Average Error: 0.0 → 0.0
Time: 5.7s
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 r166182 = x;
        double r166183 = r166182 * r166182;
        double r166184 = y;
        double r166185 = r166184 * r166184;
        double r166186 = r166183 + r166185;
        return r166186;
}
↓
double f(double x, double y) {
        double r166187 = x;
        double r166188 = y;
        double r166189 = r166188 * r166188;
        double r166190 = fma(r166187, r166187, r166189);
        return r166190;
}

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 2020043 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))