Average Error: 28.9 → 0.0
Time: 24.2s
Precision: 64
Internal Precision: 1600
\[\log \left(N + 1\right) - \log N\]
↓
\[\log_* (1 + \frac{1}{N})\]

Error

Bits error versus N

Derivation

  1. Initial program 28.9

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

  3. Applied diff-log28.8

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

  4. Taylor expanded around 0 28.8

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

  5. Applied simplify0.0

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

Runtime

Time bar (total: 24.2s)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' +o rules:numerics
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))