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

Average Error: 0.05% → 0.02%

Time: 4.1s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[(x * 200.0 + N[(-200.0 * y), $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. Applied egg-rr 0.02

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

4. Final simplification 0.02

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

Alternatives

Alternative 1
Error	0.03%
Cost	6720

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

Alternative 2
Error	26.09%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-51}:\\ \;\;\;\;x \cdot 200\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+53}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 200\\ \end{array} \]

Alternative 3
Error	0.05%
Cost	448

\[-200 \cdot y + x \cdot 200 \]

Alternative 4
Error	0.05%
Cost	320

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

Alternative 5
Error	50.33%
Cost	192

\[-200 \cdot y \]

Reproduce

herbie shell --seed 2023088 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))