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

Average Error: 0.0 → 0.0

Time: 7.8s

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	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

   \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]
   Proof
   (/.f64 (-.f64 x y) (-.f64 (-.f64 2 x) y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (-.f64 x y) (Rewrite<= associate--r+_binary64 (-.f64 2 (+.f64 x y)))): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	25.1
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -8.201056688049326 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.1024076725150928 \cdot 10^{-259}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq 1.3257957287716956 \cdot 10^{-149}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.518753335729693 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	17.3
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ t_1 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -2.568444241552186 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.561950186669376 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1575088066995321 \cdot 10^{-66}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.8761159927652646 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	25.3
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -8.201056688049326 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.1024076725150928 \cdot 10^{-259}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.3257957287716956 \cdot 10^{-149}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 8.05218369403718 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	25.2
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -8.201056688049326 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.1024076725150928 \cdot 10^{-259}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq 1.3257957287716956 \cdot 10^{-149}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 8.05218369403718 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	16.2
Cost	584

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -8.201056688049326 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.518753335729693 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	24.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -8.201056688049326 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.05218369403718 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	40.0
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022308 
(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))))