Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[x \cdot x + y \cdot y\]
↓
\[\mathsf{hypot}\left(x, y\right) \cdot \mathsf{hypot}\left(x, y\right)\]
x \cdot x + y \cdot y
↓
\mathsf{hypot}\left(x, y\right) \cdot \mathsf{hypot}\left(x, y\right)
double f(double x, double y) {
        double r111512 = x;
        double r111513 = r111512 * r111512;
        double r111514 = y;
        double r111515 = r111514 * r111514;
        double r111516 = r111513 + r111515;
        return r111516;
}
↓
double f(double x, double y) {
        double r111517 = x;
        double r111518 = y;
        double r111519 = hypot(r111517, r111518);
        double r111520 = r111519 * r111519;
        return r111520;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  4. Applied add-sqr-sqrt0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))