Average Error: 30.1 → 0.1
Time: 2.8s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double N) {
	return ((double) (((double) log(((double) (N + 1.0)))) - ((double) log(N))));
}

↓
double code(double N) {
	double VAR;
	if ((N <= 6245.064955424139)) {
		VAR = ((double) (((double) log(((double) sqrt(((double) (((double) (N + 1.0)) / N)))))) + ((double) log(((double) sqrt(((double) (((double) (N + 1.0)) / N))))))));
	} else {
		VAR = ((double) (((double) (1.0 / N)) + ((double) (((double) (((double) (0.3333333333333333 / N)) - 0.5)) / ((double) (N * N))))));
	}
	return VAR;
}

Error
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  < 6245.064955424139
    1. Initial program 0.1
      \[\]
    2. Using strategy rm
    3. Applied diff-log0.1
      \[\leadsto \]
    4. Using strategy rm
    5. Applied add-sqr-sqrt0.1
      \[\leadsto \]
    6. Applied log-prod0.1
      \[\leadsto \]
    if 6245.064955424139 <  N 
    1. Initial program 59.7
      \[\]
    2. Taylor expanded around inf 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (N)
  :name "2log (problem 3.3.6)"
  :precision binary64
  (- (log (+ N 1.0)) (log N)))