Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Precision: binary64

Cost: 320

Math

\[x \cdot \left(1 - y\right) \]

↓

\[x - x \cdot y \]

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

   \[x \cdot \left(1 - y\right) \]

2. Simplified 100.0%

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

   [Start] 100.0%	\[ x \cdot \left(1 - y\right) \]
   distribute-lft-out-- [<=] 100.0%	\[ \color{blue}{x \cdot 1 - x \cdot y} \]
   *-rgt-identity [=>] 100.0%	\[ \color{blue}{x} - x \cdot y \]

3. Final simplification 100.0%

   \[\leadsto x - x \cdot y \]

Alternatives

Alternative 1
Accuracy	100.0%
Cost	320

\[x - x \cdot y \]

Alternative 2
Accuracy	97.6%
Cost	521

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	100.0%
Cost	320

\[x \cdot \left(1 - y\right) \]

Alternative 4
Accuracy	50.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023263 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))