Average Error: 0.0 → 0.0
Time: 6.5s
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 r144358 = x;
        double r144359 = y;
        double r144360 = r144358 + r144359;
        double r144361 = r144358 * r144359;
        double r144362 = r144360 - r144361;
        return r144362;
}
↓
double f(double x, double y) {
        double r144363 = 1.0;
        double r144364 = x;
        double r144365 = r144363 - r144364;
        double r144366 = y;
        double r144367 = fma(r144365, r144366, r144364);
        return r144367;
}

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)))