if beta < 1.6334032f+19

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   24.8
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}}\]
   17.4
3. Using strategy rm
   17.4
4. Applied add-sqr-sqrt to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{\color{red}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{\color{blue}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2}}\]
   17.4
5. Applied add-sqr-sqrt to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\color{red}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\color{blue}{{\left(\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^2}}}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2}\]
   17.4
6. Applied square-undiv to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{red}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{{\left(\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^2}}}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{blue}{{\left(\frac{\left(\beta + \alpha\right) + 2 \cdot i}{\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2}\]
   17.4
7. Applied add-sqr-sqrt to get
   \[\frac{\frac{\color{red}{i \cdot \left(\beta + \left(i + \alpha\right)\right)}}{{\left(\frac{\left(\beta + \alpha\right) + 2 \cdot i}{\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2} \leadsto \frac{\frac{\color{blue}{{\left(\sqrt{i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^2}}{{\left(\frac{\left(\beta + \alpha\right) + 2 \cdot i}{\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2}\]
   17.4
8. Applied square-undiv to get
   \[\frac{\color{red}{\frac{{\left(\sqrt{i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^2}{{\left(\frac{\left(\beta + \alpha\right) + 2 \cdot i}{\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2} \leadsto \frac{\color{blue}{{\left(\frac{\sqrt{i \cdot \left(\beta + \left(i + \alpha\right)\right)}}{\frac{\left(\beta + \alpha\right) + 2 \cdot i}{\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}\right)}^2}}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2}\]
   17.4
9. Applied square-undiv to get
   \[\color{red}{\frac{{\left(\frac{\sqrt{i \cdot \left(\beta + \left(i + \alpha\right)\right)}}{\frac{\left(\beta + \alpha\right) + 2 \cdot i}{\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}\right)}^2}{{\left(\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}^2}} \leadsto \color{blue}{{\left(\frac{\frac{\sqrt{i \cdot \left(\beta + \left(i + \alpha\right)\right)}}{\frac{\left(\beta + \alpha\right) + 2 \cdot i}{\sqrt{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{\sqrt{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}}\right)}^2}\]
   17.4

if 1.6334032f+19 < beta

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   31.0
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}}\]
   24.7
3. Applied taylor to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto 0\]
   0
4. Taylor expanded around inf to get
   \[\color{red}{0} \leadsto \color{blue}{0}\]
   0