if beta < 9.753696f+22

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   1.0
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   1.7
3. Using strategy rm
   1.7
4. Applied add-sqr-sqrt to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \color{red}{\left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
   1.1
5. Applied add-sqr-sqrt to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right)} \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}\right)}^2} \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   1.1
6. Applied square-unprod to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}\right)}^2 \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
   1.1
7. Applied add-sqr-sqrt to get
   \[\frac{\color{red}{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\color{blue}{{\left(\sqrt{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}\right)}^2}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   1.2
8. Applied square-undiv to get
   \[\color{red}{\frac{{\left(\sqrt{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}\right)}^2}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \color{blue}{{\left(\frac{\sqrt{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}}{\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}\]
   1.2

if 9.753696f+22 < beta

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   27.9
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   27.9
3. Applied taylor to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   26.8
4. Taylor expanded around 0 to get
   \[\frac{\color{red}{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   26.8
5. Applied simplify to get
   \[\color{red}{\frac{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{0.25 \cdot \left(\alpha + \beta\right) + 0.5}{\left(\left(\alpha + \beta\right) + 2\right) \cdot \left(\left(\alpha + \beta\right) + \left(2 + 1.0\right)\right)}}\]
   26.8