Average Error: 0.0 → 0.0
Time: 634.0ms
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 r172232 = x;
        double r172233 = r172232 * r172232;
        double r172234 = y;
        double r172235 = r172234 * r172234;
        double r172236 = r172233 + r172235;
        return r172236;
}
↓
double f(double x, double y) {
        double r172237 = x;
        double r172238 = y;
        double r172239 = r172238 * r172238;
        double r172240 = fma(r172237, r172237, r172239);
        return r172240;
}

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 2019353 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))