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

Average Error: 0.0 → 0.0

Time: 2.6s

Precision: binary64

Cost: 1600

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x - y}{x + y}\\ t_0 \cdot \left(t_0 \cdot \frac{1}{t_0}\right) \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (+ x y)))) (* t_0 (* t_0 (/ 1.0 t_0)))))

C

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

↓

double code(double x, double y) {
	double t_0 = (x - y) / (x + y);
	return t_0 * (t_0 * (1.0 / t_0));
}

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
    real(8) :: t_0
    t_0 = (x - y) / (x + y)
    code = t_0 * (t_0 * (1.0d0 / t_0))
end function

Java

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

↓

public static double code(double x, double y) {
	double t_0 = (x - y) / (x + y);
	return t_0 * (t_0 * (1.0 / t_0));
}

Python

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

↓

def code(x, y):
	t_0 = (x - y) / (x + y)
	return t_0 * (t_0 * (1.0 / t_0))

Julia

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

↓

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(x + y))
	return Float64(t_0 * Float64(t_0 * Float64(1.0 / t_0)))
end

MATLAB

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

↓

function tmp = code(x, y)
	t_0 = (x - y) / (x + y);
	tmp = t_0 * (t_0 * (1.0 / t_0));
end

Wolfram

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

↓

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(t$95$0 * N[(t$95$0 * N[(1.0 / t$95$0), $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

   \[\leadsto \color{blue}{\frac{x - y}{x + y} \cdot \left(\frac{x - y}{x + y} \cdot \frac{1}{\frac{x - y}{x + y}}\right)} \]

3. Final simplification 0.0

   \[\leadsto \frac{x - y}{x + y} \cdot \left(\frac{x - y}{x + y} \cdot \frac{1}{\frac{x - y}{x + y}}\right) \]

Alternatives

Alternative 1
Error	16.1
Cost	712

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -0.0038:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.165:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	15.7
Cost	712

\[\begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -0.0023:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \frac{x}{y} - 1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.0
Cost	448

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

Alternative 4
Error	16.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -0.003:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-11}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	32.2
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023090 
(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)))