Average Error: 0.0 → 0.0
Time: 624.0ms
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 r134262 = x;
        double r134263 = r134262 * r134262;
        double r134264 = y;
        double r134265 = r134264 * r134264;
        double r134266 = r134263 + r134265;
        return r134266;
}
↓
double f(double x, double y) {
        double r134267 = x;
        double r134268 = y;
        double r134269 = r134268 * r134268;
        double r134270 = fma(r134267, r134267, r134269);
        return r134270;
}

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 2020060 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))