if x < 6.741693610388393e+16

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   1.6
2. Using strategy rm
   1.6
3. Applied flip3-- to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   1.4
4. Applied simplify to get
   \[\frac{\color{red}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto \frac{\color{blue}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
   1.4

if 6.741693610388393e+16 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   45.3
2. Using strategy rm
   45.3
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   61.9
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   61.9
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto e^{\color{blue}{\frac{\log \left(x + 1\right)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   61.6
6. Using strategy rm
   61.6
7. Applied add-cube-cbrt to get
   \[e^{\frac{\log \left(x + 1\right)}{3}} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto e^{\frac{\log \left(x + 1\right)}{3}} - \color{blue}{{\left(\sqrt[3]{{x}^{\left(\frac{1}{3}\right)}}\right)}^3}\]
   61.6
8. Applied taylor to get
   \[e^{\frac{\log \left(x + 1\right)}{3}} - {\left(\sqrt[3]{{x}^{\left(\frac{1}{3}\right)}}\right)}^3 \leadsto \left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)\]
   46.9
9. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)} \leadsto \color{blue}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)}\]
   46.9
10. Applied simplify to get
    \[\color{red}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)} \leadsto \color{blue}{\left({x}^{\frac{-1}{3}} - \frac{1}{9} \cdot \sqrt[3]{\frac{1}{{x}^{7}}}\right) - \left(\sqrt[3]{\frac{1}{x}} - \frac{1}{3} \cdot \sqrt[3]{\frac{1}{{x}^{4}}}\right)}\]
    60.4