Average Error: 31.7 → 31.7
Time: 641.0ms
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\sqrt{x \cdot x + y \cdot y}\]
\sqrt{x \cdot x + y \cdot y}
↓
\sqrt{x \cdot x + y \cdot y}
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
}
↓
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
}

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 31.7

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

  2. Final simplification31.7

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(sqrt (+ (* x x) (* y y)))"
  :precision binary64
  (sqrt (+ (* x x) (* y y))))