Average Error: 0.0 → 0.0
Time: 544.0ms
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 r136525 = x;
        double r136526 = r136525 * r136525;
        double r136527 = y;
        double r136528 = r136527 * r136527;
        double r136529 = r136526 + r136528;
        return r136529;
}
↓
double f(double x, double y) {
        double r136530 = x;
        double r136531 = y;
        double r136532 = r136531 * r136531;
        double r136533 = fma(r136530, r136530, r136532);
        return r136533;
}

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 2020039 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))