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

Average Error: 0.0 → 0.0

Time: 7.3s

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	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. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	25.7
Cost	1120

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+62}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+26}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-160}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-233}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-156}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-112}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 195:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	25.7
Cost	1120

\[\begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-233}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 195:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	18.1
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-112}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-12}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	17.9
Cost	1112

\[\begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-110}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-12}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	25.1
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+62}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-154}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-112}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	18.1
Cost	856

\[\begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-108}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 195:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	24.6
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 195:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	0.0
Cost	576

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

Alternative 9
Error	39.8
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022329 
(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))))