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

Average Error: 0.0 → 0.0

Time: 1.3s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

   \[\leadsto \color{blue}{\mathsf{fma}\left(500, x, -500 \cdot y\right)} \]
   Proof
   (fma.f64 500 x (*.f64 -500 y)): 0 points increase in error, 0 points decrease in error
   (Rewrite<= fma-def_binary64 (+.f64 (*.f64 500 x) (*.f64 -500 y))): 2 points increase in error, 0 points decrease in error

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-19}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-70}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

\[-500 \cdot y + 500 \cdot x \]

Alternative 3
Error	0.0
Cost	320

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

Alternative 4
Error	31.7
Cost	192

\[-500 \cdot y \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))