Average Error: 0.0 → 0.0
Time: 7.4s
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 r158410 = x;
        double r158411 = y;
        double r158412 = r158410 + r158411;
        double r158413 = r158410 * r158411;
        double r158414 = r158412 - r158413;
        return r158414;
}
↓
double f(double x, double y) {
        double r158415 = 1.0;
        double r158416 = x;
        double r158417 = r158415 - r158416;
        double r158418 = y;
        double r158419 = fma(r158417, r158418, r158416);
        return r158419;
}

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 2019209 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))