Average Error: 0.0 → 0.0
Time: 4.6s
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 r11450924 = x;
        double r11450925 = r11450924 * r11450924;
        double r11450926 = y;
        double r11450927 = r11450926 * r11450926;
        double r11450928 = r11450925 + r11450927;
        return r11450928;
}
↓
double f(double x, double y) {
        double r11450929 = x;
        double r11450930 = y;
        double r11450931 = r11450930 * r11450930;
        double r11450932 = fma(r11450929, r11450929, r11450931);
        return r11450932;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  (+ (* x x) (* y y)))