Average Error: 0.0 → 0.0
Time: 13.3s
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 r96497 = x;
        double r96498 = r96497 * r96497;
        double r96499 = y;
        double r96500 = r96499 * r96499;
        double r96501 = r96498 + r96500;
        return r96501;
}
↓
double f(double x, double y) {
        double r96502 = x;
        double r96503 = y;
        double r96504 = r96503 * r96503;
        double r96505 = fma(r96502, r96502, r96504);
        return r96505;
}

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 2019326 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))