\[\log \left(N + 1\right) - \log N\]
Test:
NMSE problem 3.3.6
Bits:
128 bits
Bits error versus N
Time: 5.1 s
Input Error: 12.8
Output Error: 12.7
Log: ⚲
Profile: 🕒
\({\left(\sqrt{\log \left(\frac{N + 1}{N}\right)}\right)}^2\)
  1. Started with
    \[\log \left(N + 1\right) - \log N\]
    12.8
  2. Using strategy rm
    12.8
  3. Applied diff-log to get
    \[\color{red}{\log \left(N + 1\right) - \log N} \leadsto \color{blue}{\log \left(\frac{N + 1}{N}\right)}\]
    12.5
  4. Using strategy rm
    12.5
  5. Applied add-sqr-sqrt to get
    \[\color{red}{\log \left(\frac{N + 1}{N}\right)} \leadsto \color{blue}{{\left(\sqrt{\log \left(\frac{N + 1}{N}\right)}\right)}^2}\]
    12.7

Original test:


(lambda ((N default))
  #:name "NMSE problem 3.3.6"
  (- (log (+ N 1)) (log N)))