Average Error: 0.0 → 0.0
Time: 674.0ms
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 r215175 = x;
        double r215176 = r215175 * r215175;
        double r215177 = y;
        double r215178 = r215177 * r215177;
        double r215179 = r215176 + r215178;
        return r215179;
}
↓
double f(double x, double y) {
        double r215180 = x;
        double r215181 = y;
        double r215182 = r215181 * r215181;
        double r215183 = fma(r215180, r215180, r215182);
        return r215183;
}

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 2020020 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))