Average Error: 0.0 → 0.0
Time: 1.7s
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 r169881 = x;
        double r169882 = r169881 * r169881;
        double r169883 = y;
        double r169884 = r169883 * r169883;
        double r169885 = r169882 + r169884;
        return r169885;
}
↓
double f(double x, double y) {
        double r169886 = x;
        double r169887 = y;
        double r169888 = r169887 * r169887;
        double r169889 = fma(r169886, r169886, r169888);
        return r169889;
}

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 2020033 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))