Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[x \cdot x + y \cdot y\]
↓
\[\mathsf{fma}\left(y, y, x \cdot x\right)\]
x \cdot x + y \cdot y
↓
\mathsf{fma}\left(y, y, x \cdot x\right)
double f(double x, double y) {
        double r6177515 = x;
        double r6177516 = r6177515 * r6177515;
        double r6177517 = y;
        double r6177518 = r6177517 * r6177517;
        double r6177519 = r6177516 + r6177518;
        return r6177519;
}
↓
double f(double x, double y) {
        double r6177520 = y;
        double r6177521 = x;
        double r6177522 = r6177521 * r6177521;
        double r6177523 = fma(r6177520, r6177520, r6177522);
        return r6177523;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot x + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, y, x \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, y, x \cdot x\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  (+ (* x x) (* y y)))