Error

Derivation

1. Split input into 2 regimes.

2. if N < 659531696.815955

   1. Initial program 31.8

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

   3. Applied diff-log 29.4

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

   4. Applied taylor 29.4

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

   5. Taylor expanded around 0 29.4

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

   if 659531696.815955 < 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

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

   5. Applied simplify 0.0

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

Runtime

Time bar (total: 10.1s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(644180380 3784176976 401987740 22459203 1940947670 3323606534)'
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))