Error

Derivation

1. Split input into 2 regimes

2. if (- (log (+ N 1)) (log N)) < 6.834657517917895e-09

   1. Initial program 60.0

      \[\log \left(N + 1\right) - \log N\]

   2. Taylor expanded around inf 60.0

      \[\leadsto \color{blue}{\left(\frac{1}{N} - \left(\log \left(\frac{1}{N}\right) + \frac{1}{2} \cdot \frac{1}{{N}^{2}}\right)\right)} - \log N\]

   3. Applied simplify0.0

      \[\leadsto \color{blue}{\left(0 + \frac{1}{N}\right) - \frac{\frac{\frac{1}{2}}{N}}{N}}\]

   if 6.834657517917895e-09 < (- (log (+ N 1)) (log N))

   1. Initial program 0.4

      \[\log \left(N + 1\right) - \log N\]
   2. Using strategy rm

   3. Applied diff-log0.3

      \[\leadsto \color{blue}{\log \left(\frac{N + 1}{N}\right)}\]
3. Recombined 2 regimes into one program.

4. Applied simplify0.2

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\log \left(1 + N\right) - \log N \le 6.834657517917895 \cdot 10^{-09}:\\ \;\;\;\;\frac{1}{N} - \frac{\frac{\frac{1}{2}}{N}}{N}\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{1 + N}{N}\right)\\ \end{array}}\]

Runtime

Time bar (total: 58.6s)Debug logProfile

herbie shell --seed '#(1070833653 108281690 3330367898 3632331308 3494323072 43156186)' 
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))