Average Error: 0.0 → 0.0
Time: 2.3s
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 r187428 = x;
        double r187429 = r187428 * r187428;
        double r187430 = y;
        double r187431 = r187430 * r187430;
        double r187432 = r187429 + r187431;
        return r187432;
}
↓
double f(double x, double y) {
        double r187433 = x;
        double r187434 = r187433 * r187433;
        double r187435 = y;
        double r187436 = r187435 * r187435;
        double r187437 = r187434 + r187436;
        double r187438 = sqrt(r187437);
        double r187439 = r187438 * r187438;
        return r187439;
}

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 2020034 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))