Average Error: 32.8 → 23.5
Time: 12.4s
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)) <= -26006705407507.965)) {
		VAR = ((double) exp(((double) log(((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)) <= 5.032089602153485e-13)) {
			VAR_1 = ((double) (((double) (1.0 / x)) / n));
		} else {
			VAR_1 = ((double) exp(((double) log(((double) (((double) (((double) pow(((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))), 3.0)) - ((double) pow(((double) pow(x, ((double) (1.0 / n)))), 3.0)))) / ((double) (((double) pow(((double) (1.0 + x)), ((double) (((double) (1.0 / n)) * 2.0)))) + ((double) (((double) pow(x, ((double) (1.0 / n)))) * ((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) + ((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)  < -26006705407507.9648
    1. Initial program 0
      \[\]
    2. Using strategy rm
    3. Applied add-exp-log0
      \[\leadsto \]
    if -26006705407507.9648 <  (/ 1.0 n)  < 5.03208960215348494e-13
    1. Initial program 44.7
      \[\]
    2. Taylor expanded around -inf 64.0
      \[\leadsto \]
    3. Simplified32.1
      \[\leadsto \]
    4. Using strategy rm
    5. Applied associate-/r*31.6
      \[\leadsto \]
    if 5.03208960215348494e-13 <  (/ 1.0 n) 
    1. Initial program 8.0
      \[\]
    2. Using strategy rm
    3. Applied add-exp-log8.0
      \[\leadsto \]
    4. Using strategy rm
    5. Applied flip3--8.0
      \[\leadsto \]
    6. Simplified8.0
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification23.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))