Average Error: 0.0 → 0.0
Time: 584.0ms
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 r167991 = x;
        double r167992 = r167991 * r167991;
        double r167993 = y;
        double r167994 = r167993 * r167993;
        double r167995 = r167992 + r167994;
        return r167995;
}
↓
double f(double x, double y) {
        double r167996 = x;
        double r167997 = y;
        double r167998 = r167997 * r167997;
        double r167999 = fma(r167996, r167996, r167998);
        return r167999;
}

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 2020045 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))