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 r163031 = x;
        double r163032 = r163031 * r163031;
        double r163033 = y;
        double r163034 = r163033 * r163033;
        double r163035 = r163032 + r163034;
        return r163035;
}
↓
double f(double x, double y) {
        double r163036 = x;
        double r163037 = y;
        double r163038 = r163037 * r163037;
        double r163039 = fma(r163036, r163036, r163038);
        return r163039;
}

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 2019198 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  (+ (* x x) (* y y)))