Average Error: 0.0 → 0.0
Time: 1.1s
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 r115220 = x;
        double r115221 = r115220 * r115220;
        double r115222 = y;
        double r115223 = r115222 * r115222;
        double r115224 = r115221 + r115223;
        return r115224;
}
↓
double f(double x, double y) {
        double r115225 = x;
        double r115226 = y;
        double r115227 = r115226 * r115226;
        double r115228 = fma(r115225, r115225, r115227);
        return r115228;
}

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 2019325 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))