Average Error: 0.0 → 0.0
Time: 652.0ms
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 r149919 = x;
        double r149920 = r149919 * r149919;
        double r149921 = y;
        double r149922 = r149921 * r149921;
        double r149923 = r149920 + r149922;
        return r149923;
}
↓
double f(double x, double y) {
        double r149924 = x;
        double r149925 = y;
        double r149926 = r149925 * r149925;
        double r149927 = fma(r149924, r149924, r149926);
        return r149927;
}

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 2020001 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))