if x < 0.03150794f0

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-exp-log to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   0.1
4. Using strategy rm
   0.1
5. Applied add-sqr-sqrt to get
   \[e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}}\right)} \leadsto e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\right)}\]
   0.1
6. Using strategy rm
   0.1
7. Applied flip-- to get
   \[e^{\log \color{red}{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}} \leadsto e^{\log \color{blue}{\left(\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\right)}}\]
   0.1
8. Applied log-div to get
   \[e^{\color{red}{\log \left(\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\right)}} \leadsto e^{\color{blue}{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right) - \log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}}\]
   0.3
9. Applied exp-diff to get
   \[\color{red}{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right) - \log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}} \leadsto \color{blue}{\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}}}\]
   0.3
10. Applied simplify to get
    \[\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{\color{red}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}}} \leadsto \frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{\color{blue}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}}\]
    0.1
11. Applied taylor to get
    \[\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} \leadsto \frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\frac{1}{3}}}\right)}^2\right)}^2\right)}}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\]
    0.1
12. Taylor expanded around 0 to get
    \[\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{\color{red}{{x}^{\frac{1}{3}}}}\right)}^2\right)}^2\right)}}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} \leadsto \frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{\color{blue}{{x}^{\frac{1}{3}}}}\right)}^2\right)}^2\right)}}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\]
    0.1
13. Applied simplify to get
    \[\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\frac{1}{3}}}\right)}^2\right)}^2\right)}}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} \leadsto \frac{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \sqrt[3]{x}\right)}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\]
    0.1

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14. Applied final simplification

if 0.03150794f0 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   25.0
2. Using strategy rm
   25.0
3. Applied add-exp-log to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
   25.0
4. Using strategy rm
   25.0
5. Applied flip3-- to get
   \[e^{\log \color{red}{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}} \leadsto e^{\log \color{blue}{\left(\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\right)}}\]
   24.6
6. Applied log-div to get
   \[e^{\color{red}{\log \left(\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\right)}} \leadsto e^{\color{blue}{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}\right) - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)}}\]
   24.6
7. Applied simplify to get
   \[e^{\color{red}{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}\right)} - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)} \leadsto e^{\color{blue}{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3\right)} - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)}\]
   25.0
8. Applied taylor to get
   \[e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3\right) - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)} \leadsto e^{\log \left({\left({\left(1 + \frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3 - {\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3\right) - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)}\]
   3.0
9. Taylor expanded around inf to get
   \[e^{\log \color{red}{\left({\left({\left(1 + \frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3 - {\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3\right)} - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)} \leadsto e^{\log \color{blue}{\left({\left({\left(1 + \frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3 - {\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3\right)} - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)}\]
   3.0
10. Applied simplify to get
    \[e^{\log \left({\left({\left(1 + \frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3 - {\left({\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right)}^3\right) - \log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)\right)} \leadsto \frac{\left(\frac{1}{x} + 1\right) - \frac{1}{x}}{(\left({x}^{\left(\frac{1}{3}\right)}\right) * \left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right) + \left({\left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)}\right)}^2\right))_*}\]
    3.2

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11. Applied final simplification