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

Average Error: 0.04% → 0.04%

Time: 5.1s

Precision: binary64

Cost: 704

Math

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

↓

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

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	0.04%
Target	0.04%
Herbie	0.04%

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

Derivation

1. Initial program 0.04

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

2. Applied egg-rr 0.04

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

3. Final simplification 0.04

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

Alternatives

Alternative 1
Error	25.62%
Cost	978

\[\begin{array}{l} \mathbf{if}\;y \leq -250000000 \lor \neg \left(y \leq 2.25 \cdot 10^{-28}\right) \land \left(y \leq 5.8 \cdot 10^{+27} \lor \neg \left(y \leq 7.2 \cdot 10^{+59}\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	26.19%
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -6000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+29}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	0.04%
Cost	448

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

Alternative 4
Error	49.45%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023089 
(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)))