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

Average Error: 0.04% → 0.04%

Time: 8.1s

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	0.04%
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	27.2%
Cost	1376

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-75}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-128}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	38.93%
Cost	1112

\[\begin{array}{l} t_0 := -1 + \frac{y}{x}\\ t_1 := 1 - \frac{x}{y}\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-51}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-297}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	39.18%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-219}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-297}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	40.2%
Cost	856

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+106}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-219}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-297}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	26.94%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+65}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-6}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-51} \lor \neg \left(x \leq 4.15 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 6
Error	26.84%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+64}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(0.5 + x \cdot 0.25\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 7
Error	26.99%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+64}:\\ \;\;\;\;\frac{-1}{\frac{x}{x - y}}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-6}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(0.5 + x \cdot 0.25\right)\\ \mathbf{elif}\;x \leq 1.58 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 8
Error	39.14%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -4.35 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.12 \cdot 10^{-219}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-295}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9
Error	38.8%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+66}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 10
Error	61.93%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023088 
(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))))