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

Percentage Accurate: 99.9% → 100.0%

Time: 4.3s

Precision: binary64

Cost: 6720

Math

\[200 \cdot \left(x - y\right) \]

↓

\[\mathsf{fma}\left(200, x, -200 \cdot y\right) \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

↓

(FPCore (x y) :precision binary64 (fma 200.0 x (* -200.0 y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

↓

double code(double x, double y) {
	return fma(200.0, x, (-200.0 * y));
}

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

↓

function code(x, y)
	return fma(200.0, x, Float64(-200.0 * y))
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(200.0 * x + N[(-200.0 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{200 \cdot x + -200 \cdot y} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]
   Step-by-step derivation

   [Start] 99.9%	\[ 200 \cdot x + -200 \cdot y \]
   +-commutative [=>] 99.9%	\[ \color{blue}{-200 \cdot y + 200 \cdot x} \]
   fma-def [=>] 100.0%	\[ \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]

4. Taylor expanded in y around 0 99.9%

   \[\leadsto \color{blue}{-200 \cdot y + 200 \cdot x} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(200, x, -200 \cdot y\right)} \]
   Step-by-step derivation

   [Start] 99.9%	\[ -200 \cdot y + 200 \cdot x \]
   +-commutative [=>] 99.9%	\[ \color{blue}{200 \cdot x + -200 \cdot y} \]
   fma-def [=>] 100.0%	\[ \color{blue}{\mathsf{fma}\left(200, x, -200 \cdot y\right)} \]

6. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(200, x, -200 \cdot y\right) \]

Alternatives

Alternative 1
Accuracy	100.0%
Cost	6720

\[\mathsf{fma}\left(200, x, -200 \cdot y\right) \]

Alternative 2
Accuracy	100.0%
Cost	6720

\[\mathsf{fma}\left(-200, y, 200 \cdot x\right) \]

Alternative 3
Accuracy	75.2%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+44}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-45}:\\ \;\;\;\;200 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]

Alternative 4
Accuracy	99.9%
Cost	320

\[200 \cdot \left(x - y\right) \]

Alternative 5
Accuracy	50.2%
Cost	192

\[-200 \cdot y \]

Reproduce

herbie shell --seed 2023272 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))