Average Error: 0.0 → 0.0
Time: 671.0ms
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 r268879 = x;
        double r268880 = y;
        double r268881 = r268879 + r268880;
        double r268882 = r268879 * r268880;
        double r268883 = r268881 - r268882;
        return r268883;
}
↓
double f(double x, double y) {
        double r268884 = 1.0;
        double r268885 = x;
        double r268886 = r268884 - r268885;
        double r268887 = y;
        double r268888 = fma(r268886, r268887, r268885);
        return r268888;
}

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 2019362 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))