Average Error: 0.0 → 0.0
Time: 906.0ms
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 r210229 = x;
        double r210230 = y;
        double r210231 = r210229 + r210230;
        double r210232 = r210229 * r210230;
        double r210233 = r210231 - r210232;
        return r210233;
}
↓
double f(double x, double y) {
        double r210234 = 1.0;
        double r210235 = x;
        double r210236 = r210234 - r210235;
        double r210237 = y;
        double r210238 = fma(r210236, r210237, r210235);
        return r210238;
}

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 2019353 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))