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 r10941546 = x;
        double r10941547 = y;
        double r10941548 = r10941546 + r10941547;
        double r10941549 = r10941546 * r10941547;
        double r10941550 = r10941548 - r10941549;
        return r10941550;
}
↓
double f(double x, double y) {
        double r10941551 = 1.0;
        double r10941552 = x;
        double r10941553 = r10941551 - r10941552;
        double r10941554 = y;
        double r10941555 = fma(r10941553, r10941554, r10941552);
        return r10941555;
}

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 2019172 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))