if (/ (- beta alpha) (+ (+ alpha beta) 2.0)) < -0.99999964f0

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   28.1
2. Using strategy rm
   28.1
3. Applied div-sub to get
   \[\frac{\color{red}{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]
   28.1
4. Applied associate-+l- to get
   \[\frac{\color{red}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) + 1.0}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
   24.0
5. Using strategy rm
   24.0
6. Applied add-log-exp to get
   \[\frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{red}{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0} \leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\log \left(e^{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0}\right)}}{2.0}\]
   24.0
7. Applied add-log-exp to get
   \[\frac{\color{red}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0}} - \log \left(e^{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0}\right)}{2.0} \leadsto \frac{\color{blue}{\log \left(e^{\frac{\beta}{\left(\alpha + \beta\right) + 2.0}}\right)} - \log \left(e^{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0}\right)}{2.0}\]
   28.1
8. Applied diff-log to get
   \[\frac{\color{red}{\log \left(e^{\frac{\beta}{\left(\alpha + \beta\right) + 2.0}}\right) - \log \left(e^{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0}\right)}}{2.0} \leadsto \frac{\color{blue}{\log \left(\frac{e^{\frac{\beta}{\left(\alpha + \beta\right) + 2.0}}}{e^{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0}}\right)}}{2.0}\]
   28.1
9. Applied simplify to get
   \[\frac{\log \color{red}{\left(\frac{e^{\frac{\beta}{\left(\alpha + \beta\right) + 2.0}}}{e^{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0}}\right)}}{2.0} \leadsto \frac{\log \color{blue}{\left(e^{\frac{\beta}{\left(\alpha + 2.0\right) + \beta} - \left(\frac{\alpha}{\left(\alpha + 2.0\right) + \beta} - 1.0\right)}\right)}}{2.0}\]
   28.1
10. Applied taylor to get
    \[\frac{\log \left(e^{\frac{\beta}{\left(\alpha + 2.0\right) + \beta} - \left(\frac{\alpha}{\left(\alpha + 2.0\right) + \beta} - 1.0\right)}\right)}{2.0} \leadsto \frac{\log \left(e^{\frac{\beta}{\left(\alpha + 2.0\right) + \beta} - \left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}\right)}{2.0}\]
    28.1
11. Taylor expanded around inf to get
    \[\frac{\log \left(e^{\frac{\beta}{\left(\alpha + 2.0\right) + \beta} - \color{red}{\left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}}\right)}{2.0} \leadsto \frac{\log \left(e^{\frac{\beta}{\left(\alpha + 2.0\right) + \beta} - \color{blue}{\left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}}\right)}{2.0}\]
    28.1
12. Applied simplify to get
    \[\frac{\log \left(e^{\frac{\beta}{\left(\alpha + 2.0\right) + \beta} - \left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}\right)}{2.0} \leadsto \frac{\frac{\beta}{\alpha + \left(\beta + 2.0\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{8.0}{{\alpha}^3}\right) - \frac{2.0}{\alpha}\right)}{2.0}\]
    0.1

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13. Applied final simplification

if -0.99999964f0 < (/ (- beta alpha) (+ (+ alpha beta) 2.0))

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   0.6
2. Using strategy rm
   0.6
3. Applied pow1 to get
   \[\frac{\frac{\beta - \alpha}{\color{red}{\left(\alpha + \beta\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\frac{\beta - \alpha}{\color{blue}{{\left(\left(\alpha + \beta\right) + 2.0\right)}^{1}}} + 1.0}{2.0}\]
   0.2