Average Error: 0.0 → 0.0
Time: 3.1s
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 r181153 = x;
        double r181154 = r181153 * r181153;
        double r181155 = y;
        double r181156 = r181155 * r181155;
        double r181157 = r181154 + r181156;
        return r181157;
}
↓
double f(double x, double y) {
        double r181158 = x;
        double r181159 = y;
        double r181160 = r181159 * r181159;
        double r181161 = fma(r181158, r181158, r181160);
        return r181161;
}

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 2020042 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))