if x < 19436852.0f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   1.9
2. Using strategy rm
   1.9
3. Applied add-exp-log to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   1.9

if 19436852.0f0 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   0.0
2. Using strategy rm
   0.0
3. Applied add-exp-log to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   0.0
4. Using strategy rm
   0.0
5. Applied add-sqr-sqrt to get
   \[e^{\log \left(\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto e^{\log \left(\color{blue}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2} - {x}^{\left(\frac{1}{3}\right)}\right)}\]
   30.5
6. Applied taylor to get
   \[e^{\log \left({\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2 - {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto e^{\left(\frac{1}{3} \cdot \left({\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right) + \log \left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)\right) - \left(\frac{1}{18} \cdot \left({\left(\frac{1}{{x}^{8}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)}^2}\right) + \frac{1}{9} \cdot \left({\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right)\right)}\]
   30.9
7. Taylor expanded around inf to get
   \[e^{\color{red}{\left(\frac{1}{3} \cdot \left({\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right) + \log \left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)\right) - \left(\frac{1}{18} \cdot \left({\left(\frac{1}{{x}^{8}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)}^2}\right) + \frac{1}{9} \cdot \left({\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right)\right)}} \leadsto e^{\color{blue}{\left(\frac{1}{3} \cdot \left({\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right) + \log \left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)\right) - \left(\frac{1}{18} \cdot \left({\left(\frac{1}{{x}^{8}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)}^2}\right) + \frac{1}{9} \cdot \left({\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right)\right)}}\]
   30.9
8. Applied simplify to get
   \[e^{\left(\frac{1}{3} \cdot \left({\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right) + \log \left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)\right) - \left(\frac{1}{18} \cdot \left({\left(\frac{1}{{x}^{8}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}\right)}^2}\right) + \frac{1}{9} \cdot \left({\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} \cdot \frac{1}{{\left(\frac{1}{x}\right)}^{\frac{1}{3}} - {x}^{\frac{-1}{3}}}\right)\right)} \leadsto e^{\left(\log \left(\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}\right) + \frac{\sqrt[3]{\frac{1}{{x}^{4}}}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \frac{1}{3}\right) - \left(\frac{\sqrt[3]{\frac{1}{{x}^{7}}}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \frac{1}{9} + \frac{\frac{1}{18}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \frac{\sqrt[3]{\frac{1}{{x}^{8}}}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}}\right)}\]
   29.3

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9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{e^{\left(\log \left(\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}\right) + \frac{\sqrt[3]{\frac{1}{{x}^{4}}}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \frac{1}{3}\right) - \left(\frac{\sqrt[3]{\frac{1}{{x}^{7}}}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \frac{1}{9} + \frac{\frac{1}{18}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \frac{\sqrt[3]{\frac{1}{{x}^{8}}}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}}\right)}} \leadsto \color{blue}{e^{\left(\log \left(\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}\right) - \frac{\frac{1}{9}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \sqrt[3]{\frac{1}{{x}^{7}}}\right) + \left(\frac{\frac{1}{3}}{\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}} \cdot \sqrt[3]{\frac{1}{{x}^{4}}} - \frac{\sqrt[3]{\frac{1}{{x}^{8}}} \cdot \frac{1}{18}}{{\left(\sqrt[3]{\frac{1}{x}} - {x}^{\frac{-1}{3}}\right)}^2}\right)}}\]
    29.3