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

Average Error: 0.05% → 0.02%

Time: 2.8s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.05

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

2. Taylor expanded in x around 0 0.05

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

3. Simplified 0.02

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

   [Start] 0.05	\[ 200 \cdot x + -200 \cdot y \]
   +-commutative [=>] 0.05	\[ \color{blue}{-200 \cdot y + 200 \cdot x} \]
   fma-def [=>] 0.02	\[ \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]

4. Final simplification 0.02

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

Alternatives

Alternative 1
Error	26.77%
Cost	721

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+64}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-37} \lor \neg \left(y \leq 1450000000\right) \land y \leq 5.9 \cdot 10^{+69}:\\ \;\;\;\;200 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]

Alternative 2
Error	0.05%
Cost	320

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

Alternative 3
Error	49.62%
Cost	192

\[-200 \cdot y \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))