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

Average Error: 0.0 → 0.0

Time: 14.3s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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
    code = (y - x) / (x + (y - 2.0d0))
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 (y - x) / (x + (y - 2.0));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

   [Start] 0.0	\[ \frac{x - y}{2 - \left(x + y\right)} \]
   rational.json-simplify-50 [=>] 0.0	\[ \color{blue}{\frac{-\left(x - y\right)}{\left(x + y\right) - 2}} \]
   rational.json-simplify-12 [=>] 0.0	\[ \frac{\color{blue}{0 - \left(x - y\right)}}{\left(x + y\right) - 2} \]
   rational.json-simplify-45 [=>] 0.0	\[ \frac{\color{blue}{y - \left(x - 0\right)}}{\left(x + y\right) - 2} \]
   rational.json-simplify-5 [=>] 0.0	\[ \frac{y - \color{blue}{x}}{\left(x + y\right) - 2} \]
   rational.json-simplify-1 [=>] 0.0	\[ \frac{y - x}{\color{blue}{\left(y + x\right)} - 2} \]
   rational.json-simplify-48 [=>] 0.0	\[ \frac{y - x}{\color{blue}{x + \left(y - 2\right)}} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-45}:\\ \;\;\;\;-\frac{x}{x - 2}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{-2 \cdot y}{x}\\ \end{array} \]

Alternative 2
Error	25.9
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-164}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-153}:\\ \;\;\;\;--0.5 \cdot x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+14}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	17.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	17.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;-\frac{x}{x - 2}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	0.0
Cost	576

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

Alternative 6
Error	25.0
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -0.32:\\ \;\;\;\;-1 - \frac{2}{x}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-109}:\\ \;\;\;\;--0.5 \cdot x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7
Error	24.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Error	40.0
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023073 
(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))))