if x < 13.5327772596717

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   0.0
2. Using strategy rm
   0.0
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   0.0
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   0.0
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   0.0
6. Using strategy rm
   0.0
7. Applied add-cbrt-cube to get
   \[\color{red}{e^{\frac{\log_* (1 + x)}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{\sqrt[3]{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3}} - {x}^{\left(\frac{1}{3}\right)}\]
   0.1
8. Applied taylor to get
   \[\sqrt[3]{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3} - {x}^{\left(\frac{1}{3}\right)} \leadsto \sqrt[3]{{\left(e^{\frac{1}{3} \cdot \log_* (1 + x)}\right)}^3} - {x}^{\left(\frac{1}{3}\right)}\]
   0.1
9. Taylor expanded around 0 to get
   \[\sqrt[3]{{\color{red}{\left(e^{\frac{1}{3} \cdot \log_* (1 + x)}\right)}}^3} - {x}^{\left(\frac{1}{3}\right)} \leadsto \sqrt[3]{{\color{blue}{\left(e^{\frac{1}{3} \cdot \log_* (1 + x)}\right)}}^3} - {x}^{\left(\frac{1}{3}\right)}\]
   0.1
10. Applied simplify to get
    \[\color{red}{\sqrt[3]{{\left(e^{\frac{1}{3} \cdot \log_* (1 + x)}\right)}^3} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log_* (1 + x)\right)} - {x}^{\left(\frac{1}{3}\right)}}\]
    0.0

if 13.5327772596717 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   59.8
2. Using strategy rm
   59.8
3. Applied add-exp-log to get
   \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   60.3
4. Applied pow-exp to get
   \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   60.3
5. Applied simplify to get
   \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
   59.7
6. Using strategy rm
   59.7
7. Applied flip3-- to get
   \[\color{red}{e^{\frac{\log_* (1 + x)}{3}} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{\frac{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   59.6
8. Applied simplify to get
   \[\frac{\color{red}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto \frac{\color{blue}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
   59.6
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
    \[\frac{{\left(e^{\frac{1}{3} \cdot \log_* (1 + \frac{-1}{x})}\right)}^3 - {\left({\left(\frac{-1}{x}\right)}^{\frac{1}{3}}\right)}^3}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log_* (1 + x)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)} \leadsto \frac{{\left({\left(e^{\frac{1}{3}}\right)}^{\left(\log_* (1 + \frac{-1}{x})\right)}\right)}^3 - \frac{-1}{x}}{(\left({x}^{\left(\frac{1}{3}\right)}\right) * \left(e^{\frac{\log_* (1 + x)}{3}} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^2\right))_*}\]
    4.9

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12. Applied final simplification