Average Error: 29.8 → 0.0
Time: 26.8s
Precision: 64
Internal Precision: 1408
\[\log \left(N + 1\right) - \log N\]
↓
\[\log_* (1 + \frac{1}{N})\]

Error

Bits error versus N

Derivation

  1. Initial program 29.8

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

  3. Applied diff-log29.7

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

  4. Taylor expanded around 0 29.7

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

  5. Applied simplify0.0

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

Runtime

Time bar (total: 26.8s)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' +o rules:numerics
(FPCore (N)
  :name "2log (problem 3.3.6)"
  (- (log (+ N 1)) (log N)))