if x < 7110581.0f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   1.7
2. Using strategy rm
   1.7
3. Applied add-exp-log to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   1.7
4. Using strategy rm
   1.7
5. Applied pow1 to get
   \[e^{\log \color{red}{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}} \leadsto e^{\log \color{blue}{\left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}^{1}\right)}}\]
   1.7
6. Applied log-pow to get
   \[e^{\color{red}{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}^{1}\right)}} \leadsto e^{\color{blue}{1 \cdot \log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   1.7
7. Applied exp-prod to get
   \[\color{red}{e^{1 \cdot \log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}} \leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)\right)}}\]
   1.7
8. Applied simplify to get
   \[{\color{red}{\left(e^{1}\right)}}^{\left(\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)\right)} \leadsto {\color{blue}{e}}^{\left(\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)\right)}\]
   1.7

if 7110581.0f0 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   20.6
2. Using strategy rm
   20.6
3. Applied add-sqr-sqrt to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2} - {x}^{\left(\frac{1}{3}\right)}\]
   29.8
4. Applied taylor to get
   \[{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2 - {x}^{\left(\frac{1}{3}\right)} \leadsto \left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)\]
   19.3
5. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)} \leadsto \color{blue}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)}\]
   19.3
6. Applied simplify to get
   \[\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) \leadsto (\left(\sqrt[3]{\frac{1}{{x}^{4}}}\right) * \frac{1}{3} + \left(\sqrt[3]{\frac{1}{x}}\right))_* - (\frac{1}{9} * \left(\sqrt[3]{\frac{1}{{x}^{7}}}\right) + \left({x}^{\frac{-1}{3}}\right))_*\]
   28.3

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7. Applied final simplification