Average Error: 0.0 → 0.0
Time: 19.1s
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 r145285 = x;
        double r145286 = r145285 * r145285;
        double r145287 = y;
        double r145288 = r145287 * r145287;
        double r145289 = r145286 + r145288;
        return r145289;
}
↓
double f(double x, double y) {
        double r145290 = x;
        double r145291 = y;
        double r145292 = r145291 * r145291;
        double r145293 = fma(r145290, r145290, r145292);
        return r145293;
}

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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))