if (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) < 1.752335950282756e+129

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   0.1
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   0.9
3. Using strategy rm
   0.9
4. Applied *-un-lft-identity to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{red}{\alpha + \left(2 + \beta\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{blue}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   0.9
5. Applied *-un-lft-identity to get
   \[\frac{\frac{\color{red}{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\color{blue}{1 \cdot \left(\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)\right)}}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   0.9
6. Applied times-frac to get
   \[\frac{\color{red}{\frac{1 \cdot \left(\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)\right)}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   0.9
7. Applied times-frac to get
   \[\color{red}{\frac{\frac{1}{1} \cdot \frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{\frac{1}{1}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}}\]
   0.2
8. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{1}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)} \leadsto \color{blue}{\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)}} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}\]
   0.2
9. Using strategy rm
   0.2
10. Applied add-sqr-sqrt to get
    \[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{\alpha + \left(2 + \beta\right)}} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
    0.7
11. Applied add-sqr-sqrt to get
    \[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{red}{\alpha + \left(2 + \beta\right)}}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
    1.2
12. Applied add-sqr-sqrt to get
    \[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\color{red}{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
    1.1
13. Applied square-undiv to get
    \[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\color{red}{\frac{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}\right)}^2}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\color{blue}{{\left(\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
    1.1
14. Applied square-undiv to get
    \[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \color{red}{\frac{{\left(\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \color{blue}{{\left(\frac{\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}\]
    0.7
15. Applied simplify to get
    \[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot {\color{red}{\left(\frac{\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}}^2 \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot {\color{blue}{\left(\frac{\sqrt{\beta + \left(\alpha \cdot \beta + \left(\alpha + 1.0\right)\right)}}{\left(2 + \alpha\right) + \beta}\right)}}^2\]
    0.2

if 1.752335950282756e+129 < (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   62.8
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   62.9
3. Applied taylor to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   37.9
4. Taylor expanded around 0 to get
   \[\frac{\color{red}{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   37.9
5. Applied simplify to get
   \[\color{red}{\frac{0.25 \cdot \beta + \left(0.5 + 0.25 \cdot \alpha\right)}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{0.25 \cdot \left(\alpha + \beta\right) + 0.5}{\left(\left(\alpha + \beta\right) + 2\right) \cdot \left(\left(\alpha + \beta\right) + \left(2 + 1.0\right)\right)}}\]
   37.9