if (/ (- beta alpha) (+ (+ alpha beta) 2.0)) < -0.9070372875212327

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   58.9
2. Using strategy rm
   58.9
3. Applied div-sub to get
   \[\frac{\color{red}{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]
   58.9
4. Applied associate-+l- to get
   \[\frac{\color{red}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) + 1.0}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
   48.9
5. Using strategy rm
   48.9
6. Applied flip3-- to get
   \[\frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{red}{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0} \leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}}{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)}}}{2.0}\]
   48.9
7. Applied frac-sub to get
   \[\frac{\color{red}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}}{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)}}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}}{2.0}\]
   49.0
8. Applied taylor to get
   \[\frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0} \leadsto \frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0}\]
   0.5
9. Taylor expanded around inf to get
   \[\frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \color{red}{\left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0} \leadsto \frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \color{blue}{\left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0}\]
   0.5
10. Applied simplify to get
    \[\frac{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(24.0 \cdot \frac{1}{{\alpha}^2} - \left(80.0 \cdot \frac{1}{{\alpha}^{3}} + 6.0 \cdot \frac{1}{\alpha}\right)\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}{2.0} \leadsto \frac{(\left((\left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta}\right) * \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta}\right) + \left(1.0 \cdot 1.0\right))_*\right) * \beta + \left(\frac{\alpha \cdot 1.0}{\left(2.0 + \alpha\right) + \beta} \cdot \beta\right))_* - \left(\left(2.0 + \alpha\right) + \beta\right) \cdot \left(\frac{\frac{24.0}{\alpha}}{\alpha} - \left(\frac{80.0}{{\alpha}^3} + \frac{6.0}{\alpha}\right)\right)}{\left(2.0 \cdot \left(\left(2.0 + \alpha\right) + \beta\right)\right) \cdot (1.0 * \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} + 1.0\right) + \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} \cdot \frac{\alpha}{\left(2.0 + \alpha\right) + \beta}\right))_*}\]
    0.5

---

11. Applied final simplification
12. Applied simplify to get
    \[\color{red}{\frac{(\left((\left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta}\right) * \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta}\right) + \left(1.0 \cdot 1.0\right))_*\right) * \beta + \left(\frac{\alpha \cdot 1.0}{\left(2.0 + \alpha\right) + \beta} \cdot \beta\right))_* - \left(\left(2.0 + \alpha\right) + \beta\right) \cdot \left(\frac{\frac{24.0}{\alpha}}{\alpha} - \left(\frac{80.0}{{\alpha}^3} + \frac{6.0}{\alpha}\right)\right)}{\left(2.0 \cdot \left(\left(2.0 + \alpha\right) + \beta\right)\right) \cdot (1.0 * \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} + 1.0\right) + \left(\frac{\alpha}{\left(2.0 + \alpha\right) + \beta} \cdot \frac{\alpha}{\left(2.0 + \alpha\right) + \beta}\right))_*}} \leadsto \color{blue}{\frac{(\left((\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) * \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) + \left({1.0}^2\right))_*\right) * \beta + \left(\frac{\left(\alpha \cdot \beta\right) \cdot 1.0}{2.0 + \left(\beta + \alpha\right)}\right))_* - \left(2.0 + \left(\beta + \alpha\right)\right) \cdot \left(\left(\frac{24.0}{{\alpha}^2} - \frac{80.0}{{\alpha}^3}\right) - \frac{6.0}{\alpha}\right)}{(1.0 * \left(1.0 + \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) + \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right))_* \cdot (2.0 * \left(\beta + \alpha\right) + \left(2.0 \cdot 2.0\right))_*}}\]
    6.4

if -0.9070372875212327 < (/ (- beta alpha) (+ (+ alpha beta) 2.0))

1. Started with
   \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
   0.0
2. Using strategy rm
   0.0
3. Applied div-sub to get
   \[\frac{\color{red}{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0}} + 1.0}{2.0} \leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]
   0.0
4. Applied associate-+l- to get
   \[\frac{\color{red}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) + 1.0}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
   0.0
5. Using strategy rm
   0.0
6. Applied flip3-- to get
   \[\frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{red}{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0} \leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}}{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)}}}{2.0}\]
   0.0
7. Applied frac-sub to get
   \[\frac{\color{red}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}}{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)}}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {1.0}^{3}\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left({\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^2 + \left({1.0}^2 + \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot 1.0\right)\right)}}}{2.0}\]
   0.0