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

Average Accuracy: 100.0% → 100.0%

Time: 11.3s

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	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	59.8%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-262}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-223}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+129}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Accuracy	61.8%
Cost	852

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-308}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-119}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 940:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Accuracy	74.3%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-23}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Accuracy	71.7%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ t_1 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -2 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Accuracy	72.1%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ t_1 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{x}\\ \end{array} \]

Alternative 6
Accuracy	87.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+19} \lor \neg \left(y \leq 3.2 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \end{array} \]

Alternative 7
Accuracy	60.4%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+129}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Accuracy	38.0%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023157 
(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))))