Error

Derivation

1. Split input into 2 regimes.

2. if N < 550698777842538.4

   1. Initial program 31.4

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

   3. Applied diff-log 29.0

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

   if 550698777842538.4 < N

   1. Initial program 60.4

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

   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 simplify 0.0

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

Runtime

Time bar (total: 5.7s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067901057 3396600083 3715501224 3126139233 3908045574 1593683916)'
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))