if x < 2.2992657633277677e+17

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   1.5
2. Using strategy rm
   1.5
3. Applied add-log-exp to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{\log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right)}\]
   2.1
4. Applied add-log-exp to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - \log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right) \leadsto \color{blue}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)} - \log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right)\]
   2.1
5. Applied diff-log to get
   \[\color{red}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right) - \log \left(e^{{x}^{\left(\frac{1}{3}\right)}}\right)} \leadsto \color{blue}{\log \left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}}{e^{{x}^{\left(\frac{1}{3}\right)}}}\right)}\]
   2.1
6. Applied simplify to get
   \[\log \color{red}{\left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}}{e^{{x}^{\left(\frac{1}{3}\right)}}}\right)} \leadsto \log \color{blue}{\left(e^{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}}\right)}\]
   1.6

if 2.2992657633277677e+17 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   45.0
2. Using strategy rm
   45.0
3. Applied add-cbrt-cube to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{\sqrt[3]{{\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}\]
   53.0
4. Applied taylor to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \sqrt[3]{{\left({x}^{\left(\frac{1}{3}\right)}\right)}^3} \leadsto \left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)\]
   46.1
5. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)} \leadsto \color{blue}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)}\]
   46.1
6. Applied simplify to get
   \[\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) \leadsto \left({x}^{\frac{-1}{3}} - \frac{1}{9} \cdot \sqrt[3]{\frac{1}{{x}^{7}}}\right) - \left(\sqrt[3]{\frac{1}{x}} - \frac{1}{3} \cdot \sqrt[3]{\frac{1}{{x}^{4}}}\right)\]
   60.5

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7. Applied final simplification