Average Error: 0.0 → 0.0
Time: 844.0ms
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 r301826 = x;
        double r301827 = y;
        double r301828 = r301826 + r301827;
        double r301829 = r301826 * r301827;
        double r301830 = r301828 - r301829;
        return r301830;
}
↓
double f(double x, double y) {
        double r301831 = 1.0;
        double r301832 = x;
        double r301833 = r301831 - r301832;
        double r301834 = y;
        double r301835 = fma(r301833, r301834, r301832);
        return r301835;
}

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 2020062 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))