if beta < 1.176174917700771e+170

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   1.4
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   2.3
3. Using strategy rm
   2.3
4. Applied add-sqr-sqrt to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \color{red}{\left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
   2.9
5. Applied add-sqr-sqrt to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right)} \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}\right)}^2} \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   2.5
6. Applied square-unprod to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}\right)}^2 \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
   3.0
7. Applied add-sqr-sqrt to get
   \[\frac{\color{red}{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\color{blue}{{\left(\sqrt{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}\right)}^2}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   3.0
8. Applied square-undiv to get
   \[\color{red}{\frac{{\left(\sqrt{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}\right)}^2}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \color{blue}{{\left(\frac{\sqrt{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}}{\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}\]
   1.7

if 1.176174917700771e+170 < beta

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   60.3
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   60.3
3. Applied taylor to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   59.2
4. Taylor expanded around 0 to get
   \[\frac{\color{red}{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   59.2
5. Applied simplify to get
   \[\color{red}{\frac{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{0.25 \cdot \left(\alpha + \beta\right) + 0.5}{\left(\left(\alpha + \beta\right) + 2\right) \cdot \left(\left(\alpha + \beta\right) + \left(2 + 1.0\right)\right)}}\]
   59.2