if x < 12708545.0f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   2.0
2. Using strategy rm
   2.0
3. Applied add-exp-log to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   2.0

if 12708545.0f0 < 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 pow-to-exp to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{e^{\log x \cdot \frac{1}{3}}}\]
   29.5
4. Applied simplify to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{red}{\log x \cdot \frac{1}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{blue}{\frac{\log x}{3}}}\]
   29.4
5. Using strategy rm
   29.4
6. Applied *-un-lft-identity to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{red}{\frac{\log x}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{blue}{1 \cdot \frac{\log x}{3}}}\]
   29.4
7. Applied exp-prod to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{e^{1 \cdot \frac{\log x}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(e^{1}\right)}^{\left(\frac{\log x}{3}\right)}}\]
   29.4
8. Applied simplify to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {\color{red}{\left(e^{1}\right)}}^{\left(\frac{\log x}{3}\right)} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {\color{blue}{e}}^{\left(\frac{\log x}{3}\right)}\]
   29.4
9. Using strategy rm
   29.4
10. Applied add-sqr-sqrt to get
    \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - {e}^{\left(\frac{\log x}{3}\right)} \leadsto \color{blue}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2} - {e}^{\left(\frac{\log x}{3}\right)}\]
    29.5
11. Applied taylor to get
    \[{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2 - {e}^{\left(\frac{\log x}{3}\right)} \leadsto \left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + e^{\frac{-1}{3} \cdot \left(\log e \cdot \log x\right)}\right)\]
    28.5
12. Taylor expanded around inf to get
    \[\color{red}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + e^{\frac{-1}{3} \cdot \left(\log e \cdot \log x\right)}\right)} \leadsto \color{blue}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + e^{\frac{-1}{3} \cdot \left(\log e \cdot \log x\right)}\right)}\]
    28.5
13. Applied simplify to get
    \[\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + e^{\frac{-1}{3} \cdot \left(\log e \cdot \log x\right)}\right) \leadsto \left(\sqrt[3]{\frac{1}{x}} + \frac{1}{3} \cdot \sqrt[3]{\frac{1}{{x}^{4}}}\right) - \left({x}^{\left(\log e \cdot \frac{-1}{3}\right)} + \frac{1}{9} \cdot \sqrt[3]{\frac{1}{{x}^{7}}}\right)\]
    28.3

---

14. Applied final simplification