if n < -11332946.0f0 or 3620.3909f0 < n

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   21.0
2. Using strategy rm
   21.0
3. Applied add-log-exp to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{red}{{x}^{\left(\frac{1}{n}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{\log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)}\]
   21.1
4. Applied add-log-exp to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}} - \log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right) \leadsto \color{blue}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}\right)} - \log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)\]
   21.0
5. Applied diff-log to get
   \[\color{red}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}\right) - \log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)} \leadsto \color{blue}{\log \left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}{e^{{x}^{\left(\frac{1}{n}\right)}}}\right)}\]
   21.0
6. Applied simplify to get
   \[\log \color{red}{\left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}{e^{{x}^{\left(\frac{1}{n}\right)}}}\right)} \leadsto \log \color{blue}{\left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}\]
   21.0
7. Applied taylor to get
   \[\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right) \leadsto \log \left(e^{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}\right)\]
   18.8
8. Taylor expanded around inf to get
   \[\log \left(e^{\color{red}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}}\right) \leadsto \log \left(e^{\color{blue}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}}\right)\]
   18.8
9. Applied simplify to get
   \[\color{red}{\log \left(e^{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}\right)} \leadsto \color{blue}{\left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{\frac{\log x}{n \cdot x}}{n}}\]
   1.6
10. Applied taylor to get
    \[\left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{\frac{\log x}{n \cdot x}}{n} \leadsto \left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{-1 \cdot \frac{\log x}{n \cdot x}}{n}\]
    1.2
11. Taylor expanded around inf to get
    \[\left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{\color{red}{-1 \cdot \frac{\log x}{n \cdot x}}}{n} \leadsto \left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{\color{blue}{-1 \cdot \frac{\log x}{n \cdot x}}}{n}\]
    1.2
12. Applied simplify to get
    \[\left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{-1 \cdot \frac{\log x}{n \cdot x}}{n} \leadsto \left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{\log x}{n \cdot x} \cdot \frac{-1}{n}\]
    1.2

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13. Applied final simplification
14. Applied simplify to get
    \[\color{red}{\left(\frac{1}{n \cdot x} - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}\right) - \frac{\log x}{n \cdot x} \cdot \frac{-1}{n}} \leadsto \color{blue}{\left(\frac{\frac{1}{n}}{x} - \frac{\frac{\frac{1}{2}}{n}}{x \cdot x}\right) - \frac{-\log x}{\left(n \cdot x\right) \cdot n}}\]
    3.9

if -11332946.0f0 < n < 3620.3909f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   5.5
2. Using strategy rm
   5.5
3. Applied add-cube-cbrt to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}^3}\]
   5.5