Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B

Average Accuracy: 100.0% → 100.0%

Time: 2.0s

Precision: binary64

Cost: 6592

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

\[x + x \cdot y \]

Derivation

1. Initial program 100.0%

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

2. Simplified 100.0%

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

   [Start] 100.0	\[ x \cdot \left(y + 1\right) \]
   distribute-lft-in [=>] 100.0	\[ \color{blue}{x \cdot y + x \cdot 1} \]
   fma-def [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(x, y, x \cdot 1\right)} \]
   *-rgt-identity [=>] 100.0	\[ \mathsf{fma}\left(x, y, \color{blue}{x}\right) \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	97.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Accuracy	100.0%
Cost	320

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

Alternative 3
Accuracy	100.0%
Cost	320

\[x + x \cdot y \]

Alternative 4
Accuracy	51.2%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023160 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ x (* x y))

  (* x (+ y 1.0)))