Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[x \cdot x + y \cdot y\]
↓
\[\mathsf{hypot}\left(y, x\right) \cdot \mathsf{hypot}\left(y, x\right)\]
x \cdot x + y \cdot y
↓
\mathsf{hypot}\left(y, x\right) \cdot \mathsf{hypot}\left(y, x\right)
double f(double x, double y) {
        double r174406 = x;
        double r174407 = r174406 * r174406;
        double r174408 = y;
        double r174409 = r174408 * r174408;
        double r174410 = r174407 + r174409;
        return r174410;
}
↓
double f(double x, double y) {
        double r174411 = y;
        double r174412 = x;
        double r174413 = hypot(r174411, r174412);
        double r174414 = r174413 * r174413;
        return r174414;
}

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

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))