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

Average Error: 0.0 → 0.1

Time: 9.9s

Precision: binary64

Cost: 1216

Math

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

↓

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

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (+ y -2.0)))) (- (/ (+ y x) t_0) (/ (* 2.0 x) 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 = x + (y + -2.0);
	return ((y + x) / t_0) - ((2.0 * x) / 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 = x + (y + (-2.0d0))
    code = ((y + x) / t_0) - ((2.0d0 * x) / 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 = x + (y + -2.0);
	return ((y + x) / t_0) - ((2.0 * x) / t_0);
}

Python

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

↓

def code(x, y):
	t_0 = x + (y + -2.0)
	return ((y + x) / t_0) - ((2.0 * x) / 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(x + Float64(y + -2.0))
	return Float64(Float64(Float64(y + x) / t_0) - Float64(Float64(2.0 * x) / t_0))
end

MATLAB

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

↓

function tmp = code(x, y)
	t_0 = x + (y + -2.0);
	tmp = ((y + x) / t_0) - ((2.0 * x) / 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[(x + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(y + x), $MachinePrecision] / t$95$0), $MachinePrecision] - N[(N[(2.0 * x), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Target

Original	0.0
Target	0.0
Herbie	0.1

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

   [Start] 0.0	\[ \frac{x - y}{2 - \left(x + y\right)} \]
   rational_best-simplify-58 [=>] 0.0	\[ \frac{x - y}{\color{blue}{\left(2 - y\right) - x}} \]

3. Applied egg-rr 0.0

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

4. Simplified 0.1

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

   [Start] 0.0	\[ \left(\frac{y}{x + \left(y + -2\right)} + \frac{x}{x + \left(y + -2\right)}\right) - 2 \cdot \frac{x}{x + \left(y + -2\right)} \]
   rational_best-simplify-76 [=>] 0.0	\[ \color{blue}{\frac{y + x}{x + \left(y + -2\right)}} - 2 \cdot \frac{x}{x + \left(y + -2\right)} \]
   rational_best-simplify-62 [=>] 0.1	\[ \frac{y + x}{x + \left(y + -2\right)} - \color{blue}{\frac{x \cdot 2}{x + \left(y + -2\right)}} \]
   rational_best-simplify-1 [<=] 0.1	\[ \frac{y + x}{x + \left(y + -2\right)} - \frac{\color{blue}{2 \cdot x}}{x + \left(y + -2\right)} \]

5. Final simplification 0.1

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

Alternatives

Alternative 1
Error	0.0
Cost	960

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

Alternative 2
Error	25.0
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-138}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-194}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-276}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-252}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	0.1
Cost	832

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

Alternative 4
Error	15.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+17}:\\ \;\;\;\;1 - 2 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{\left(2 - y\right) - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \]

Alternative 5
Error	15.9
Cost	712

\[\begin{array}{l} t_0 := \frac{y}{y + \left(x + -2\right)}\\ \mathbf{if}\;y \leq -6.3 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0055:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	24.3
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-276}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-250}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7
Error	16.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -90000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 61000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	16.2
Cost	584

\[\begin{array}{l} t_0 := \frac{y}{y - 2}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	0.0
Cost	576

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

Alternative 10
Error	23.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -3800000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 61000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11
Error	39.4
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023101 
(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))))