Average Error: 0.0 → 0.0
Time: 928.0ms
Precision: binary64
\[\left(x + y\right) - x \cdot y \]
↓
\[\mathsf{fma}\left(y, 1 - x, x\right) \]
\left(x + y\right) - x \cdot y
↓
\mathsf{fma}\left(y, 1 - x, x\right)

(FPCore (x y) :precision binary64 (- (+ x y) (* x y)))
↓
(FPCore (x y) :precision binary64 (fma y (- 1.0 x) x))
double code(double x, double y) {
	return (x + y) - (x * y);
}
↓
double code(double x, double y) {
	return fma(y, (1.0 - x), x);
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{\left(y + x\right) - y \cdot x} \]

  3. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, 1 - x, x\right)} \]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, 1 - x, x\right) \]

Reproduce

herbie shell --seed 2021275 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))