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

Average Error: 0.0 → 0.0

Time: 6.6s

Precision: binary64

Cost: 960

Math

\[\frac{x - y}{2 - \left(x + y\right)} \]

↓

\[\begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t_0} - \frac{y}{t_0} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (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 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

↓

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

↓

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

↓

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

↓

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]
   Proof
   (/.f64 (-.f64 x y) (-.f64 (-.f64 2 x) y)): 0 points increase in error, 0 points decrease in error
   (/.f64 (-.f64 x y) (Rewrite<= associate--r+_binary64 (-.f64 2 (+.f64 x y)))): 0 points increase in error, 0 points decrease in error

3. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}} \]

4. Final simplification 0.0

   \[\leadsto \frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \]

Alternatives

Alternative 1
Error	17.5
Cost	849

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8000000000000 \lor \neg \left(y \leq 2 \cdot 10^{+120}\right) \land y \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	17.0
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-59}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 3
Error	17.1
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;1 - \frac{x}{\frac{y}{2}}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-59}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 4
Error	16.9
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+21}:\\ \;\;\;\;-1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{x}{\frac{y}{2}}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-59}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 5
Error	24.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-59}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6500000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6
Error	0.0
Cost	576

\[\frac{x - y}{2 - \left(x + y\right)} \]

Alternative 7
Error	24.3
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 49000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8
Error	39.9
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))