Average Error: 0.0 → 0.0
Time: 7.5s
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 r186255 = x;
        double r186256 = y;
        double r186257 = r186255 + r186256;
        double r186258 = r186255 * r186256;
        double r186259 = r186257 - r186258;
        return r186259;
}
↓
double f(double x, double y) {
        double r186260 = 1.0;
        double r186261 = x;
        double r186262 = r186260 - r186261;
        double r186263 = y;
        double r186264 = fma(r186262, r186263, r186261);
        return r186264;
}

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 2019196 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))