if (/ (- beta alpha) (+ (+ alpha beta) 2.0)) < -0.99999994f0

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   28.2
2. Using strategy rm
   28.2
3. Applied div-sub to get
   \[\frac{\color{red}{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]
   28.2
4. Applied associate-+l- to get
   \[\frac{\color{red}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) + 1.0}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
   24.5
5. Using strategy rm
   24.5
6. Applied flip3-- to get
   \[\frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{red}{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0} \leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}}{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)}}}{2.0}\]
   24.5
7. Applied frac-sub to get
   \[\frac{\color{red}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}}{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)}}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}}{2.0}\]
   24.6
8. Applied taylor to get
   \[\frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0} \leadsto \frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0}\]
   0.8
9. Taylor expanded around inf to get
   \[\frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \color{red}{\left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0} \leadsto \frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \color{blue}{\left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0}\]
   0.8
10. Applied simplify to get
    \[\frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0} \leadsto \frac{\left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} \cdot \frac{\alpha}{\left(2.0 + \alpha\right) + \beta} + \left(\frac{\alpha \cdot 1.0}{\left(2.0 + \alpha\right) + \beta} + 1.0 \cdot 1.0\right)\right) \cdot \beta - \left(\left(2.0 + \alpha\right) + \beta\right) \cdot \left(\left(\frac{\frac{24.0}{\alpha}}{\alpha} - \frac{80.0}{{\alpha}^3}\right) - \frac{6.0}{\alpha}\right)}{\left(2.0 \cdot \left(\left(2.0 + \alpha\right) + \beta\right)\right) \cdot \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} \cdot \frac{\alpha}{\left(2.0 + \alpha\right) + \beta} + \left(\frac{\alpha \cdot 1.0}{\left(2.0 + \alpha\right) + \beta} + 1.0 \cdot 1.0\right)\right)}\]
    1.2

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11. Applied final simplification
12. Applied simplify to get
    \[\color{red}{\frac{\left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} \cdot \frac{\alpha}{\left(2.0 + \alpha\right) + \beta} + \left(\frac{\alpha \cdot 1.0}{\left(2.0 + \alpha\right) + \beta} + 1.0 \cdot 1.0\right)\right) \cdot \beta - \left(\left(2.0 + \alpha\right) + \beta\right) \cdot \left(\left(\frac{\frac{24.0}{\alpha}}{\alpha} - \frac{80.0}{{\alpha}^3}\right) - \frac{6.0}{\alpha}\right)}{\left(2.0 \cdot \left(\left(2.0 + \alpha\right) + \beta\right)\right) \cdot \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} \cdot \frac{\alpha}{\left(2.0 + \alpha\right) + \beta} + \left(\frac{\alpha \cdot 1.0}{\left(2.0 + \alpha\right) + \beta} + 1.0 \cdot 1.0\right)\right)}} \leadsto \color{blue}{\frac{1}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\beta}{2.0} - \frac{\frac{\left(\frac{\frac{24.0}{\alpha}}{\alpha} - \frac{\frac{80.0}{\alpha}}{{\alpha}^2}\right) - \frac{6.0}{\alpha}}{\frac{2.0 \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{2.0 + \left(\beta + \alpha\right)}}}{\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + \left(\frac{1.0 \cdot \alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0 \cdot 1.0\right)}}\]
    0.5

if -0.99999994f0 < (/ (- beta alpha) (+ (+ alpha beta) 2.0))

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   0.8
2. Using strategy rm
   0.8
3. Applied pow1 to get
   \[\frac{\frac{\beta - \alpha}{\color{red}{\left(\alpha + \beta\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\frac{\beta - \alpha}{\color{blue}{{\left(\left(\alpha + \beta\right) + 2.0\right)}^{1}}} + 1.0}{2.0}\]
   0.3