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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Precision: binary64

Cost: 704

Math

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

↓

\[\begin{array}{l} \\ \frac{x}{x + y} - \frac{y}{x + y} \end{array} \]

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

MATLAB

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

↓

function tmp = code(x, y)
	tmp = (x / (x + y)) - (y / (x + 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[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 99.9%

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

2. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}} \]
   Step-by-step derivation

   [Start] 99.9%	\[ \frac{x - y}{x + y} \]
   div-sub [=>] 99.9%	\[ \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}} \]

3. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	704

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

Alternative 2
Accuracy	72.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+45} \lor \neg \left(y \leq 2.5 \cdot 10^{-128}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 3
Accuracy	71.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+52}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-128}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Accuracy	100.0%
Cost	448

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

Alternative 5
Accuracy	71.6%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Accuracy	50.4%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023167 
(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)))