Average Error: 0.0 → 0.0
Time: 1.5s
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 r170278 = x;
        double r170279 = r170278 * r170278;
        double r170280 = y;
        double r170281 = r170280 * r170280;
        double r170282 = r170279 + r170281;
        return r170282;
}
↓
double f(double x, double y) {
        double r170283 = x;
        double r170284 = y;
        double r170285 = r170284 * r170284;
        double r170286 = fma(r170283, r170283, r170285);
        return r170286;
}

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 2020002 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))