Average Error: 2.5 → 2.5
Time: 8.5s
Precision: binary64
\[x - \frac{{x}^{\left(\frac{1}{n}\right)}}{\frac{{x}^{\left(\frac{1 - n}{n}\right)}}{n}}\]
↓
\[x - \frac{{x}^{\left(\frac{1}{n}\right)}}{\frac{{x}^{\left(\frac{1 - n}{n}\right)}}{n}}\]
x - \frac{{x}^{\left(\frac{1}{n}\right)}}{\frac{{x}^{\left(\frac{1 - n}{n}\right)}}{n}}
↓
x - \frac{{x}^{\left(\frac{1}{n}\right)}}{\frac{{x}^{\left(\frac{1 - n}{n}\right)}}{n}}
double code(double x, double n) {
	return ((double) (x - ((double) (((double) pow(x, ((double) (1.0 / n)))) / ((double) (((double) pow(x, ((double) (((double) (1.0 - n)) / n)))) / n))))));
}
↓
double code(double x, double n) {
	return ((double) (x - ((double) (((double) pow(x, ((double) (1.0 / n)))) / ((double) (((double) pow(x, ((double) (((double) (1.0 - n)) / n)))) / n))))));
}

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 2.5

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

  2. Final simplification2.5

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x n)
  :name "(- x (/ (pow x (/ 1 n)) (/ (pow x (/ (- 1 n) n)) n)))"
  :precision binary64
  (- x (/ (pow x (/ 1.0 n)) (/ (pow x (/ (- 1.0 n) n)) n))))