Average Error: 0.0 → 0.0
Time: 855.0ms
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 r300367 = x;
        double r300368 = y;
        double r300369 = r300367 + r300368;
        double r300370 = r300367 * r300368;
        double r300371 = r300369 - r300370;
        return r300371;
}
↓
double f(double x, double y) {
        double r300372 = 1.0;
        double r300373 = x;
        double r300374 = r300372 - r300373;
        double r300375 = y;
        double r300376 = fma(r300374, r300375, r300373);
        return r300376;
}

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 2020057 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))