if i < 3.0574282f+18

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   20.4
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}}\]
   7.5
3. Using strategy rm
   7.5
4. Applied add-cube-cbrt to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\color{red}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\color{blue}{{\left(\sqrt[3]{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^3}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
   7.9
5. Applied add-cube-cbrt to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{\color{red}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}}{{\left(\sqrt[3]{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^3}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{\color{blue}{{\left(\sqrt[3]{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}\right)}^3}}{{\left(\sqrt[3]{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^3}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
   7.9
6. Applied cube-undiv to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{red}{\frac{{\left(\sqrt[3]{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}\right)}^3}{{\left(\sqrt[3]{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}\right)}^3}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{blue}{{\left(\frac{\sqrt[3]{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}}{\sqrt[3]{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^3}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
   7.9
7. Applied taylor to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{{\left(\frac{\sqrt[3]{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}}{\sqrt[3]{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^3}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{\alpha \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \left(\frac{\beta \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \frac{{i}^2}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3}\right)}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
   7.9
8. Taylor expanded around 0 to get
   \[\frac{\color{red}{\frac{\alpha \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \left(\frac{\beta \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \frac{{i}^2}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3}\right)}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\color{blue}{\frac{\alpha \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \left(\frac{\beta \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \frac{{i}^2}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3}\right)}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
   7.9
9. Applied simplify to get
   \[\frac{\frac{\alpha \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \left(\frac{\beta \cdot i}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3} + \frac{{i}^2}{{\left(\frac{\sqrt[3]{{\left(\beta + \left(\alpha + 2 \cdot i\right)\right)}^2}}{\sqrt[3]{{i}^2 + \left(\beta \cdot \alpha + \left(\alpha \cdot i + \beta \cdot i\right)\right)}}\right)}^3}\right)}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \alpha}{\frac{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right)}{\left(i \cdot i + \alpha \cdot \beta\right) + \left(\beta + \alpha\right) \cdot i}} + \left(\frac{i \cdot i}{\frac{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right)}{\left(i \cdot i + \alpha \cdot \beta\right) + \left(\beta + \alpha\right) \cdot i}} + \frac{\beta \cdot i}{\frac{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right)}{\left(i \cdot i + \alpha \cdot \beta\right) + \left(\beta + \alpha\right) \cdot i}}\right)}{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right) - 1.0}\]
   7.5

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10. Applied final simplification
11. Applied simplify to get
    \[\color{red}{\frac{\frac{i \cdot \alpha}{\frac{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right)}{\left(i \cdot i + \alpha \cdot \beta\right) + \left(\beta + \alpha\right) \cdot i}} + \left(\frac{i \cdot i}{\frac{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right)}{\left(i \cdot i + \alpha \cdot \beta\right) + \left(\beta + \alpha\right) \cdot i}} + \frac{\beta \cdot i}{\frac{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right)}{\left(i \cdot i + \alpha \cdot \beta\right) + \left(\beta + \alpha\right) \cdot i}}\right)}{\left(i \cdot 2 + \left(\beta + \alpha\right)\right) \cdot \left(i \cdot 2 + \left(\beta + \alpha\right)\right) - 1.0}} \leadsto \color{blue}{\frac{\left(\frac{{i}^2}{\frac{\left(i \cdot 2 + \left(\alpha + \beta\right)\right) \cdot \left(i \cdot 2 + \left(\alpha + \beta\right)\right)}{i \cdot \left(\alpha + \beta\right) + \left({i}^2 + \beta \cdot \alpha\right)}} + \frac{i}{i \cdot 2 + \left(\alpha + \beta\right)} \cdot \left(\frac{\beta}{i \cdot 2 + \left(\alpha + \beta\right)} \cdot \left(i \cdot \left(\alpha + \beta\right) + \left({i}^2 + \beta \cdot \alpha\right)\right)\right)\right) + \frac{i \cdot \left(\alpha + \beta\right) + \left({i}^2 + \beta \cdot \alpha\right)}{\frac{i \cdot 2 + \left(\alpha + \beta\right)}{i}} \cdot \frac{\alpha}{i \cdot 2 + \left(\alpha + \beta\right)}}{\left(i \cdot 2 + \left(\alpha + \beta\right)\right) \cdot \left(i \cdot 2 + \left(\alpha + \beta\right)\right) - 1.0}}\]
    7.5

if 3.0574282f+18 < i

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   30.0
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}}\]
   29.6
3. Using strategy rm
   29.6
4. Applied add-sqr-sqrt to get
   \[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{red}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{blue}{{\left(\sqrt{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
   29.6
5. Using strategy rm
   29.6
6. Applied add-exp-log to get
   \[\color{red}{\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{{\left(\sqrt{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}} \leadsto \color{blue}{e^{\log \left(\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{{\left(\sqrt{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)}}\]
   29.6
7. Applied taylor to get
   \[e^{\log \left(\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{{\left(\sqrt{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}\right)}^2}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\right)} \leadsto e^{0.25 \cdot \frac{1}{{i}^2} + \log \frac{1}{16}}\]
   0
8. Taylor expanded around inf to get
   \[e^{\color{red}{0.25 \cdot \frac{1}{{i}^2} + \log \frac{1}{16}}} \leadsto e^{\color{blue}{0.25 \cdot \frac{1}{{i}^2} + \log \frac{1}{16}}}\]
   0
9. Applied simplify to get
   \[e^{0.25 \cdot \frac{1}{{i}^2} + \log \frac{1}{16}} \leadsto \frac{1}{16} \cdot e^{\frac{\frac{0.25}{i}}{i}}\]
   0

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10. Applied final simplification