Average Error: 0.0 → 0.0
Time: 1.8s
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 r173930 = x;
        double r173931 = r173930 * r173930;
        double r173932 = y;
        double r173933 = r173932 * r173932;
        double r173934 = r173931 + r173933;
        return r173934;
}
↓
double f(double x, double y) {
        double r173935 = x;
        double r173936 = y;
        double r173937 = r173936 * r173936;
        double r173938 = fma(r173935, r173935, r173937);
        return r173938;
}

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 2020036 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))