Average Error: 0.0 → 0.0
Time: 856.0ms
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 r213201 = x;
        double r213202 = r213201 * r213201;
        double r213203 = y;
        double r213204 = r213203 * r213203;
        double r213205 = r213202 + r213204;
        return r213205;
}
↓
double f(double x, double y) {
        double r213206 = x;
        double r213207 = y;
        double r213208 = r213207 * r213207;
        double r213209 = fma(r213206, r213206, r213208);
        return r213209;
}

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 2020083 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))