Average Error: 0.0 → 0.0
Time: 4.5s
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 r197719 = x;
        double r197720 = r197719 * r197719;
        double r197721 = y;
        double r197722 = r197721 * r197721;
        double r197723 = r197720 + r197722;
        return r197723;
}
↓
double f(double x, double y) {
        double r197724 = x;
        double r197725 = r197724 * r197724;
        double r197726 = y;
        double r197727 = r197726 * r197726;
        double r197728 = r197725 + r197727;
        double r197729 = sqrt(r197728);
        double r197730 = r197729 * r197729;
        return r197730;
}

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)))