if x < -1052.4147f0 or 19.416372f0 < x

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   8.1
2. Applied taylor to get
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \leadsto 2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)\]
   0.8
3. Taylor expanded around inf to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
   0.8
4. Applied simplify to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^3}\right) + \frac{2}{{x}^{5}}}\]
   0.8

if -1052.4147f0 < x < 19.416372f0

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   0.4
2. Using strategy rm
   0.4
3. Applied add-cube-cbrt to get
   \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}} \leadsto \color{blue}{{\left(\sqrt[3]{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}}\right)}^3}\]
   1.0
4. Using strategy rm
   1.0
5. Applied frac-sub to get
   \[{\left(\sqrt[3]{\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right)} + \frac{1}{x - 1}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}}\right)}^3\]
   1.0
6. Applied frac-add to get
   \[{\left(\sqrt[3]{\color{red}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}}\right)}^3\]
   0.8
7. Applied cbrt-div to get
   \[{\color{red}{\left(\sqrt[3]{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\right)}}^3 \leadsto {\color{blue}{\left(\frac{\sqrt[3]{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}}{\sqrt[3]{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\right)}}^3\]
   0.9
8. Applied cube-div to get
   \[\color{red}{{\left(\frac{\sqrt[3]{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}}{\sqrt[3]{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\right)}^3} \leadsto \color{blue}{\frac{{\left(\sqrt[3]{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}\right)}^3}{{\left(\sqrt[3]{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\right)}^3}}\]
   0.9
9. Applied simplify to get
   \[\frac{\color{red}{{\left(\sqrt[3]{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}\right)}^3}}{{\left(\sqrt[3]{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\right)}^3} \leadsto \frac{\color{blue}{\left(x + x \cdot x\right) + \left(\left(x - 2\right) - x \cdot 2\right) \cdot \left(x - 1\right)}}{{\left(\sqrt[3]{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\right)}^3}\]
   0.8
10. Applied simplify to get
    \[\frac{\left(x + x \cdot x\right) + \left(\left(x - 2\right) - x \cdot 2\right) \cdot \left(x - 1\right)}{\color{red}{{\left(\sqrt[3]{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\right)}^3}} \leadsto \frac{\left(x + x \cdot x\right) + \left(\left(x - 2\right) - x \cdot 2\right) \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(\left(x + 1\right) \cdot \left(x - 1\right)\right)}}\]
    0.2