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

Average Accuracy: 100.0% → 100.0%

Time: 8.3s

Precision: binary64

Cost: 576

Math

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

↓

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

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(Float64(2.0 - 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[(N[(2.0 - x), $MachinePrecision] - y), $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. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	57.2%
Cost	988

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-189}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-169}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-70}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-6}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Accuracy	58.5%
Cost	988

\[\begin{array}{l} \mathbf{if}\;y \leq -31:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-189}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-173}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-69}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-42}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-6}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+26}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Accuracy	59.7%
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-168}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-47}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-5}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Accuracy	73.9%
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -31:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.00102:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	74.1%
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 80:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Accuracy	100.0%
Cost	576

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

Alternative 7
Accuracy	59.3%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+160}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Accuracy	37.8%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023135 
(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))))