Error

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Derivation

1. Initial program 29.4

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

2. Initial simplification29.4

   \[\leadsto \log_* (1 + N) - \log N\]
3. Using strategy rm

4. Applied log1p-udef29.4

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

5. Applied diff-log29.3

   \[\leadsto \color{blue}{\log \left(\frac{1 + N}{N}\right)}\]
6. Using strategy rm

7. Applied log1p-expm1-u29.3

   \[\leadsto \color{blue}{\log_* (1 + (e^{\log \left(\frac{1 + N}{N}\right)} - 1)^*)}\]

8. Taylor expanded around -inf 0.0

   \[\leadsto \log_* (1 + \color{blue}{\frac{1}{N}})\]

9. Final simplification0.0

   \[\leadsto \log_* (1 + \frac{1}{N})\]

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))

Details

Time bar (total: 4.2s)Debug log