Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[x \cdot x + y \cdot y\]
↓
\[\sqrt{x \cdot x + y \cdot y} \cdot \sqrt{x \cdot x + y \cdot y}\]
x \cdot x + y \cdot y
↓
\sqrt{x \cdot x + y \cdot y} \cdot \sqrt{x \cdot x + y \cdot y}
double f(double x, double y) {
        double r7073644 = x;
        double r7073645 = r7073644 * r7073644;
        double r7073646 = y;
        double r7073647 = r7073646 * r7073646;
        double r7073648 = r7073645 + r7073647;
        return r7073648;
}
↓
double f(double x, double y) {
        double r7073649 = x;
        double r7073650 = r7073649 * r7073649;
        double r7073651 = y;
        double r7073652 = r7073651 * r7073651;
        double r7073653 = r7073650 + r7073652;
        double r7073654 = sqrt(r7073653);
        double r7073655 = r7073654 * r7073654;
        return r7073655;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{x \cdot x + y \cdot y} \cdot \sqrt{x \cdot x + y \cdot y}}\]

  4. Final simplification0.0

    \[\leadsto \sqrt{x \cdot x + y \cdot y} \cdot \sqrt{x \cdot x + y \cdot y}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  (+ (* x x) (* y y)))