Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[\left(x + y\right) - x \cdot y\]
↓
\[\mathsf{fma}\left(1 - x, y, x\right)\]
\left(x + y\right) - x \cdot y
↓
\mathsf{fma}\left(1 - x, y, x\right)
double f(double x, double y) {
        double r12328638 = x;
        double r12328639 = y;
        double r12328640 = r12328638 + r12328639;
        double r12328641 = r12328638 * r12328639;
        double r12328642 = r12328640 - r12328641;
        return r12328642;
}
↓
double f(double x, double y) {
        double r12328643 = 1.0;
        double r12328644 = x;
        double r12328645 = r12328643 - r12328644;
        double r12328646 = y;
        double r12328647 = fma(r12328645, r12328646, r12328644);
        return r12328647;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))