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

Average Error: 0.0 → 0.0

Time: 1.7s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = 1.0d0 - (y / x)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[(1.0 - N[(y / x), $MachinePrecision]), $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. Simplified 0.0

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

   [Start] 0.0	\[ \frac{x - y}{x} \]
   div-sub [=>] 0.0	\[ \color{blue}{\frac{x}{x} - \frac{y}{x}} \]
   *-inverses [=>] 0.0	\[ \color{blue}{1} - \frac{y}{x} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	21.3
Cost	1051

\[\begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+25} \lor \neg \left(y \leq -1.18 \cdot 10^{-7}\right) \land \left(y \leq -3.1 \cdot 10^{-33} \lor \neg \left(y \leq -6.6 \cdot 10^{-70}\right) \land \left(y \leq -2.2 \cdot 10^{-158} \lor \neg \left(y \leq 4.5 \cdot 10^{+137}\right)\right)\right):\\ \;\;\;\;\frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	27.6
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023073 
(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))