Average Error: 0.0 → 0.0
Time: 44.0s
Precision: 64
\[\left(x + y\right) - x \cdot y\]
↓
\[\mathsf{fma}\left(x, 1 - y, y\right)\]
\left(x + y\right) - x \cdot y
↓
\mathsf{fma}\left(x, 1 - y, y\right)
double f(double x, double y) {
        double r11506524 = x;
        double r11506525 = y;
        double r11506526 = r11506524 + r11506525;
        double r11506527 = r11506524 * r11506525;
        double r11506528 = r11506526 - r11506527;
        return r11506528;
}
↓
double f(double x, double y) {
        double r11506529 = x;
        double r11506530 = 1.0;
        double r11506531 = y;
        double r11506532 = r11506530 - r11506531;
        double r11506533 = fma(r11506529, r11506532, r11506531);
        return r11506533;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 - y, y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, 1 - y, y\right)\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))