Average Error: 0.0 → 0.0
Time: 7.5s
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 r10826358 = x;
        double r10826359 = y;
        double r10826360 = r10826358 + r10826359;
        double r10826361 = r10826358 * r10826359;
        double r10826362 = r10826360 - r10826361;
        return r10826362;
}
↓
double f(double x, double y) {
        double r10826363 = 1.0;
        double r10826364 = x;
        double r10826365 = r10826363 - r10826364;
        double r10826366 = y;
        double r10826367 = fma(r10826365, r10826366, r10826364);
        return r10826367;
}

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)))