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

Average Error: 0.0 → 0.0

Time: 12.6s

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	25.0
Cost	1112

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-220}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-278}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 530000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;1 - \frac{-2}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	25.1
Cost	1112

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{y}{x} - 1\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-277}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 48000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+62}:\\ \;\;\;\;1 - \frac{-2}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	25.1
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -2600000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-219}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-276}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 950000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;1 - \frac{-2}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	16.9
Cost	976

\[\begin{array}{l} t_0 := -\frac{y}{2 - y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 230000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - 2 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5
Error	17.0
Cost	912

\[\begin{array}{l} t_0 := -\frac{y}{2 - y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 210000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-y}\\ \end{array} \]

Alternative 6
Error	25.1
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-220}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	17.0
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.58 \cdot 10^{+44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+62}:\\ \;\;\;\;1 - \frac{-2}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	17.0
Cost	848

\[\begin{array}{l} t_0 := -\frac{y}{2 - y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3150000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 9
Error	8.7
Cost	776

\[\begin{array}{l} \mathbf{if}\;x \leq -235:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+78}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;-1 - 2 \cdot \left(-\frac{y}{x}\right)\\ \end{array} \]

Alternative 10
Error	8.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -0.74:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+78}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} - 1\\ \end{array} \]

Alternative 11
Error	24.4
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+96}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12
Error	39.3
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023077 
(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))))