Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[x \cdot x + y \cdot y\]
↓
\[\mathsf{fma}\left(y, y, x \cdot x\right)\]
x \cdot x + y \cdot y
↓
\mathsf{fma}\left(y, y, x \cdot x\right)
double f(double x, double y) {
        double r8748719 = x;
        double r8748720 = r8748719 * r8748719;
        double r8748721 = y;
        double r8748722 = r8748721 * r8748721;
        double r8748723 = r8748720 + r8748722;
        return r8748723;
}
↓
double f(double x, double y) {
        double r8748724 = y;
        double r8748725 = x;
        double r8748726 = r8748725 * r8748725;
        double r8748727 = fma(r8748724, r8748724, r8748726);
        return r8748727;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot x + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, y, x \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, y, x \cdot x\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  (+ (* x x) (* y y)))