Average Error: 0.0 → 0.0
Time: 902.0ms
Precision: 64
\[x \cdot x + y \cdot y\]
↓
\[\mathsf{fma}\left(x, x, y \cdot y\right)\]
x \cdot x + y \cdot y
↓
\mathsf{fma}\left(x, x, y \cdot y\right)
double f(double x, double y) {
        double r201654 = x;
        double r201655 = r201654 * r201654;
        double r201656 = y;
        double r201657 = r201656 * r201656;
        double r201658 = r201655 + r201657;
        return r201658;
}
↓
double f(double x, double y) {
        double r201659 = x;
        double r201660 = y;
        double r201661 = r201660 * r201660;
        double r201662 = fma(r201659, r201659, r201661);
        return r201662;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot x + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, y \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, y \cdot y\right)\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))