Average Error: 0.0 → 0.0
Time: 592.0ms
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 r261925 = x;
        double r261926 = y;
        double r261927 = r261925 + r261926;
        double r261928 = r261925 * r261926;
        double r261929 = r261927 - r261928;
        return r261929;
}
↓
double f(double x, double y) {
        double r261930 = 1.0;
        double r261931 = x;
        double r261932 = r261930 - r261931;
        double r261933 = y;
        double r261934 = fma(r261932, r261933, r261931);
        return r261934;
}

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 2020018 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))