Average Error: 0.0 → 0.0
Time: 861.0ms
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 r300943 = x;
        double r300944 = y;
        double r300945 = r300943 + r300944;
        double r300946 = r300943 * r300944;
        double r300947 = r300945 - r300946;
        return r300947;
}
↓
double f(double x, double y) {
        double r300948 = 1.0;
        double r300949 = x;
        double r300950 = r300948 - r300949;
        double r300951 = y;
        double r300952 = fma(r300950, r300951, r300949);
        return r300952;
}

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 2020060 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))