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

Average Error: 0.0 → 0.0

Time: 3.9s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.2
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -9.964282885721964 \cdot 10^{+31}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq -2.6679706475365947 \cdot 10^{-95}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{elif}\;x \leq -2.5637148537663068 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-58}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	31.5
Cost	192

\[x \cdot 500 \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))