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

Average Error: 0.01% → 0%

Time: 1.7s

Precision: binary64

Cost: 6656

Math

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

↓

\[\mathsf{fma}\left(x, -y, x\right) \]

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.01

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

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, -y, x\right)} \]
   Proof

   [Start] 0.01	\[ x \cdot \left(1 - y\right) \]
   sub-neg [=>] 0.01	\[ x \cdot \color{blue}{\left(1 + \left(-y\right)\right)} \]
   distribute-lft-in [=>] 0.01	\[ \color{blue}{x \cdot 1 + x \cdot \left(-y\right)} \]
   +-commutative [=>] 0.01	\[ \color{blue}{x \cdot \left(-y\right) + x \cdot 1} \]
   *-rgt-identity [=>] 0.01	\[ x \cdot \left(-y\right) + \color{blue}{x} \]
   fma-def [=>] 0	\[ \color{blue}{\mathsf{fma}\left(x, -y, x\right)} \]

3. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, -y, x\right) \]

Alternatives

Alternative 1
Error	2.28%
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 2
Error	0.01%
Cost	320

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

Alternative 3
Error	41.86%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023102 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))