Average Error: 0.0 → 0.0
Time: 6.4s
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 r165669 = x;
        double r165670 = y;
        double r165671 = r165669 + r165670;
        double r165672 = r165669 * r165670;
        double r165673 = r165671 - r165672;
        return r165673;
}
↓
double f(double x, double y) {
        double r165674 = 1.0;
        double r165675 = x;
        double r165676 = r165674 - r165675;
        double r165677 = y;
        double r165678 = fma(r165676, r165677, r165675);
        return r165678;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))