Error

Derivation

1. Split input into 2 regimes.

2. if N < 37798.39342058285

   1. Initial program 31.2

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

   3. Applied diff-log 28.9

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

   if 37798.39342058285 < N

   1. Initial program 59.5

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

   2. Applied taylor 0.0

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

   3. Taylor expanded around inf 0.0

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

   4. Applied simplify 0.0

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

   5. Applied simplify 0.0

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

Runtime

Time bar (total: 15.1s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3042209127 2022729764 3313166321 4075783413 705100875 65069737)'
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))