Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}\]
↓
\[\sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}\]
\sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}
↓
\sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}
double code(double x, double n) {
	return ((double) sqrt(((double) (1.0 - ((double) pow(((double) (x / ((double) pow(2.0, n)))), 2.0))))));
}
↓
double code(double x, double n) {
	return ((double) sqrt(((double) (1.0 - ((double) pow(((double) (x / ((double) pow(2.0, n)))), 2.0))))));
}

Error

Bits error versus x

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}\]

  2. Final simplification0.0

    \[\leadsto \sqrt{1 - {\left(\frac{x}{{2}^{n}}\right)}^{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x n)
  :name "(sqrt (- 1 (pow (/ x (pow 2 n)) 2)))"
  :precision binary64
  (sqrt (- 1.0 (pow (/ x (pow 2.0 n)) 2.0))))