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

Average Error: 0.0 → 0.0

Time: 9.0s

Precision: binary64

Cost: 832

Math

\[\frac{x - y}{x + y} \]

↓

\[\frac{x}{x + y} + \frac{-1}{\frac{x + y}{y}} \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (+ (/ x (+ x y)) (/ -1.0 (/ (+ x y) y))))

C

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

↓

double code(double x, double y) {
	return (x / (x + y)) + (-1.0 / ((x + y) / y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (x + y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / (x + y)) + ((-1.0d0) / ((x + y) / y))
end function

Java

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

↓

public static double code(double x, double y) {
	return (x / (x + y)) + (-1.0 / ((x + y) / y));
}

Python

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

↓

def code(x, y):
	return (x / (x + y)) + (-1.0 / ((x + y) / y))

Julia

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

↓

function code(x, y)
	return Float64(Float64(x / Float64(x + y)) + Float64(-1.0 / Float64(Float64(x + y) / y)))
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = (x / (x + y)) + (-1.0 / ((x + y) / y));
end

Wolfram

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

↓

code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{x + y} - \frac{y}{x + y} \]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{x + y} \]

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}} \]

3. Applied egg-rr 0.0

   \[\leadsto \frac{x}{x + y} - \color{blue}{{\left(\sqrt[3]{\frac{y}{x + y}}\right)}^{3}} \]

4. Applied egg-rr 0.0

   \[\leadsto \frac{x}{x + y} - \color{blue}{\frac{1}{\frac{y + x}{y}}} \]

5. Final simplification 0.0

   \[\leadsto \frac{x}{x + y} + \frac{-1}{\frac{x + y}{y}} \]

Alternatives

Alternative 1
Error	16.4
Cost	1240

\[\begin{array}{l} t_0 := 2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-52}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 600000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.6
Cost	1176

\[\begin{array}{l} t_0 := \frac{-y}{x + y}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+96}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-45}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;y \leq 38000000:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	16.3
Cost	1176

\[\begin{array}{l} t_0 := \frac{-y}{x + y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+40}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 27000000:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	16.5
Cost	1112

\[\begin{array}{l} t_0 := \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-45}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;y \leq 215000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	16.5
Cost	1112

\[\begin{array}{l} t_0 := \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;y \leq 88000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	16.9
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+93}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 200000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7
Error	16.8
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+94}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-45}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;y \leq 61000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Error	0.0
Cost	704

\[\frac{x}{x + y} - \frac{y}{x + y} \]

Alternative 9
Error	0.0
Cost	448

\[\frac{x - y}{x + y} \]

Alternative 10
Error	32.2
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022329 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))