Average Error: 0.0 → 0.0
Time: 1.5s
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 r134762 = x;
        double r134763 = r134762 * r134762;
        double r134764 = y;
        double r134765 = r134764 * r134764;
        double r134766 = r134763 + r134765;
        return r134766;
}
↓
double f(double x, double y) {
        double r134767 = y;
        double r134768 = x;
        double r134769 = r134768 * r134768;
        double r134770 = fma(r134767, r134767, r134769);
        return r134770;
}

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 2019196 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  (+ (* x x) (* y y)))