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

Average Error: 0.0 → 0.0

Time: 4.5s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{200 \cdot x + -200 \cdot y} \]

3. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]
   Proof
   (fma.f64 -200 y (*.f64 200 x)): 0 points increase in error, 0 points decrease in error
   (Rewrite<= fma-def_binary64 (+.f64 (*.f64 -200 y) (*.f64 200 x))): 7 points increase in error, 0 points decrease in error
   (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 200 x) (*.f64 -200 y))): 0 points increase in error, 0 points decrease in error

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6720

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

Alternative 2
Error	16.9
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -4.554913430096951 \cdot 10^{-13}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 1.342708388736852 \cdot 10^{-17}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;y \leq 451237092.5939129:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 9.769044260590569 \cdot 10^{+94}:\\ \;\;\;\;200 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]

Alternative 3
Error	0.0
Cost	320

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

Alternative 4
Error	31.8
Cost	192

\[200 \cdot x \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))