Average Error: 0.0 → 0.0
Time: 12.9s
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 r140122 = x;
        double r140123 = r140122 * r140122;
        double r140124 = y;
        double r140125 = r140124 * r140124;
        double r140126 = r140123 + r140125;
        return r140126;
}
↓
double f(double x, double y) {
        double r140127 = x;
        double r140128 = y;
        double r140129 = r140128 * r140128;
        double r140130 = fma(r140127, r140127, r140129);
        return r140130;
}

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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))