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 r165511 = x;
        double r165512 = r165511 * r165511;
        double r165513 = y;
        double r165514 = r165513 * r165513;
        double r165515 = r165512 + r165514;
        return r165515;
}
↓
double f(double x, double y) {
        double r165516 = x;
        double r165517 = y;
        double r165518 = r165517 * r165517;
        double r165519 = fma(r165516, r165516, r165518);
        return r165519;
}

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 2019347 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))