Average Error: 32.8 → 24.3
Time: 13.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double n) {
	return ((double) (((double) pow(((double) (x + 1.0)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n))))));
}

↓
double code(double x, double n) {
	double VAR;
	if ((((double) (1.0 / n)) <= -7.410239730006016e-26)) {
		VAR = ((double) cbrt(((double) pow(((double) cbrt(((double) pow(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(((double) exp(((double) (((double) log(x)) / n)))), 1.0)))), 3.0)))), 3.0))));
	} else {
		double VAR_1;
		if ((((double) (1.0 / n)) <= 1.7465690654858e-17)) {
			VAR_1 = ((double) (((double) (1.0 / ((double) (n * x)))) + ((double) (((double) (((double) (1.0 / ((double) (n * n)))) * ((double) (((double) (((double) log(1.0)) / x)) + ((double) (((double) log(x)) / x)))))) - ((double) (0.5 / ((double) (x * ((double) (n * x))))))))));
		} else {
			VAR_1 = ((double) (((double) cbrt(((double) pow(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(((double) exp(((double) (((double) log(x)) / n)))), 1.0)))), 1.5)))) * ((double) cbrt(((double) pow(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(((double) exp(((double) (((double) log(x)) / n)))), 1.0)))), 1.5))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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. Split input into 3 regimes
  2. if  (/ 1.0 n)  < -7.41023973000601582e-26
    1. Initial program 6.7
      \[\]
    2. Using strategy rm
    3. Applied add-exp-log6.8
      \[\leadsto \]
    4. Applied pow-exp6.8
      \[\leadsto \]
    5. Simplified6.8
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-cbrt-cube6.8
      \[\leadsto \]
    8. Simplified6.8
      \[\leadsto \]
    9. Using strategy rm
    10. Applied add-cbrt-cube6.8
      \[\leadsto \]
    11. Simplified6.8
      \[\leadsto \]
    if -7.41023973000601582e-26 <  (/ 1.0 n)  < 1.7465690654858e-17
    1. Initial program 44.7
      \[\]
    2. Taylor expanded around inf 32.3
      \[\leadsto \]
    3. Simplified32.2
      \[\leadsto \]
    if 1.7465690654858e-17 <  (/ 1.0 n) 
    1. Initial program 9.3
      \[\]
    2. Using strategy rm
    3. Applied add-exp-log9.3
      \[\leadsto \]
    4. Applied pow-exp9.3
      \[\leadsto \]
    5. Simplified9.3
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-cbrt-cube9.3
      \[\leadsto \]
    8. Simplified9.3
      \[\leadsto \]
    9. Using strategy rm
    10. Applied sqr-pow9.3
      \[\leadsto \]
    11. Applied cbrt-prod9.3
      \[\leadsto \]
    12. Simplified9.3
      \[\leadsto \]
    13. Simplified9.3
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification24.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))