Average Error: 24.7 → 24.7
Time: 753.0ms
Precision: binary64
\[\sqrt{1 + \frac{x \cdot x}{y \cdot y}}\]
↓
\[\sqrt{1 + \frac{x \cdot x}{y \cdot y}}\]
\sqrt{1 + \frac{x \cdot x}{y \cdot y}}
↓
\sqrt{1 + \frac{x \cdot x}{y \cdot y}}
double code(double x, double y) {
	return ((double) sqrt(((double) (1.0 + ((double) (((double) (x * x)) / ((double) (y * y))))))));
}
↓
double code(double x, double y) {
	return ((double) sqrt(((double) (1.0 + ((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 24.7

    \[\sqrt{1 + \frac{x \cdot x}{y \cdot y}}\]

  2. Final simplification24.7

    \[\leadsto \sqrt{1 + \frac{x \cdot x}{y \cdot y}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(sqrt (+ 1 (/ (* x x) (* y y))))"
  :precision binary64
  (sqrt (+ 1.0 (/ (* x x) (* y y)))))