if n < -36550324.0f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   20.1
2. Using strategy rm
   20.1
3. Applied add-cube-cbrt to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}^3}\]
   20.1
4. Applied taylor to get
   \[{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}\right)}^3\]
   5.2
5. Taylor expanded around inf to get
   \[{\left(\sqrt[3]{\color{red}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}}\right)}^3\]
   5.2
6. Applied simplify to get
   \[\color{red}{{\left(\sqrt[3]{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}\right)}^3} \leadsto \color{blue}{\left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{n}}{x \cdot x}\right) - \frac{\frac{\log x}{n \cdot x}}{n}}\]
   4.9

if -36550324.0f0 < n < 150622.2f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   5.8
2. Using strategy rm
   5.8
3. Applied add-cube-cbrt to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}^3}\]
   5.9
4. Using strategy rm
   5.9
5. Applied add-cube-cbrt to get
   \[{\color{red}{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}}^3 \leadsto {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}\right)}^3\right)}}^3\]
   5.9

if 150622.2f0 < n

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   21.0
2. Applied taylor to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto \frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\]
   4.8
3. Taylor expanded around inf to get
   \[\color{red}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)} \leadsto \color{blue}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}\]
   4.8