Average Error: 0.0 → 0.0
Time: 7.5s
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 r136361 = x;
        double r136362 = r136361 * r136361;
        double r136363 = y;
        double r136364 = r136363 * r136363;
        double r136365 = r136362 + r136364;
        return r136365;
}
↓
double f(double x, double y) {
        double r136366 = x;
        double r136367 = y;
        double r136368 = r136367 * r136367;
        double r136369 = fma(r136366, r136366, r136368);
        return r136369;
}

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 2019306 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))