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

Average Error: 0.04% → 0.04%

Time: 6.8s

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	0.04%
Target	0.03%
Herbie	0.04%

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

Derivation

1. Initial program 0.04

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

2. Final simplification 0.04

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

Alternatives

Alternative 1
Error	40.51%
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-55}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-154}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-231}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-287}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	41.12%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-154}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-233}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-286}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 13500000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	40.73%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-154}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-235}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-287}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 880000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	26.51%
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -15500:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	27.08%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-149}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-122}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 6
Error	39.42%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-227}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-287}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4400000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7
Error	38.39%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 660000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Error	61.81%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023090 
(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))))