Average Error: 0.0 → 0.0
Time: 573.0ms
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 r184516 = x;
        double r184517 = r184516 * r184516;
        double r184518 = y;
        double r184519 = r184518 * r184518;
        double r184520 = r184517 + r184519;
        return r184520;
}
↓
double f(double x, double y) {
        double r184521 = x;
        double r184522 = y;
        double r184523 = r184522 * r184522;
        double r184524 = fma(r184521, r184521, r184523);
        return r184524;
}

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 2020064 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))