Average Error: 0.0 → 0.0
Time: 5.2s
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 r200171 = x;
        double r200172 = r200171 * r200171;
        double r200173 = y;
        double r200174 = r200173 * r200173;
        double r200175 = r200172 + r200174;
        return r200175;
}
↓
double f(double x, double y) {
        double r200176 = x;
        double r200177 = r200176 * r200176;
        double r200178 = y;
        double r200179 = r200178 * r200178;
        double r200180 = r200177 + r200179;
        double r200181 = sqrt(r200180);
        double r200182 = r200181 * r200181;
        return r200182;
}

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