Average Error: 0.0 → 0.0
Time: 914.0ms
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 r97996 = x;
        double r97997 = r97996 * r97996;
        double r97998 = y;
        double r97999 = r97998 * r97998;
        double r98000 = r97997 + r97999;
        return r98000;
}
↓
double f(double x, double y) {
        double r98001 = x;
        double r98002 = y;
        double r98003 = r98002 * r98002;
        double r98004 = fma(r98001, r98001, r98003);
        return r98004;
}

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 2019347 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))