Average Error: 0.0 → 0.0
Time: 839.0ms
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 r233265 = x;
        double r233266 = y;
        double r233267 = r233265 + r233266;
        double r233268 = r233265 * r233266;
        double r233269 = r233267 - r233268;
        return r233269;
}
↓
double f(double x, double y) {
        double r233270 = 1.0;
        double r233271 = x;
        double r233272 = r233270 - r233271;
        double r233273 = y;
        double r233274 = fma(r233272, r233273, r233271);
        return r233274;
}

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 2020046 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))