Average Error: 0.0 → 0.0
Time: 7.1s
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 r134492 = x;
        double r134493 = y;
        double r134494 = r134492 + r134493;
        double r134495 = r134492 * r134493;
        double r134496 = r134494 - r134495;
        return r134496;
}
↓
double f(double x, double y) {
        double r134497 = 1.0;
        double r134498 = x;
        double r134499 = r134497 - r134498;
        double r134500 = y;
        double r134501 = fma(r134499, r134500, r134498);
        return r134501;
}

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 2019325 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))