Average Error: 0.0 → 0.0
Time: 560.0ms
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 r182105 = x;
        double r182106 = r182105 * r182105;
        double r182107 = y;
        double r182108 = r182107 * r182107;
        double r182109 = r182106 + r182108;
        return r182109;
}
↓
double f(double x, double y) {
        double r182110 = x;
        double r182111 = y;
        double r182112 = r182111 * r182111;
        double r182113 = fma(r182110, r182110, r182112);
        return r182113;
}

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 2020018 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))