Average Error: 0.0 → 0.0
Time: 2.4s
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 r21794 = x;
        double r21795 = y;
        double r21796 = r21794 + r21795;
        double r21797 = r21794 * r21795;
        double r21798 = r21796 - r21797;
        return r21798;
}
↓
double f(double x, double y) {
        double r21799 = 1.0;
        double r21800 = x;
        double r21801 = r21799 - r21800;
        double r21802 = y;
        double r21803 = fma(r21801, r21802, r21800);
        return r21803;
}

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 2019310 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))