Data.Colour.RGB:hslsv from colour-2.3.3, C

Average Error: 0.0 → 0.0

Time: 6.1s

Precision: binary64

Cost: 576

Math

\[\frac{x - y}{2 - \left(x + y\right)} \]

↓

\[\frac{x - y}{2 - \left(x + y\right)} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

↓

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

↓

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

↓

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

↓

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Final simplification 0.0

   \[\leadsto \frac{x - y}{2 - \left(x + y\right)} \]

Alternatives

Alternative 1
Error	16.1
Cost	976

\[\begin{array}{l} t_0 := 1 + \frac{x}{\frac{y}{-2}}\\ \mathbf{if}\;y \leq -1609937080.519046:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6904691148230.956:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 9.127801624445415 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.912935470652846 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.0
Cost	976

\[\begin{array}{l} t_0 := 1 + \frac{x}{\frac{y}{-2}}\\ \mathbf{if}\;y \leq -1609937080.519046:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6904691148230.956:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 9.127801624445415 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.912935470652846 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	23.8
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1609937080.519046:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.272522764648639 \cdot 10^{-70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.0075617377262683 \cdot 10^{-44}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6904691148230.956:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.127801624445415 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.912935470652846 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	23.7
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1609937080.519046:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 7.272522764648639 \cdot 10^{-70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.0075617377262683 \cdot 10^{-44}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6904691148230.956:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.127801624445415 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.912935470652846 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	23.8
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1609937080.519046:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6904691148230.956:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.127801624445415 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.912935470652846 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	16.3
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1609937080.519046:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6904691148230.956:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 9.127801624445415 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.912935470652846 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	39.3
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))