Average Error: 0.0 → 0.0
Time: 918.0ms
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 r188862 = x;
        double r188863 = r188862 * r188862;
        double r188864 = y;
        double r188865 = r188864 * r188864;
        double r188866 = r188863 + r188865;
        return r188866;
}
↓
double f(double x, double y) {
        double r188867 = x;
        double r188868 = y;
        double r188869 = r188868 * r188868;
        double r188870 = fma(r188867, r188867, r188869);
        return r188870;
}

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 2020021 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))