Average Error: 0.0 → 0.0
Time: 607.0ms
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 r247258 = x;
        double r247259 = y;
        double r247260 = r247258 + r247259;
        double r247261 = r247258 * r247259;
        double r247262 = r247260 - r247261;
        return r247262;
}
↓
double f(double x, double y) {
        double r247263 = 1.0;
        double r247264 = x;
        double r247265 = r247263 - r247264;
        double r247266 = y;
        double r247267 = fma(r247265, r247266, r247264);
        return r247267;
}

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 2020027 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))