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

Average Accuracy: 87.1% → 87.1%

Time: 1.6s

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	87.1%
Target	87.1%
Herbie	87.1%

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

Derivation

1. Initial program 89.0%

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

2. Simplified 89.1%

   \[\leadsto \color{blue}{1 - \frac{y}{x}} \]
   Step-by-step derivation

   [Start] 89.0	\[ \frac{x - y}{x} \]
   div-sub [=>] 89.1	\[ \color{blue}{\frac{x}{x} - \frac{y}{x}} \]
   *-inverses [=>] 89.1	\[ \color{blue}{1} - \frac{y}{x} \]

3. Final simplification 89.1%

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

Alternatives

Alternative 1
Accuracy	58.2%
Cost	785

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-125}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-208} \lor \neg \left(x \leq 1.35 \cdot 10^{-92}\right) \land x \leq 3.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Accuracy	50.8%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023157 
(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))