if x < 6809.194157769488

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   0.1
2. Using strategy rm
   0.1
3. Applied add-sqr-sqrt to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\]
   0.1

if 6809.194157769488 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   60.1
2. Using strategy rm
   60.1
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   60.6
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   60.6
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   60.0
6. Using strategy rm
   60.0
7. Applied flip3-- to get
   \[\color{red}{e^{\frac{\log_* (1 + x)}{3}} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{\frac{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   59.9
8. Applied simplify to get
   \[\frac{\color{red}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto \frac{\color{blue}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
   59.9
9. Applied taylor to get
   \[\frac{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto \frac{{\left(e^{\frac{1}{3} \cdot \log_* (1 + \frac{-1}{x})}\right)}^3 - {\left({\left(\frac{-1}{x}\right)}^{\frac{1}{3}}\right)}^3}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
   62.4
10. Taylor expanded around -inf to get
    \[\frac{\color{red}{{\left(e^{\frac{1}{3} \cdot \log_* (1 + \frac{-1}{x})}\right)}^3 - {\left({\left(\frac{-1}{x}\right)}^{\frac{1}{3}}\right)}^3}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto \frac{\color{blue}{{\left(e^{\frac{1}{3} \cdot \log_* (1 + \frac{-1}{x})}\right)}^3 - {\left({\left(\frac{-1}{x}\right)}^{\frac{1}{3}}\right)}^3}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
    62.4
11. Applied simplify to get
    \[\color{red}{\frac{{\left(e^{\frac{1}{3} \cdot \log_* (1 + \frac{-1}{x})}\right)}^3 - {\left({\left(\frac{-1}{x}\right)}^{\frac{1}{3}}\right)}^3}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}} \leadsto \color{blue}{\frac{e^{\left(\left(\frac{1}{3} + \frac{1}{3}\right) + \frac{1}{3}\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\left({x}^{\left(\frac{1}{3}\right)}\right) * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2\right))_*}}\]
    4.9
12. Applied taylor to get
    \[\frac{e^{\left(\left(\frac{1}{3} + \frac{1}{3}\right) + \frac{1}{3}\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\left({x}^{\left(\frac{1}{3}\right)}\right) * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2\right))_*} \leadsto \frac{e^{\left(\left(\frac{1}{3} + \frac{1}{3}\right) + \frac{1}{3}\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\left({x}^{\frac{1}{3}}\right) * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2\right))_*}\]
    4.9
13. Taylor expanded around 0 to get
    \[\frac{e^{\left(\left(\frac{1}{3} + \frac{1}{3}\right) + \frac{1}{3}\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\color{red}{\left({x}^{\frac{1}{3}}\right)} * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2\right))_*} \leadsto \frac{e^{\left(\left(\frac{1}{3} + \frac{1}{3}\right) + \frac{1}{3}\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\color{blue}{\left({x}^{\frac{1}{3}}\right)} * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2\right))_*}\]
    4.9
14. Applied simplify to get
    \[\frac{e^{\left(\left(\frac{1}{3} + \frac{1}{3}\right) + \frac{1}{3}\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\left({x}^{\frac{1}{3}}\right) * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2\right))_*} \leadsto \frac{e^{\left(\frac{1}{3} + \left(\frac{1}{3} + \frac{1}{3}\right)\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\left(\sqrt[3]{x}\right) * \left({x}^{\left(\frac{1}{3}\right)} + e^{\frac{\log_* (1 + x)}{3}}\right) + \left(e^{\frac{\log_* (1 + x)}{3} + \frac{\log_* (1 + x)}{3}}\right))_*}\]
    4.6

---

15. Applied final simplification
16. Applied simplify to get
    \[\color{red}{\frac{e^{\left(\frac{1}{3} + \left(\frac{1}{3} + \frac{1}{3}\right)\right) \cdot \log_* (1 + \frac{-1}{x})} - \frac{-1}{x}}{(\left(\sqrt[3]{x}\right) * \left({x}^{\left(\frac{1}{3}\right)} + e^{\frac{\log_* (1 + x)}{3}}\right) + \left(e^{\frac{\log_* (1 + x)}{3} + \frac{\log_* (1 + x)}{3}}\right))_*}} \leadsto \color{blue}{\frac{{\left({\left(e^{\frac{1}{3}}\right)}^3\right)}^{\left(\log_* (1 + \frac{-1}{x})\right)} - \frac{-1}{x}}{(\left(\sqrt[3]{x}\right) * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left(e^{\frac{\log_* (1 + x)}{3}} \cdot e^{\frac{\log_* (1 + x)}{3}}\right))_*}}\]
    4.6