Average Error: 0.0 → 0.0
Time: 1.2s
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 r164668 = x;
        double r164669 = r164668 * r164668;
        double r164670 = y;
        double r164671 = r164670 * r164670;
        double r164672 = r164669 + r164671;
        return r164672;
}
↓
double f(double x, double y) {
        double r164673 = x;
        double r164674 = y;
        double r164675 = r164674 * r164674;
        double r164676 = fma(r164673, r164673, r164675);
        return r164676;
}

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 2020036 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))