if x < 64.50448f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   19.8
2. Using strategy rm
   19.8
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   19.8
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{n}\right)}} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   19.8
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{n}}} - {x}^{\left(\frac{1}{n}\right)} \leadsto e^{\color{blue}{\frac{\log \left(x + 1\right)}{n}}} - {x}^{\left(\frac{1}{n}\right)}\]
   19.8

if 64.50448f0 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   10.1
2. Using strategy rm
   10.1
3. Applied add-sqr-sqrt to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{red}{{x}^{\left(\frac{1}{n}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{{\left(\sqrt{{x}^{\left(\frac{1}{n}\right)}}\right)}^2}\]
   10.6
4. Applied add-sqr-sqrt to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} - {\left(\sqrt{{x}^{\left(\frac{1}{n}\right)}}\right)}^2 \leadsto \color{blue}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}\right)}^2} - {\left(\sqrt{{x}^{\left(\frac{1}{n}\right)}}\right)}^2\]
   10.1
5. Applied difference-of-squares to get
   \[\color{red}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}\right)}^2 - {\left(\sqrt{{x}^{\left(\frac{1}{n}\right)}}\right)}^2} \leadsto \color{blue}{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} + \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} - \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right)}\]
   10.1
6. Applied taylor to get
   \[\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} + \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} - \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \leadsto \left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} + \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{n \cdot x} - \left(\frac{1}{4} \cdot \frac{\log x}{{n}^2 \cdot x} + \frac{1}{4} \cdot \frac{1}{n \cdot {x}^2}\right)\right)\]
   5.9
7. Taylor expanded around inf to get
   \[\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} + \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \color{red}{\left(\frac{1}{2} \cdot \frac{1}{n \cdot x} - \left(\frac{1}{4} \cdot \frac{\log x}{{n}^2 \cdot x} + \frac{1}{4} \cdot \frac{1}{n \cdot {x}^2}\right)\right)} \leadsto \left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} + \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{n \cdot x} - \left(\frac{1}{4} \cdot \frac{\log x}{{n}^2 \cdot x} + \frac{1}{4} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}\]
   5.9
8. Applied simplify to get
   \[\color{red}{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} + \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{n \cdot x} - \left(\frac{1}{4} \cdot \frac{\log x}{{n}^2 \cdot x} + \frac{1}{4} \cdot \frac{1}{n \cdot {x}^2}\right)\right)} \leadsto \color{blue}{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} + \sqrt{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \left(\left(\frac{\frac{\frac{1}{2}}{n}}{x} - \frac{\frac{\log x}{\frac{x}{\frac{1}{4}}}}{n \cdot n}\right) - \frac{\frac{\frac{1}{4}}{n}}{{x}^2}\right)}\]
   4.6