if beta < 1.0516358404724637e+204

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   1.8
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   2.8
3. Using strategy rm
   2.8
4. Applied associate-/r* to get
   \[\color{red}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}}\]
   1.8

if 1.0516358404724637e+204 < beta

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   60.0
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   60.0
3. Using strategy rm
   60.0
4. Applied add-sqr-sqrt to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \color{red}{\left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
   60.0
5. Applied add-sqr-sqrt to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right)} \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}\right)}^2} \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   60.0
6. Applied square-unprod to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}\right)}^2 \cdot {\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
   60.0
7. Applied add-sqr-sqrt to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{red}{\alpha + \left(2 + \beta\right)}}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   60.0
8. Applied add-sqr-sqrt to get
   \[\frac{\frac{\color{red}{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\frac{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   60.0
9. Applied square-undiv to get
   \[\frac{\color{red}{\frac{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}\right)}^2}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{\color{blue}{{\left(\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
   60.0
10. Applied square-undiv to get
    \[\color{red}{\frac{{\left(\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \color{blue}{{\left(\frac{\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}}{\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}\]
    60.0
11. Applied simplify to get
    \[{\color{red}{\left(\frac{\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}}{\sqrt{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \sqrt{\alpha + \left(2 + \beta\right)}}\right)}}^2 \leadsto {\color{blue}{\left(\frac{\sqrt{\left(\alpha \cdot \beta + 1.0\right) + \left(\beta + \alpha\right)}}{\sqrt{\left(2 + \beta\right) + \left(\alpha + 1.0\right)} \cdot \left(\left(\beta + \alpha\right) + 2\right)}\right)}}^2\]
    60.0
12. Applied taylor to get
    \[{\left(\frac{\sqrt{\left(\alpha \cdot \beta + 1.0\right) + \left(\beta + \alpha\right)}}{\sqrt{\left(2 + \beta\right) + \left(\alpha + 1.0\right)} \cdot \left(\left(\beta + \alpha\right) + 2\right)}\right)}^2 \leadsto {\left(\frac{\frac{1}{2} \cdot \left(\sqrt{1.0} \cdot \alpha\right) + \left(\sqrt{1.0} + \frac{1}{2} \cdot \frac{\beta}{\sqrt{1.0}}\right)}{\sqrt{\left(2 + \beta\right) + \left(\alpha + 1.0\right)} \cdot \left(\left(\beta + \alpha\right) + 2\right)}\right)}^2\]
    58.4
13. Taylor expanded around 0 to get
    \[{\left(\frac{\color{red}{\frac{1}{2} \cdot \left(\sqrt{1.0} \cdot \alpha\right) + \left(\sqrt{1.0} + \frac{1}{2} \cdot \frac{\beta}{\sqrt{1.0}}\right)}}{\sqrt{\left(2 + \beta\right) + \left(\alpha + 1.0\right)} \cdot \left(\left(\beta + \alpha\right) + 2\right)}\right)}^2 \leadsto {\left(\frac{\color{blue}{\frac{1}{2} \cdot \left(\sqrt{1.0} \cdot \alpha\right) + \left(\sqrt{1.0} + \frac{1}{2} \cdot \frac{\beta}{\sqrt{1.0}}\right)}}{\sqrt{\left(2 + \beta\right) + \left(\alpha + 1.0\right)} \cdot \left(\left(\beta + \alpha\right) + 2\right)}\right)}^2\]
    58.4
14. Applied simplify to get
    \[{\left(\frac{\frac{1}{2} \cdot \left(\sqrt{1.0} \cdot \alpha\right) + \left(\sqrt{1.0} + \frac{1}{2} \cdot \frac{\beta}{\sqrt{1.0}}\right)}{\sqrt{\left(2 + \beta\right) + \left(\alpha + 1.0\right)} \cdot \left(\left(\beta + \alpha\right) + 2\right)}\right)}^2 \leadsto \frac{\left(\alpha \cdot \frac{1}{2}\right) \cdot \sqrt{1.0} + \left(\sqrt{1.0} + \frac{\frac{1}{2} \cdot \beta}{\sqrt{1.0}}\right)}{\left(2 + \left(\beta + \alpha\right)\right) \cdot \sqrt{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}} \cdot \frac{\left(\alpha \cdot \frac{1}{2}\right) \cdot \sqrt{1.0} + \left(\sqrt{1.0} + \frac{\frac{1}{2} \cdot \beta}{\sqrt{1.0}}\right)}{\left(2 + \left(\beta + \alpha\right)\right) \cdot \sqrt{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}}\]
    58.4

---

15. Applied final simplification
16. Applied simplify to get
    \[\color{red}{\frac{\left(\alpha \cdot \frac{1}{2}\right) \cdot \sqrt{1.0} + \left(\sqrt{1.0} + \frac{\frac{1}{2} \cdot \beta}{\sqrt{1.0}}\right)}{\left(2 + \left(\beta + \alpha\right)\right) \cdot \sqrt{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}} \cdot \frac{\left(\alpha \cdot \frac{1}{2}\right) \cdot \sqrt{1.0} + \left(\sqrt{1.0} + \frac{\frac{1}{2} \cdot \beta}{\sqrt{1.0}}\right)}{\left(2 + \left(\beta + \alpha\right)\right) \cdot \sqrt{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}}} \leadsto \color{blue}{\frac{\sqrt{1.0} \cdot \left(\frac{1}{2} \cdot \alpha\right) + \left(\sqrt{1.0} + \frac{\beta \cdot \frac{1}{2}}{\sqrt{1.0}}\right)}{\left(\left(1.0 + \alpha\right) + \left(\beta + 2\right)\right) \cdot \left(\left(\beta + 2\right) + \alpha\right)} \cdot \frac{\sqrt{1.0} \cdot \left(\frac{1}{2} \cdot \alpha\right) + \left(\sqrt{1.0} + \frac{\beta \cdot \frac{1}{2}}{\sqrt{1.0}}\right)}{\left(\beta + 2\right) + \alpha}}\]
    58.8