Average Error: 0.0 → 0.0
Time: 6.5s
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 r146340 = x;
        double r146341 = y;
        double r146342 = r146340 + r146341;
        double r146343 = r146340 * r146341;
        double r146344 = r146342 - r146343;
        return r146344;
}
↓
double f(double x, double y) {
        double r146345 = 1.0;
        double r146346 = x;
        double r146347 = r146345 - r146346;
        double r146348 = y;
        double r146349 = fma(r146347, r146348, r146346);
        return r146349;
}

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 2019306 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))