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

Average Error: 0.0 → 0.0

Time: 11.9s

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	0.0
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. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.2
Cost	976

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -7.4 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-96}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y} \cdot 2 + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 2
Error	16.4
Cost	850

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-12} \lor \neg \left(x \leq -1.65 \cdot 10^{-77}\right) \land \left(x \leq -2.6 \cdot 10^{-97} \lor \neg \left(x \leq 5.8 \cdot 10^{+63}\right)\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]

Alternative 3
Error	16.6
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-77} \lor \neg \left(x \leq -8.5 \cdot 10^{-95}\right) \land x \leq 3.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	16.4
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-77} \lor \neg \left(x \leq -3 \cdot 10^{-95}\right) \land x \leq 3.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 5
Error	16.4
Cost	848

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ t_1 := \frac{x}{y} + -1\\ \mathbf{if}\;x \leq -7.4 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 6
Error	16.9
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-74}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-95}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	31.8
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023054 
(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)))