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

Average Error: 0.1 → 0.1

Time: 7.5s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

def code(x, y, z, t):
	return ((y * (x * y)) + (y * z)) + 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(y * Float64(x * y)) + Float64(y * z)) + 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 = ((y * (x * y)) + (y * z)) + 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[(y * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\left(\left(x \cdot y\right) \cdot y + z \cdot y\right)} + t \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	25.8
Cost	984

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;t \leq -3.257442775400132 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.0461205227154176 \cdot 10^{-229}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.9282024663912063 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7229447038234774 \cdot 10^{-114}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 6.309788258062418 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6949710219950935 \cdot 10^{-46}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 2
Error	25.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;t \leq -3.257442775400132 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.0461205227154176 \cdot 10^{-229}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.9282024663912063 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;t \leq 1.936231027305437 \cdot 10^{-95}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3
Error	13.8
Cost	716

\[\begin{array}{l} t_1 := t + y \cdot z\\ t_2 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq 1024955.113786615:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	9.7
Cost	712

\[\begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.144752934837097 \cdot 10^{-13}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	5.0
Cost	712

\[\begin{array}{l} t_1 := t + y \cdot z\\ \mathbf{if}\;z \leq -1849051290919909600:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.797961030596841 \cdot 10^{+41}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	0.1
Cost	576

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

Alternative 7
Error	25.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -3.257442775400132 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.936231027305437 \cdot 10^{-95}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	30.0
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))