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

Average Error: 0.04% → 0.04%

Time: 9.0s

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	38.73%
Cost	1112

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.8:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-162}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-179}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-188}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	39.06%
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -2:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-62}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-162}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-181}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-189}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	36.37%
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -400000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-285}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-279}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	36.79%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -650000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.52 \cdot 10^{-282}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-283}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	26.31%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+74} \lor \neg \left(y \leq 7 \cdot 10^{+49}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 6
Error	24.83%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-9} \lor \neg \left(x \leq 14\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 7
Error	38.36%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	61.43%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023125 
(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))))