Error

Derivation

1. Split input into 2 regimes.

2. if N < 155712.94519128354

   1. Initial program 31.7

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

   3. Applied diff-log 29.5

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

   4. Applied taylor 29.5

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

   5. Taylor expanded around 0 29.5

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

   if 155712.94519128354 < N

   1. Initial program 59.8

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

   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

Total time: 26.8s Debug log

Please include this information when filing a bug report:

herbie --seed '#(3300460555 843096705 673485548 1507387360 1814934995 3443200150)'
(FPCore (N)
  :name "NMSE problem 3.3.6"
  (- (log (+ N 1)) (log N)))