Average Error: 0.0 → 0.0
Time: 25.9s
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 r144823 = x;
        double r144824 = r144823 * r144823;
        double r144825 = y;
        double r144826 = r144825 * r144825;
        double r144827 = r144824 + r144826;
        return r144827;
}
↓
double f(double x, double y) {
        double r144828 = x;
        double r144829 = y;
        double r144830 = r144829 * r144829;
        double r144831 = fma(r144828, r144828, r144830);
        return r144831;
}

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 2019199 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  (+ (* x x) (* y y)))