Average Error: 33.0 → 23.9
Time: 13.3s
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)) <= -2.5542558241396368e-09)) {
		VAR = ((double) log(((double) exp(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n))))))))));
	} else {
		double VAR_1;
		if ((((double) (1.0 / n)) <= 3.2984038541839436e-18)) {
			VAR_1 = ((double) (1.0 / ((double) (n * x))));
		} else {
			VAR_1 = ((double) (((double) (((double) (((double) pow(((double) pow(((double) sqrt(((double) (1.0 + x)))), ((double) (1.0 / n)))), 3.0)) - ((double) pow(((double) sqrt(((double) pow(x, ((double) (1.0 / n)))))), 3.0)))) * ((double) (((double) pow(((double) sqrt(((double) (1.0 + x)))), ((double) (((double) (1.0 / n)) * 2.0)))) - ((double) pow(x, ((double) (1.0 / n)))))))) / ((double) (((double) (((double) pow(((double) sqrt(((double) (1.0 + x)))), ((double) (1.0 / n)))) - ((double) sqrt(((double) pow(x, ((double) (1.0 / n)))))))) * ((double) (((double) pow(x, ((double) (1.0 / n)))) + ((double) (((double) pow(((double) sqrt(((double) (1.0 + x)))), ((double) (1.0 / n)))) * ((double) (((double) pow(((double) sqrt(((double) (1.0 + x)))), ((double) (1.0 / n)))) + ((double) sqrt(((double) pow(x, ((double) (1.0 / n))))))))))))))));
		}
		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)  < -2.55425582413963677e-9
    1. Initial program 2.4
      \[\]
    2. Using strategy rm
    3. Applied add-log-exp2.9
      \[\leadsto \]
    4. Applied add-log-exp2.7
      \[\leadsto \]
    5. Applied diff-log2.7
      \[\leadsto \]
    6. Simplified2.7
      \[\leadsto \]
    if -2.55425582413963677e-9 <  (/ 1.0 n)  < 3.2984038541839436e-18
    1. Initial program 44.9
      \[\]
    2. Taylor expanded around -inf 64.0
      \[\leadsto \]
    3. Simplified31.7
      \[\leadsto \]
    if 3.2984038541839436e-18 <  (/ 1.0 n) 
    1. Initial program 10.8
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt10.9
      \[\leadsto \]
    4. Applied add-sqr-sqrt10.9
      \[\leadsto \]
    5. Applied unpow-prod-down10.9
      \[\leadsto \]
    6. Applied difference-of-squares10.9
      \[\leadsto \]
    7. Using strategy rm
    8. Applied flip3--10.9
      \[\leadsto \]
    9. Applied flip-+11.2
      \[\leadsto \]
    10. Applied frac-times11.2
      \[\leadsto \]
    11. Simplified11.1
      \[\leadsto \]
    12. Simplified11.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification23.9
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))