Error

Derivation

1. Split input into 2 regimes.

2. if N < 70172005.42724477

   1. Initial program 31.3

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

   3. Applied diff-log 29.0

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

   if 70172005.42724477 < N

   1. Initial program 60.0

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

   2. Applied taylor 0.0

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

   3. Taylor expanded around inf 0.0

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

   4. Applied simplify 0.0

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

   5. Applied taylor 0.0

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

   6. Taylor expanded around 0 0.0

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

   7. Applied simplify 0.0

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

Runtime

Time bar (total: 11.6s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1068028399 4028058041 2917032441 2563479541 765645300 1132738916)'
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))