Average Error: 0.0 → 0.0
Time: 12.6s
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 r146250 = x;
        double r146251 = r146250 * r146250;
        double r146252 = y;
        double r146253 = r146252 * r146252;
        double r146254 = r146251 + r146253;
        return r146254;
}
↓
double f(double x, double y) {
        double r146255 = x;
        double r146256 = y;
        double r146257 = r146256 * r146256;
        double r146258 = fma(r146255, r146255, r146257);
        return r146258;
}

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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))