if n < -2.1541062f+08 or 1.4894959f+09 < n

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   28.4
2. Using strategy rm
   28.4
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   28.4
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{n}\right)}} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   28.4
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   28.4
6. Applied taylor to get
   \[e^{\frac{\log_* (1 + x)}{n}} - {x}^{\left(\frac{1}{n}\right)} \leadsto \left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right) - {x}^{\left(\frac{1}{n}\right)}\]
   27.4
7. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{\left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   27.4
8. Applied simplify to get
   \[\color{red}{\left(\frac{\log_* (1 + \frac{1}{x})}{n} + \left(1 + \frac{1}{2} \cdot \frac{{\left(\log_* (1 + \frac{1}{x})\right)}^2}{{n}^2}\right)\right) - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{(\left(\frac{\log_* (1 + \frac{1}{x})}{n}\right) * \left((\left(\frac{\log_* (1 + \frac{1}{x})}{n}\right) * \frac{1}{2} + 1)_*\right) + \left(1 - {x}^{\left(\frac{1}{n}\right)}\right))_*}\]
   25.7

if -2.1541062f+08 < n < 1.4894959f+09

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   7.6
2. Using strategy rm
   7.6
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   7.8
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{n}\right)}} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   7.8
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   6.5
6. Using strategy rm
   6.5
7. Applied add-cube-cbrt to get
   \[\color{red}{e^{\frac{\log_* (1 + x)}{n}} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{{\left(\sqrt[3]{e^{\frac{\log_* (1 + x)}{n}} - {x}^{\left(\frac{1}{n}\right)}}\right)}^3}\]
   6.6