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

Percentage Accurate: 100.0% → 100.0%

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	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	100.0%
Cost	576

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

Alternative 2
Accuracy	57.4%
Cost	1376

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -2800000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-187}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-235}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	71.1%
Cost	1376

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1900000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-60}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2500000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+122}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Accuracy	57.2%
Cost	1120

\[\begin{array}{l} \mathbf{if}\;x \leq -10000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-90}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-188}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-235}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-161}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Accuracy	57.1%
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -6000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-91}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-235}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Accuracy	74.7%
Cost	648

\[\begin{array}{l} \mathbf{if}\;x \leq -15200000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \]

Alternative 7
Accuracy	74.7%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -960000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 8
Accuracy	62.3%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9
Accuracy	37.6%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023269 
(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))))