Average Error: 0.0 → 0.0
Time: 2.2s
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 r185055 = x;
        double r185056 = r185055 * r185055;
        double r185057 = y;
        double r185058 = r185057 * r185057;
        double r185059 = r185056 + r185058;
        return r185059;
}
↓
double f(double x, double y) {
        double r185060 = x;
        double r185061 = r185060 * r185060;
        double r185062 = y;
        double r185063 = r185062 * r185062;
        double r185064 = r185061 + r185063;
        double r185065 = sqrt(r185064);
        double r185066 = r185065 * r185065;
        return r185066;
}

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 2020027 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))