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

Average Accuracy: 100.0% → 100.0%

Time: 7.9s

Precision: binary64

Cost: 960

Math

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

↓

\[\begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t_0} - \frac{y}{t_0} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

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
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
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) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

↓

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

↓

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

↓

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $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. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]
   Proof

   [Start] 100.0	\[ \frac{x - y}{2 - \left(x + y\right)} \]
   associate--r+ [=>] 100.0	\[ \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	57.8%
Cost	1248

\[\begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-78}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-125}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-159}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-216}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-260}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-143}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.3:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Accuracy	58.0%
Cost	1248

\[\begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-89}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-125}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \frac{-1}{y}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-213}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-263}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-143}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3.3:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Accuracy	74.1%
Cost	1240

\[\begin{array}{l} t_0 := 2 \cdot \frac{y}{x} + -1\\ t_1 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Accuracy	73.5%
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Accuracy	61.0%
Cost	852

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+39}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-90}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-128}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-123}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Accuracy	72.7%
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2.8:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Accuracy	100.0%
Cost	576

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

Alternative 8
Accuracy	62.7%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 26500000000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9
Accuracy	37.5%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023122 
(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))))