if x < 4.6312522f+08

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   2.7
2. Using strategy rm
   2.7
3. Applied add-cube-cbrt to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(\sqrt[3]{{x}^{\left(\frac{1}{3}\right)}}\right)}^3}\]
   2.8

if 4.6312522f+08 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   20.3
2. Using strategy rm
   20.3
3. Applied expm1-log1p-u to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{(e^{\log_* (1 + \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right))} - 1)^*}\]
   20.3
4. Using strategy rm
   20.3
5. Applied add-sqr-sqrt to get
   \[(e^{\log_* (1 + \left(\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)}\right))} - 1)^* \leadsto (e^{\log_* (1 + \left(\color{blue}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2} - {x}^{\left(\frac{1}{3}\right)}\right))} - 1)^*\]
   30.1
6. Applied taylor to get
   \[(e^{\log_* (1 + \left({\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2 - {x}^{\left(\frac{1}{3}\right)}\right))} - 1)^* \leadsto (e^{\log_* (1 + \left(\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)\right))} - 1)^*\]
   20.4
7. Taylor expanded around inf to get
   \[(e^{\log_* (1 + \color{red}{\left(\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)\right)})} - 1)^* \leadsto (e^{\log_* (1 + \color{blue}{\left(\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)\right)})} - 1)^*\]
   20.4
8. Applied simplify to get
   \[(e^{\log_* (1 + \left(\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)\right))} - 1)^* \leadsto (\left(\sqrt[3]{\frac{1}{{x}^{4}}}\right) * \frac{1}{3} + \left(\sqrt[3]{\frac{1}{x}}\right))_* - (\frac{1}{9} * \left(\sqrt[3]{\frac{1}{{x}^{7}}}\right) + \left({x}^{\frac{-1}{3}}\right))_*\]
   28.5

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9. Applied final simplification