if N < 91.210335f0

1. Started with
   \[\log \left(N + 1\right) - \log N\]
   15.5
2. Using strategy rm
   15.5
3. Applied diff-log to get
   \[\color{red}{\log \left(N + 1\right) - \log N} \leadsto \color{blue}{\log \left(\frac{N + 1}{N}\right)}\]
   12.2
4. Applied taylor to get
   \[\log \left(\frac{N + 1}{N}\right) \leadsto \log \left(1 + \frac{1}{N}\right)\]
   12.2
5. Taylor expanded around 0 to get
   \[\log \color{red}{\left(1 + \frac{1}{N}\right)} \leadsto \log \color{blue}{\left(1 + \frac{1}{N}\right)}\]
   12.2

if 91.210335f0 < N

1. Started with
   \[\log \left(N + 1\right) - \log N\]
   26.6
2. Applied taylor to get
   \[\log \left(N + 1\right) - \log N \leadsto \left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}\]
   0.0
3. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}} \leadsto \color{blue}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}}\]
   0.0
4. Applied simplify to get
   \[\color{red}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}} \leadsto \color{blue}{\frac{1}{N} + \left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \frac{\frac{1}{2}}{N \cdot N}\right)}\]
   0.0
5. Applied simplify to get
   \[\frac{1}{N} + \color{red}{\left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \frac{\frac{1}{2}}{N \cdot N}\right)} \leadsto \frac{1}{N} + \color{blue}{\left(\frac{\frac{1}{3}}{{N}^3} - \frac{\frac{1}{2}}{N \cdot N}\right)}\]
   0.0