if b/2 < -6.5355834f+18

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   28.4
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

if -6.5355834f+18 < b/2 < 1.9763165f-38

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   3.9
2. Using strategy rm
   3.9
3. Applied pow1 to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{{\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right)}^{1}}}{a}\]
   3.9

if 1.9763165f-38 < b/2 < 1.5139723f+14

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   14.9
2. Using strategy rm
   14.9
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   16.2
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   6.8
5. Using strategy rm
   6.8
6. Applied *-un-lft-identity to get
   \[\frac{\frac{a \cdot c}{\color{red}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a} \leadsto \frac{\frac{a \cdot c}{\color{blue}{1 \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)}}}{a}\]
   6.8
7. Applied times-frac to get
   \[\frac{\color{red}{\frac{a \cdot c}{1 \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)}}}{a} \leadsto \frac{\color{blue}{\frac{a}{1} \cdot \frac{c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   3.9

if 1.5139723f+14 < b/2

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   29.2
2. Using strategy rm
   29.2
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   30.5
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   16.0
5. Applied taylor to get
   \[\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{a \cdot c}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}\]
   7.0
6. Taylor expanded around inf to get
   \[\frac{\frac{a \cdot c}{\color{red}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}}{a} \leadsto \frac{\frac{a \cdot c}{\color{blue}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}}{a}\]
   7.0
7. Applied simplify to get
   \[\color{red}{\frac{\frac{a \cdot c}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}} \leadsto \color{blue}{\frac{c}{\left(\frac{1}{2} \cdot c\right) \cdot \frac{a}{b/2} - 2 \cdot b/2}}\]
   0.6