Average Error: 21.7 → 21.7
Time: 3.2s
Precision: binary64
\[\left(n \cdot \log \left(1 + \frac{1}{n}\right) + \log \left(n + 1\right)\right) - 1\]
↓
\[\left(n \cdot \log \left(1 + \frac{1}{n}\right) + \log \left(n + 1\right)\right) - 1\]
\left(n \cdot \log \left(1 + \frac{1}{n}\right) + \log \left(n + 1\right)\right) - 1
↓
\left(n \cdot \log \left(1 + \frac{1}{n}\right) + \log \left(n + 1\right)\right) - 1
double code(double n) {
	return ((double) (((double) (((double) (n * ((double) log(((double) (1.0 + ((double) (1.0 / n)))))))) + ((double) log(((double) (n + 1.0)))))) - 1.0));
}
↓
double code(double n) {
	return ((double) (((double) (((double) (n * ((double) log(((double) (1.0 + ((double) (1.0 / n)))))))) + ((double) log(((double) (n + 1.0)))))) - 1.0));
}

Error

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 21.7

    \[\left(n \cdot \log \left(1 + \frac{1}{n}\right) + \log \left(n + 1\right)\right) - 1\]

  2. Final simplification21.7

    \[\leadsto \left(n \cdot \log \left(1 + \frac{1}{n}\right) + \log \left(n + 1\right)\right) - 1\]

Reproduce

herbie shell --seed 2020152 
(FPCore (n)
  :name "(- (+ (* n (log (+ 1 (/ 1 n)))) (log (+ n 1))) 1)"
  :precision binary64
  (- (+ (* n (log (+ 1.0 (/ 1.0 n)))) (log (+ n 1.0))) 1.0))