if b/2 < -7.0905583f+15

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   29.7
2. Applied taylor to get
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a} \leadsto \frac{\left(-b/2\right) - \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}{a}\]
   19.5
3. Taylor expanded around -inf to get
   \[\frac{\left(-b/2\right) - \color{red}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}{a} \leadsto \frac{\left(-b/2\right) - \color{blue}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}{a}\]
   19.5
4. Applied simplify to get
   \[\color{red}{\frac{\left(-b/2\right) - \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}{a}} \leadsto \color{blue}{\frac{b/2 + \left(-b/2\right)}{a} - \frac{1}{2} \cdot \frac{c}{b/2}}\]
   0.0

if -7.0905583f+15 < b/2 < -4.1222605f-29

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   16.4
2. Using strategy rm
   16.4
3. Applied flip-- to get
   \[\frac{\color{red}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   17.9
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   6.8
5. Using strategy rm
   6.8
6. Applied add-cube-cbrt to get
   \[\color{red}{\frac{\frac{a \cdot c}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\frac{a \cdot c}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}}\right)}^3}\]
   7.2
7. Applied simplify to get
   \[{\color{red}{\left(\sqrt[3]{\frac{\frac{a \cdot c}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{c}{\sqrt{b/2 \cdot b/2 - c \cdot a} + \left(-b/2\right)}}\right)}}^3\]
   4.0

if -4.1222605f-29 < b/2 < 4.0821213f+08

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   4.4
2. Using strategy rm
   4.4
3. Applied pow1 to get
   \[\frac{\color{red}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{{\left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)}^{1}}}{a}\]
   4.4

if 4.0821213f+08 < b/2

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   20.2
2. Applied taylor to get
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a} \leadsto \frac{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}{a}\]
   5.4
3. Taylor expanded around inf to get
   \[\frac{\color{red}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a} \leadsto \frac{\color{blue}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}\]
   5.4
4. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}{a}} \leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{b/2}{c}} - \frac{b/2}{a} \cdot 2}\]
   0.1