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

Average Error: 0.0 → 0.0

Time: 2.5s

Precision: binary64

Cost: 384

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -(y / x) + 1.0d0
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[((-N[(y / x), $MachinePrecision]) + 1.0), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[1 - \frac{y}{x} \]

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{1 + -1 \cdot \frac{y}{x}} \]

3. Simplified 0.0

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

   [Start] 0.0	\[ 1 + -1 \cdot \frac{y}{x} \]
   rational_best-simplify-1 [=>] 0.0	\[ \color{blue}{-1 \cdot \frac{y}{x} + 1} \]
   rational_best-simplify-2 [=>] 0.0	\[ \color{blue}{\frac{y}{x} \cdot -1} + 1 \]
   rational_best-simplify-12 [=>] 0.0	\[ \color{blue}{\left(-\frac{y}{x}\right)} + 1 \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	19.3
Cost	784

\[\begin{array}{l} t_0 := -\frac{y}{x}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	27.3
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023092 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- 1.0 (/ y x))

  (/ (- x y) x))