Average Error: 0.0 → 0.0
Time: 18.6s
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 r129928 = x;
        double r129929 = r129928 * r129928;
        double r129930 = y;
        double r129931 = r129930 * r129930;
        double r129932 = r129929 + r129931;
        return r129932;
}
↓
double f(double x, double y) {
        double r129933 = x;
        double r129934 = y;
        double r129935 = r129934 * r129934;
        double r129936 = fma(r129933, r129933, r129935);
        return r129936;
}

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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))