if (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) < -2.109379f+16

1. Started with
   \[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
   30.9
2. Using strategy rm
   30.9
3. Applied associate-/l* to get
   \[\frac{\frac{\color{red}{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0} \leadsto \frac{\frac{\color{blue}{\frac{\alpha + \beta}{\frac{\left(\alpha + \beta\right) + 2 \cdot i}{\beta - \alpha}}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
   25.3
4. Using strategy rm
   25.3
5. Applied add-cube-cbrt to get
   \[\frac{\color{red}{\frac{\frac{\alpha + \beta}{\frac{\left(\alpha + \beta\right) + 2 \cdot i}{\beta - \alpha}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{\frac{\frac{\alpha + \beta}{\frac{\left(\alpha + \beta\right) + 2 \cdot i}{\beta - \alpha}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}\right)}^3} + 1.0}{2.0}\]
   25.3
6. Applied taylor to get
   \[\frac{{\left(\sqrt[3]{\frac{\frac{\alpha + \beta}{\frac{\left(\alpha + \beta\right) + 2 \cdot i}{\beta - \alpha}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}\right)}^3 + 1.0}{2.0} \leadsto \frac{\left(\left(4.0 \cdot \frac{i}{{\left(2.0 + \alpha\right)}^2} + \left(4 \cdot \frac{\alpha \cdot i}{{\left(2.0 + \alpha\right)}^2} + \left(2.0 \cdot \frac{\beta}{{\left(2.0 + \alpha\right)}^2} + 2 \cdot \frac{\beta \cdot \alpha}{{\left(2.0 + \alpha\right)}^2}\right)\right)\right) - \frac{\alpha}{2.0 + \alpha}\right) + 1.0}{2.0}\]
   28.6
7. Taylor expanded around 0 to get
   \[\frac{\color{red}{\left(\left(4.0 \cdot \frac{i}{{\left(2.0 + \alpha\right)}^2} + \left(4 \cdot \frac{\alpha \cdot i}{{\left(2.0 + \alpha\right)}^2} + \left(2.0 \cdot \frac{\beta}{{\left(2.0 + \alpha\right)}^2} + 2 \cdot \frac{\beta \cdot \alpha}{{\left(2.0 + \alpha\right)}^2}\right)\right)\right) - \frac{\alpha}{2.0 + \alpha}\right)} + 1.0}{2.0} \leadsto \frac{\color{blue}{\left(\left(4.0 \cdot \frac{i}{{\left(2.0 + \alpha\right)}^2} + \left(4 \cdot \frac{\alpha \cdot i}{{\left(2.0 + \alpha\right)}^2} + \left(2.0 \cdot \frac{\beta}{{\left(2.0 + \alpha\right)}^2} + 2 \cdot \frac{\beta \cdot \alpha}{{\left(2.0 + \alpha\right)}^2}\right)\right)\right) - \frac{\alpha}{2.0 + \alpha}\right)} + 1.0}{2.0}\]
   28.6
8. Applied simplify to get
   \[\frac{\left(\left(4.0 \cdot \frac{i}{{\left(2.0 + \alpha\right)}^2} + \left(4 \cdot \frac{\alpha \cdot i}{{\left(2.0 + \alpha\right)}^2} + \left(2.0 \cdot \frac{\beta}{{\left(2.0 + \alpha\right)}^2} + 2 \cdot \frac{\beta \cdot \alpha}{{\left(2.0 + \alpha\right)}^2}\right)\right)\right) - \frac{\alpha}{2.0 + \alpha}\right) + 1.0}{2.0} \leadsto \frac{\left(\left(\frac{4 \cdot i}{2.0 + \alpha} \cdot \frac{\alpha}{2.0 + \alpha} + \frac{\frac{i \cdot 4.0}{2.0 + \alpha}}{2.0 + \alpha}\right) + \left(\frac{\beta}{2.0 + \alpha} \cdot \frac{2.0}{2.0 + \alpha} + \frac{2}{2.0 + \alpha} \cdot \frac{\beta \cdot \alpha}{2.0 + \alpha}\right)\right) - \left(\frac{\alpha}{2.0 + \alpha} - 1.0\right)}{2.0}\]
   17.9

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9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{\frac{\left(\left(\frac{4 \cdot i}{2.0 + \alpha} \cdot \frac{\alpha}{2.0 + \alpha} + \frac{\frac{i \cdot 4.0}{2.0 + \alpha}}{2.0 + \alpha}\right) + \left(\frac{\beta}{2.0 + \alpha} \cdot \frac{2.0}{2.0 + \alpha} + \frac{2}{2.0 + \alpha} \cdot \frac{\beta \cdot \alpha}{2.0 + \alpha}\right)\right) - \left(\frac{\alpha}{2.0 + \alpha} - 1.0\right)}{2.0}} \leadsto \color{blue}{\frac{\left(\frac{i}{\alpha + 2.0} \cdot \left(\frac{4 \cdot \alpha}{\alpha + 2.0} + \frac{4.0}{\alpha + 2.0}\right) + \frac{\beta}{\alpha + 2.0} \cdot \left(\frac{2.0}{\alpha + 2.0} + \frac{2 \cdot \alpha}{\alpha + 2.0}\right)\right) - \left(\frac{\alpha}{\alpha + 2.0} - 1.0\right)}{2.0}}\]
    13.4

if -2.109379f+16 < (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

1. Started with
   \[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
   7.0
2. Using strategy rm
   7.0
3. Applied associate-/l* to get
   \[\frac{\frac{\color{red}{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0} \leadsto \frac{\frac{\color{blue}{\frac{\alpha + \beta}{\frac{\left(\alpha + \beta\right) + 2 \cdot i}{\beta - \alpha}}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
   1.4
4. Using strategy rm
   1.4
5. Applied pow1 to get
   \[\frac{\frac{\frac{\alpha + \beta}{\color{red}{\frac{\left(\alpha + \beta\right) + 2 \cdot i}{\beta - \alpha}}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0} \leadsto \frac{\frac{\frac{\alpha + \beta}{\color{blue}{{\left(\frac{\left(\alpha + \beta\right) + 2 \cdot i}{\beta - \alpha}\right)}^{1}}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
   1.2