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

Average Error: 0.0 → 0.0

Time: 3.9s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[(-500.0 * y + 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. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(-500, y, 500 \cdot x\right)} \]
   Proof
   (fma.f64 -500 y (*.f64 500 x)): 0 points increase in error, 0 points decrease in error
   (Rewrite<= fma-def_binary64 (+.f64 (*.f64 -500 y) (*.f64 500 x))): 4 points increase in error, 0 points decrease in error
   (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 500 x) (*.f64 -500 y))): 0 points increase in error, 0 points decrease in error

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.3
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -6.278094753413382 \cdot 10^{+67}:\\ \;\;\;\;500 \cdot x\\ \mathbf{elif}\;x \leq -8.785330765823975 \cdot 10^{+22}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{elif}\;x \leq -1.3947860810472575 \cdot 10^{-53}:\\ \;\;\;\;500 \cdot x\\ \mathbf{elif}\;x \leq 13268111000.88214:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	31.0
Cost	192

\[500 \cdot x \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))