if x < 36833612.0f0

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   20.1
2. Applied taylor to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\frac{1}{3}}\]
   20.1
3. Taylor expanded around 0 to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\frac{1}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{x}^{\frac{1}{3}}}\]
   20.1
4. Applied simplify to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\frac{1}{3}}} \leadsto \color{blue}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \sqrt[3]{x}}\]
   10.6
5. Using strategy rm
   10.6
6. Applied flip3-- to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \sqrt[3]{x}} \leadsto \color{blue}{\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}}\]
   10.6
7. Applied simplify to get
   \[\frac{\color{red}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)} \leadsto \frac{\color{blue}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}\]
   10.6
8. Using strategy rm
   10.6
9. Applied add-cube-cbrt to get
   \[\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}{\color{red}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}} \leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}{\color{blue}{{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}\right)}^3}}\]
   10.9
10. Applied add-cube-cbrt to get
    \[\frac{\color{red}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}}{{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}\right)}^3} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}\right)}^3}}{{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}\right)}^3}\]
    10.9
11. Applied cube-undiv to get
    \[\color{red}{\frac{{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}\right)}^3}{{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}\right)}^3}} \leadsto \color{blue}{{\left(\frac{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}}\right)}^3}\]
    10.9
12. Applied taylor to get
    \[{\left(\frac{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - x}}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{x}\right)}}\right)}^3 \leadsto {\left(\frac{\sqrt[3]{{\left({\left(1 + x\right)}^{\frac{1}{3}}\right)}^3 - x}}{\sqrt[3]{{\left({\left(1 + x\right)}^2\right)}^{\frac{1}{3}} + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(1 + x\right)}^{\frac{1}{3}} \cdot \sqrt[3]{x}\right)}}\right)}^3\]
    10.9
13. Taylor expanded around 0 to get
    \[\color{red}{{\left(\frac{\sqrt[3]{{\left({\left(1 + x\right)}^{\frac{1}{3}}\right)}^3 - x}}{\sqrt[3]{{\left({\left(1 + x\right)}^2\right)}^{\frac{1}{3}} + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(1 + x\right)}^{\frac{1}{3}} \cdot \sqrt[3]{x}\right)}}\right)}^3} \leadsto \color{blue}{{\left(\frac{\sqrt[3]{{\left({\left(1 + x\right)}^{\frac{1}{3}}\right)}^3 - x}}{\sqrt[3]{{\left({\left(1 + x\right)}^2\right)}^{\frac{1}{3}} + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(1 + x\right)}^{\frac{1}{3}} \cdot \sqrt[3]{x}\right)}}\right)}^3}\]
    10.9
14. Applied simplify to get
    \[{\left(\frac{\sqrt[3]{{\left({\left(1 + x\right)}^{\frac{1}{3}}\right)}^3 - x}}{\sqrt[3]{{\left({\left(1 + x\right)}^2\right)}^{\frac{1}{3}} + \left({\left(\sqrt[3]{x}\right)}^2 + {\left(1 + x\right)}^{\frac{1}{3}} \cdot \sqrt[3]{x}\right)}}\right)}^3 \leadsto \frac{\left(1 + x\right) - x}{\sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) + \sqrt[3]{\left(1 + x\right) \cdot \left(1 + x\right)}}\]
    7.7

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15. Applied final simplification
16. Applied simplify to get
    \[\color{red}{\frac{\left(1 + x\right) - x}{\sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) + \sqrt[3]{\left(1 + x\right) \cdot \left(1 + x\right)}}} \leadsto \color{blue}{\frac{1}{\sqrt[3]{\left(1 + x\right) \cdot \left(1 + x\right)} + \sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right)}}\]
    4.7

if 36833612.0f0 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
   20.9
2. Using strategy rm
   20.9
3. Applied add-sqr-sqrt to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2} - {x}^{\left(\frac{1}{3}\right)}\]
   29.8
4. Applied taylor to get
   \[{\left(\sqrt{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^2 - {x}^{\left(\frac{1}{3}\right)} \leadsto \left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)\]
   20.2
5. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)} \leadsto \color{blue}{\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right)}\]
   20.2
6. Applied simplify to get
   \[\left(\frac{1}{3} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \left(\frac{1}{9} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + {x}^{\frac{-1}{3}}\right) \leadsto \left(\sqrt[3]{\frac{1}{x}} - \frac{1}{9} \cdot \sqrt[3]{\frac{1}{{x}^{7}}}\right) - \left({x}^{\frac{-1}{3}} - \frac{1}{3} \cdot \sqrt[3]{\frac{1}{{x}^{4}}}\right)\]
   28.4

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7. Applied final simplification