Data.Colour.CIE:cieLABView from colour-2.3.3, B

Average Accuracy: 100.0% → 100.0%

Time: 3.3s

Precision: binary64

Cost: 6720

Math

\[500 \cdot \left(x - y\right) \]

↓

\[\mathsf{fma}\left(y, -500, 500 \cdot x\right) \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

↓

(FPCore (x y) :precision binary64 (fma y -500.0 (* 500.0 x)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

↓

double code(double x, double y) {
	return fma(y, -500.0, (500.0 * x));
}

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

↓

function code(x, y)
	return fma(y, -500.0, Float64(500.0 * x))
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(y * -500.0 + N[(500.0 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{500 \cdot x + -500 \cdot y} \]

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, -500, 500 \cdot x\right)} \]
   Proof

   [Start] 100.0	\[ 500 \cdot x + -500 \cdot y \]
   +-commutative [=>] 100.0	\[ \color{blue}{-500 \cdot y + 500 \cdot x} \]
   *-commutative [=>] 100.0	\[ \color{blue}{y \cdot -500} + 500 \cdot x \]
   fma-def [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(y, -500, 500 \cdot x\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, -500, 500 \cdot x\right) \]

Alternatives

Alternative 1
Accuracy	74.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+41}:\\ \;\;\;\;500 \cdot x\\ \mathbf{elif}\;x \leq 0.024:\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \]

Alternative 2
Accuracy	100.0%
Cost	320

\[500 \cdot \left(x - y\right) \]

Alternative 3
Accuracy	50.6%
Cost	192

\[y \cdot -500 \]

Reproduce

herbie shell --seed 2023137 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))