Average Error: 0.0 → 0.0
Time: 893.0ms
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 r141065 = x;
        double r141066 = r141065 * r141065;
        double r141067 = y;
        double r141068 = r141067 * r141067;
        double r141069 = r141066 + r141068;
        return r141069;
}
↓
double f(double x, double y) {
        double r141070 = x;
        double r141071 = y;
        double r141072 = hypot(r141070, r141071);
        double r141073 = r141072 * r141072;
        return r141073;
}

Error

Bits error versus x

Bits error versus y

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