if b/2 < -2.874810909131491e-160

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   59.2
2. Using strategy rm
   59.2
3. Applied flip-- to get
   \[\frac{\color{red}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   59.2
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   39.8
5. Using strategy rm
   39.8
6. Applied div-inv to get
   \[\color{red}{\frac{\frac{a \cdot c}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}} \leadsto \color{blue}{\frac{a \cdot c}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}} \cdot \frac{1}{a}}\]
   39.8
7. Applied taylor to get
   \[\frac{a \cdot c}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}} \cdot \frac{1}{a} \leadsto \frac{a \cdot c}{\left(-b/2\right) + \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)} \cdot \frac{1}{a}\]
   17.7
8. Taylor expanded around -inf to get
   \[\frac{a \cdot c}{\left(-b/2\right) + \color{red}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}} \cdot \frac{1}{a} \leadsto \frac{a \cdot c}{\left(-b/2\right) + \color{blue}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}} \cdot \frac{1}{a}\]
   17.7
9. Applied simplify to get
   \[\color{red}{\frac{a \cdot c}{\left(-b/2\right) + \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)} \cdot \frac{1}{a}} \leadsto \color{blue}{\frac{c}{\frac{\frac{1}{2} \cdot c}{\frac{b/2}{a}} - \left(b/2 - \left(-b/2\right)\right)}}\]
   4.6

if -2.874810909131491e-160 < b/2 < 8.164018341878614e+86

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   11.3
2. Using strategy rm
   11.3
3. Applied clear-num to get
   \[\color{red}{\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}} \leadsto \color{blue}{\frac{1}{\frac{a}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}\]
   11.4

if 8.164018341878614e+86 < b/2

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   44.6
2. Applied taylor to get
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a} \leadsto -2 \cdot \frac{b/2}{a}\]
   0
3. Taylor expanded around inf to get
   \[\color{red}{-2 \cdot \frac{b/2}{a}} \leadsto \color{blue}{-2 \cdot \frac{b/2}{a}}\]
   0