Core.applicationArgument = a}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = b})),
Core.applicationArgument = b}))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))})) (Logic.ifElse (Equality.equal bfname (Core.Name "hydra.lib.math.logBase")) (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.subFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.log")),
Core.applicationArgument = a}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = db})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = b})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.log")),
Core.applicationArgument = b}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = da})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = a})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))}))}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.log")),
Core.applicationArgument = a}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.log")),
Core.applicationArgument = a}))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))})) (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))))))))
-- | Differentiate a function term (Float64 -> Float64) with respect to its parameter
differentiateFunction :: Core.Term -> Core.Term
differentiateFunction term =
case term of
Core.TermAnnotated v0 -> differentiateFunction (Core.annotatedTermBody v0)
Core.TermLambda v0 ->
let paramName = Core.lambdaParameter v0
body = Core.lambdaBody v0
in (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = paramName,
Core.lambdaDomain = (Core.lambdaDomain v0),
Core.lambdaBody = (differentiateTerm paramName body)}))
_ -> term
-- | Differentiate a term with respect to a named variable
differentiateTerm :: Core.Name -> Core.Term -> Core.Term
differentiateTerm dx term =
case term of
Core.TermVariable v0 -> Logic.ifElse (Equality.equal v0 dx) (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 1.0))) (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0)))
Core.TermLiteral _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermApplication v0 ->
let func = Core.applicationFunction v0
arg = Core.applicationArgument v0
in case func of
Core.TermVariable v1 -> Optionals.cases (primitiveDerivative v1) (differentiateTerm dx (Core.TermApplication (Core.Application {
Core.applicationFunction = func,
Core.applicationArgument = arg}))) (\derivTerm -> Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = derivTerm,
Core.applicationArgument = arg}))})),
Core.applicationArgument = (differentiateTerm dx arg)}))
Core.TermApplication v1 ->
let innerFunc = Core.applicationFunction v1
innerArg = Core.applicationArgument v1
in case innerFunc of
Core.TermVariable v2 -> differentiateBinary v2 innerArg arg (differentiateTerm dx innerArg) (differentiateTerm dx arg)
_ -> Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (differentiateTerm dx (Core.TermApplication (Core.Application {
Core.applicationFunction = func,
Core.applicationArgument = arg})))})),
Core.applicationArgument = (differentiateTerm dx arg)})
_ -> Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (differentiateTerm dx (Core.TermApplication (Core.Application {
Core.applicationFunction = func,
Core.applicationArgument = arg})))})),
Core.applicationArgument = (differentiateTerm dx arg)})
Core.TermLambda v0 -> Logic.ifElse (Equality.equal (Core.lambdaParameter v0) dx) (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.lambdaParameter v0),
Core.lambdaDomain = (Core.lambdaDomain v0),
Core.lambdaBody = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0)))})) (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.lambdaParameter v0),
Core.lambdaDomain = (Core.lambdaDomain v0),
Core.lambdaBody = (differentiateTerm dx (Core.lambdaBody v0))}))
Core.TermCases _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermProject _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermUnwrap _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermLet v0 -> Core.TermLet (Core.Let {
Core.letBindings = (Lists.map (\b -> Core.Binding {
Core.bindingName = (Core.bindingName b),
Core.bindingTerm = (differentiateTerm dx (Core.bindingTerm b)),
Core.bindingTypeScheme = Nothing}) (Core.letBindings v0)),
Core.letBody = (differentiateTerm dx (Core.letBody v0))})
Core.TermAnnotated v0 -> differentiateTerm dx (Core.annotatedTermBody v0)
Core.TermList v0 -> Core.TermList (Lists.map (differentiateTerm dx) v0)
Core.TermPair v0 -> Core.TermPair (differentiateTerm dx (Pairs.first v0), (differentiateTerm dx (Pairs.second v0)))
Core.TermRecord v0 -> Core.TermRecord (Core.Record {
Core.recordTypeName = (Core.recordTypeName v0),
Core.recordFields = (Lists.map (\fld -> Core.Field {
Core.fieldName = (Core.fieldName fld),
Core.fieldTerm = (differentiateTerm dx (Core.fieldTerm fld))}) (Core.recordFields v0))})
Core.TermTypeApplication v0 -> differentiateTerm dx (Core.typeApplicationTermBody v0)
Core.TermTypeLambda v0 -> differentiateTerm dx (Core.typeLambdaBody v0)
Core.TermUnit -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermSet _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermMap _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermEither _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermOptional _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermInject _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
Core.TermWrap _ -> Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.0))
-- | Compute the gradient of a term as a record of partial derivatives
gradient :: Core.Name -> [Core.Name] -> Core.Term -> Core.Term
gradient typeName vars term =
Core.TermRecord (Core.Record {
Core.recordTypeName = typeName,
Core.recordFields = (Lists.map (\v -> Core.Field {
Core.fieldName = v,
Core.fieldTerm = (differentiateTerm v term)}) vars)})
-- | Look up the derivative of a unary Float64 primitive
primitiveDerivative :: Core.Name -> Maybe Core.Term
primitiveDerivative name =
Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.sin")) (Just (Core.TermVariable (Core.Name "hydra.lib.math.cos"))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.cos")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.negateFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.sin")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.tan")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.cos")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-2.0))))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.exp")) (Just (Core.TermVariable (Core.Name "hydra.lib.math.exp"))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.log")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.sqrt")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 0.5)))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.sqrt")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.asin")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.sqrt")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.subFloat64")),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 1.0)))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))})),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))}))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.acos")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.negateFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.sqrt")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.subFloat64")),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 1.0)))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))})),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))}))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.atan")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.addFloat64")),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 1.0)))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))})),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.sinh")) (Just (Core.TermVariable (Core.Name "hydra.lib.math.cosh"))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.cosh")) (Just (Core.TermVariable (Core.Name "hydra.lib.math.sinh"))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.tanh")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.subFloat64")),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 1.0)))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.tanh")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))})),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.tanh")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))}))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.asinh")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
Core.lambdaBody = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.pow")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.sqrt")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.addFloat64")),
Core.applicationArgument = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermApplication (Core.Application {
Core.applicationFunction = (Core.TermVariable (Core.Name "hydra.lib.math.mulFloat64")),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))})),
Core.applicationArgument = (Core.TermVariable (Core.Name "_x"))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 1.0)))}))}))})),
Core.applicationArgument = (Core.TermLiteral (Core.LiteralFloat (Core.FloatValueFloat64 (-1.0))))}))}))) (Logic.ifElse (Equality.equal name (Core.Name "hydra.lib.math.acosh")) (Just (Core.TermLambda (Core.Lambda {
Core.lambdaParameter = (Core.Name "_x"),
Core.lambdaDomain = Nothing,
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