Average Error: 33.2 → 23.7
Time: 13.0s
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 <= -3526319384090.8047)) {
		VAR = ((double) (((double) (1.0 / x)) * ((double) (1.0 / n))));
	} else {
		double VAR_1;
		if ((n <= 3.0876165420064856)) {
			VAR_1 = ((double) (((double) pow(((double) (x + 1.0)), ((double) (1.0 / n)))) - ((double) pow(((double) pow(x, ((double) (1.0 / ((double) (((double) cbrt(n)) * ((double) cbrt(n)))))))), ((double) (1.0 / ((double) cbrt(n))))))));
		} else {
			VAR_1 = ((double) (((double) (1.0 / x)) / 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  n  < -3526319384090.8047
    1. Initial program 44.7
      \[\]
    2. Using strategy rm
    3. Applied add-cube-cbrt44.7
      \[\leadsto \]
    4. Applied *-un-lft-identity44.7
      \[\leadsto \]
    5. Applied times-frac44.7
      \[\leadsto \]
    6. Applied pow-unpow44.7
      \[\leadsto \]
    7. Taylor expanded around -inf 64.0
      \[\leadsto \]
    8. Simplified31.7
      \[\leadsto \]
    9. Using strategy rm
    10. Applied *-un-lft-identity31.7
      \[\leadsto \]
    11. Applied times-frac31.0
      \[\leadsto \]
    if -3526319384090.8047 <  n  < 3.0876165420064856
    1. Initial program 3.1
      \[\]
    2. Using strategy rm
    3. Applied add-cube-cbrt3.2
      \[\leadsto \]
    4. Applied *-un-lft-identity3.2
      \[\leadsto \]
    5. Applied times-frac3.2
      \[\leadsto \]
    6. Applied pow-unpow3.2
      \[\leadsto \]
    if 3.0876165420064856 <  n 
    1. Initial program 44.7
      \[\]
    2. Using strategy rm
    3. Applied add-cube-cbrt44.7
      \[\leadsto \]
    4. Applied *-un-lft-identity44.7
      \[\leadsto \]
    5. Applied times-frac44.7
      \[\leadsto \]
    6. Applied pow-unpow44.7
      \[\leadsto \]
    7. Taylor expanded around -inf 64.0
      \[\leadsto \]
    8. Simplified32.7
      \[\leadsto \]
    9. Using strategy rm
    10. Applied associate-/r*32.0
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification23.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))