Data.Colour.CIE:lightness from colour-2.3.3

Average Accuracy: 100.0% → 100.0%

Time: 2.1s

Precision: binary64

Cost: 6592

Math

\[x \cdot 116 - 16 \]

↓

\[\mathsf{fma}\left(x, 116, -16\right) \]

FPCore

(FPCore (x) :precision binary64 (- (* x 116.0) 16.0))

↓

(FPCore (x) :precision binary64 (fma x 116.0 -16.0))

C

double code(double x) {
	return (x * 116.0) - 16.0;
}

↓

double code(double x) {
	return fma(x, 116.0, -16.0);
}

Julia

function code(x)
	return Float64(Float64(x * 116.0) - 16.0)
end

↓

function code(x)
	return fma(x, 116.0, -16.0)
end

Wolfram

code[x_] := N[(N[(x * 116.0), $MachinePrecision] - 16.0), $MachinePrecision]

↓

code[x_] := N[(x * 116.0 + -16.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot 116 - 16 \]

2. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116, -16\right)} \]
   Proof

   [Start] 100.0	\[ x \cdot 116 - 16 \]
   fma-neg [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(x, 116, -16\right)} \]
   metadata-eval [=>] 100.0	\[ \mathsf{fma}\left(x, 116, \color{blue}{-16}\right) \]

3. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, 116, -16\right) \]

Alternatives

Alternative 1
Accuracy	97.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.136:\\ \;\;\;\;x \cdot 116\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-16\\ \mathbf{else}:\\ \;\;\;\;x \cdot 116\\ \end{array} \]

Alternative 2
Accuracy	100.0%
Cost	320

\[-16 + x \cdot 116 \]

Alternative 3
Accuracy	50.7%
Cost	64

\[-16 \]

Reproduce

herbie shell --seed 2023129 
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116.0) 16.0))