if (/ (- beta alpha) (+ (+ alpha beta) 2.0)) < -0.99999976f0

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   27.9
2. Using strategy rm
   27.9
3. Applied div-sub to get
   \[\frac{\color{red}{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]
   27.9
4. Applied associate-+l- to get
   \[\frac{\color{red}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) + 1.0}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
   27.8
5. Applied taylor to get
   \[\frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}{2.0} \leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}{2.0}\]
   6.3
6. Taylor expanded around inf to get
   \[\frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{red}{\left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}}{2.0} \leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}}{2.0}\]
   6.3
7. Applied simplify to get
   \[\color{red}{\frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(4.0 \cdot \frac{1}{{\alpha}^2} - \left(8.0 \cdot \frac{1}{{\alpha}^{3}} + 2.0 \cdot \frac{1}{\alpha}\right)\right)}{2.0}} \leadsto \color{blue}{\frac{2.0 + \frac{\frac{8.0}{\alpha}}{\alpha}}{2.0 \cdot \alpha} + \left(\frac{\frac{\beta}{2.0}}{\alpha + \left(2.0 + \beta\right)} - \frac{\frac{4.0}{\alpha \cdot \alpha}}{2.0}\right)}\]
   6.4
8. Applied taylor to get
   \[\frac{2.0 + \frac{\frac{8.0}{\alpha}}{\alpha}}{2.0 \cdot \alpha} + \left(\frac{\frac{\beta}{2.0}}{\alpha + \left(2.0 + \beta\right)} - \frac{\frac{4.0}{\alpha \cdot \alpha}}{2.0}\right) \leadsto \left(4.0 \cdot \frac{1}{{\alpha}^{3}} + 1.0 \cdot \frac{1}{\alpha}\right) - 2.0 \cdot \frac{1}{{\alpha}^2}\]
   0.0
9. Taylor expanded around 0 to get
   \[\color{red}{\left(4.0 \cdot \frac{1}{{\alpha}^{3}} + 1.0 \cdot \frac{1}{\alpha}\right) - 2.0 \cdot \frac{1}{{\alpha}^2}} \leadsto \color{blue}{\left(4.0 \cdot \frac{1}{{\alpha}^{3}} + 1.0 \cdot \frac{1}{\alpha}\right) - 2.0 \cdot \frac{1}{{\alpha}^2}}\]
   0.0
10. Applied simplify to get
    \[\left(4.0 \cdot \frac{1}{{\alpha}^{3}} + 1.0 \cdot \frac{1}{\alpha}\right) - 2.0 \cdot \frac{1}{{\alpha}^2} \leadsto \frac{1.0}{\alpha} + \left(\frac{4.0}{{\alpha}^3} - \frac{\frac{2.0}{\alpha}}{\alpha}\right)\]
    0.0

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11. Applied final simplification

if -0.99999976f0 < (/ (- beta alpha) (+ (+ alpha beta) 2.0))

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   0.7
2. Using strategy rm
   0.7
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