Error

Derivation

1. Split input into 2 regimes

2. if N < 15009.386462352013

   1. Initial program 31.2

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

   3. Applied diff-log28.9

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

   if 15009.386462352013 < N

   1. Initial program 59.4

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

   2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^{2}}}\]

   3. Applied simplify0.0

      \[\leadsto \color{blue}{\frac{1}{N} + \left(\frac{\frac{1}{3}}{N} - \frac{1}{2}\right) \cdot \frac{1}{N \cdot N}}\]

   4. Applied simplify0.0

      \[\leadsto \frac{1}{N} + \color{blue}{\frac{\frac{\frac{1}{3}}{N} - \frac{1}{2}}{N \cdot N}}\]
3. Recombined 2 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 33.6s)Debug logProfile

herbie shell --seed '#(1062900086 561157142 2241869825 1166610429 2484609072 2159574644)' 
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))