Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Average Error: 0.1 → 0.1

Time: 9.0s

Precision: binary64

Cost: 576

Math

\[\left(x \cdot y + z\right) \cdot y + t \]

↓

\[\left(x \cdot y + z\right) \cdot y + t \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))

↓

(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))

C

double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

↓

double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * y) + z) * y) + t
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * y) + z) * y) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

↓

public static double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}

Python

def code(x, y, z, t):
	return (((x * y) + z) * y) + t

↓

def code(x, y, z, t):
	return (((x * y) + z) * y) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * y) + z) * y) + t)
end

↓

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * y) + z) * y) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * y) + z) * y) + t;
end

↓

function tmp = code(x, y, z, t)
	tmp = (((x * y) + z) * y) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[\left(x \cdot y + z\right) \cdot y + t \]

2. Final simplification 0.1

   \[\leadsto \left(x \cdot y + z\right) \cdot y + t \]

Alternatives

Alternative 1
Error	26.8
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+89}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-177}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+141}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 2
Error	27.1
Cost	716

\[\begin{array}{l} t_1 := \left(y \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -4 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 260000:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	10.3
Cost	712

\[\begin{array}{l} t_1 := \left(y \cdot x + z\right) \cdot y\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 105:\\ \;\;\;\;z \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	8.2
Cost	712

\[\begin{array}{l} t_1 := z \cdot y + t\\ \mathbf{if}\;z \leq -7 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9000000000000:\\ \;\;\;\;x \cdot \left(y \cdot y\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	5.0
Cost	712

\[\begin{array}{l} t_1 := z \cdot y + t\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 95000000000000:\\ \;\;\;\;\left(y \cdot x\right) \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	13.6
Cost	584

\[\begin{array}{l} t_1 := \left(y \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -1000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+156}:\\ \;\;\;\;z \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	25.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+85}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+142}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 8
Error	29.5
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))