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

Average Error: 0.0 → 0.0

Time: 1.8s

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 0.0

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

2. Taylor expanded in x around 0 0.0

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

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.2
Cost	721

\[\begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot -500\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+31} \lor \neg \left(y \leq -1.05 \cdot 10^{-27}\right) \land y \leq 1.05 \cdot 10^{-32}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	31.7
Cost	192

\[y \cdot -500 \]

Reproduce

herbie shell --seed 2023039 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))