Average Error: 0.0 → 0.0
Time: 8.1s
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 r211607 = x;
        double r211608 = y;
        double r211609 = r211607 + r211608;
        double r211610 = r211607 * r211608;
        double r211611 = r211609 - r211610;
        return r211611;
}
↓
double f(double x, double y) {
        double r211612 = 1.0;
        double r211613 = x;
        double r211614 = r211612 - r211613;
        double r211615 = y;
        double r211616 = fma(r211614, r211615, r211613);
        return r211616;
}

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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))