Average Error: 1.8 → 1.8
Time: 13.5s
Precision: binary64
\[x - \frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}}\]
↓
\[x - \frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}}\]
x - \frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}}
↓
x - \frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}}
double code(double x, double n, double k) {
	return ((double) (x - ((double) (((double) (((double) pow(x, n)) - k)) / ((double) (n * ((double) pow(x, ((double) (n - 1.0))))))))));
}
↓
double code(double x, double n, double k) {
	return ((double) (x - ((double) (((double) (((double) pow(x, n)) - k)) / ((double) (n * ((double) pow(x, ((double) (n - 1.0))))))))));
}

Error

Bits error versus x

Bits error versus n

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Final simplification1.8

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

Reproduce

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