if b/2 < -0.002621575f0

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   27.8
2. Using strategy rm
   27.8
3. Applied flip-- to get
   \[\frac{\color{red}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   29.6
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   15.2
5. Applied taylor to get
   \[\frac{\frac{a \cdot c}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{a \cdot c}{\left(-b/2\right) + \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}{a}\]
   7.2
6. Taylor expanded around -inf to get
   \[\frac{\frac{a \cdot c}{\left(-b/2\right) + \color{red}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}}{a} \leadsto \frac{\frac{a \cdot c}{\left(-b/2\right) + \color{blue}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}}{a}\]
   7.2
7. Applied simplify to get
   \[\color{red}{\frac{\frac{a \cdot c}{\left(-b/2\right) + \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}{a}} \leadsto \color{blue}{\frac{c}{\left(a \cdot \frac{1}{2}\right) \cdot \frac{c}{b/2} - \left(b/2 - \left(-b/2\right)\right)}}\]
   1.6

if -0.002621575f0 < b/2 < 1.6720318f+16

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   6.3
2. Using strategy rm
   6.3
3. Applied pow1 to get
   \[\frac{\color{red}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{{\left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)}^{1}}}{a}\]
   6.3

if 1.6720318f+16 < b/2

1. Started with
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   24.7
2. Applied taylor to get
   \[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a} \leadsto \frac{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}{a}\]
   6.2
3. Taylor expanded around inf to get
   \[\frac{\color{red}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a} \leadsto \frac{\color{blue}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}\]
   6.2
4. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}{a}} \leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{b/2}{c}} - \frac{b/2}{a} \cdot 2}\]
   0.0