Average Error: 0.0 → 0.0
Time: 670.0ms
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 r163785 = x;
        double r163786 = r163785 * r163785;
        double r163787 = y;
        double r163788 = r163787 * r163787;
        double r163789 = r163786 + r163788;
        return r163789;
}
↓
double f(double x, double y) {
        double r163790 = x;
        double r163791 = y;
        double r163792 = r163791 * r163791;
        double r163793 = fma(r163790, r163790, r163792);
        return r163793;
}

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 2020065 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))