Average Error: 32.5 → 23.7
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 (((n <= -119587.8191154939) || !(n <= 4360947995.274645))) {
		VAR = ((double) (1.0 / ((double) (n * x))));
	} else {
		VAR = ((double) (((double) (((double) pow(((double) sqrt(x)), ((double) (1.0 / n)))) + ((double) sqrt(((double) log(((double) exp(((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))))))))))) * ((double) cbrt(((double) pow(((double) (((double) sqrt(((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))))) - ((double) pow(((double) sqrt(x)), ((double) (1.0 / n)))))), 3.0))))));
	}
	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 2 regimes
  2. if  n  < -119587.819115493898 or 4360947995.2746449 <  n 
    1. Initial program 45.0
      \[\]
    2. Taylor expanded around -inf 64.0
      \[\leadsto \]
    3. Simplified32.3
      \[\leadsto \]
    if -119587.819115493898 <  n  < 4360947995.2746449
    1. Initial program 3.4
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt3.4
      \[\leadsto \]
    4. Applied unpow-prod-down3.4
      \[\leadsto \]
    5. Applied add-sqr-sqrt3.4
      \[\leadsto \]
    6. Applied difference-of-squares3.4
      \[\leadsto \]
    7. Simplified3.4
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-log-exp3.5
      \[\leadsto \]
    10. Using strategy rm
    11. Applied add-cbrt-cube3.5
      \[\leadsto \]
    12. Simplified3.5
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification23.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))