Average Error: 0.0 → 0.0
Time: 1.0s
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 r180891 = x;
        double r180892 = r180891 * r180891;
        double r180893 = y;
        double r180894 = r180893 * r180893;
        double r180895 = r180892 + r180894;
        return r180895;
}
↓
double f(double x, double y) {
        double r180896 = x;
        double r180897 = y;
        double r180898 = r180897 * r180897;
        double r180899 = fma(r180896, r180896, r180898);
        return r180899;
}

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 2019209 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))