if x < 36833612.0f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   2.2
2. Using strategy rm
   2.2
3. Applied add-sqr-sqrt to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\]
   2.3

if 36833612.0f0 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   20.7
2. Using strategy rm
   20.7
3. Applied add-log-exp to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{\log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right)}\]
   31.2
4. Applied add-log-exp to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - \log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right) \leadsto \color{blue}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)} - \log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right)\]
   30.8
5. Applied diff-log to get
   \[\color{red}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right) - \log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right)} \leadsto \color{blue}{\log \left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}}{e^{{x}^{\left(\frac{1}{3}\right)}}}\right)}\]
   30.8
6. Applied simplify to get
   \[\log \color{red}{\left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}}{e^{{x}^{\left(\frac{1}{3}\right)}}}\right)} \leadsto \log \color{blue}{\left(e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}}\right)}\]
   20.7
7. Using strategy rm
   20.7
8. Applied add-sqr-sqrt to get
   \[\log \left(e^{\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)}}\right) \leadsto \log \left(e^{\color{blue}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2} - {x}^{\left(\frac{1}{3}\right)}}\right)\]
   30.1
9. Applied taylor to get
   \[\log \left(e^{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2 - {x}^{\left(\frac{1}{3}\right)}}\right) \leadsto \log \left(e^{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)}\right)\]
   20.7
10. Taylor expanded around inf to get
    \[\log \left(e^{\color{red}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)}}\right) \leadsto \log \left(e^{\color{blue}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)}}\right)\]
    20.7
11. Applied simplify to get
    \[\log \left(e^{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)}\right) \leadsto (\left(\sqrt[3]{\frac{1}{{x}^{4}}}\right) * \frac{1}{3} + \left(\sqrt[3]{\frac{1}{x}}\right))_* - (\frac{1}{9} * \left(\sqrt[3]{\frac{1}{{x}^{7}}}\right) + \left({x}^{\frac{-1}{3}}\right))_*\]
    28.4

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12. Applied final simplification