Average Error: 33.0 → 24.3
Time: 12.7s
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)) <= -0.05102895011493297)) {
		VAR = ((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) (((double) sqrt(((double) pow(x, ((double) (1.0 / n)))))) * ((double) sqrt(((double) pow(x, ((double) (1.0 / n))))))))));
	} else {
		double VAR_1;
		if ((((double) (1.0 / n)) <= 1.431004864818934e-20)) {
			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) pow(((double) pow(((double) (((double) cbrt(((double) exp(((double) cbrt(((double) log(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n)))))))))))))) * ((double) cbrt(((double) exp(((double) cbrt(((double) log(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n)))))))))))))))), ((double) cbrt(((double) log(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n)))))))))))), ((double) cbrt(((double) log(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n)))))))))))) * ((double) pow(((double) pow(((double) cbrt(((double) exp(((double) cbrt(((double) log(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n)))))))))))))), ((double) cbrt(((double) log(((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / n)))) - ((double) pow(x, ((double) (1.0 / n)))))))))))), ((double) cbrt(((double) log(((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)  < -0.051028950114932969
    1. Initial program 0.4
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt0.4
      \[\leadsto \]
    if -0.051028950114932969 <  (/ 1.0 n)  < 1.4310048648189339e-20
    1. Initial program 45.1
      \[\]
    2. Taylor expanded around inf 32.8
      \[\leadsto \]
    3. Simplified32.7
      \[\leadsto \]
    if 1.4310048648189339e-20 <  (/ 1.0 n) 
    1. Initial program 11.8
      \[\]
    2. Using strategy rm
    3. Applied add-exp-log11.8
      \[\leadsto \]
    4. Using strategy rm
    5. Applied add-cube-cbrt11.8
      \[\leadsto \]
    6. Applied exp-prod11.8
      \[\leadsto \]
    7. Simplified11.8
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-cube-cbrt11.8
      \[\leadsto \]
    10. Applied unpow-prod-down11.8
      \[\leadsto \]
    11. Applied unpow-prod-down11.8
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification24.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))