if b < -1.2459677f+19

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   28.6
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto -1 \cdot \frac{b}{a}\]
   0
3. Taylor expanded around -inf to get
   \[\color{red}{-1 \cdot \frac{b}{a}} \leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
   0
4. Applied simplify to get
   \[\color{red}{-1 \cdot \frac{b}{a}} \leadsto \color{blue}{\frac{-b}{a}}\]
   0

if -1.2459677f+19 < b < -7.3336276f-36

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   3.9
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}}{2 \cdot a}\]
   3.9
3. Taylor expanded around 0 to get
   \[\frac{\left(-b\right) + \sqrt{\color{red}{{b}^2 - 4 \cdot \left(c \cdot a\right)}}}{2 \cdot a} \leadsto \frac{\left(-b\right) + \sqrt{\color{blue}{{b}^2 - 4 \cdot \left(c \cdot a\right)}}}{2 \cdot a}\]
   3.9

if -7.3336276f-36 < b < 8.01392f+14

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   14.0
2. Using strategy rm
   14.0
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   15.2
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   7.0
5. Using strategy rm
   7.0
6. Applied clear-num to get
   \[\color{red}{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}}\]
   7.0
7. Applied simplify to get
   \[\frac{1}{\color{red}{\frac{2 \cdot a}{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}} \leadsto \frac{1}{\color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{\frac{2}{4}}{c}}}\]
   4.6
8. Applied simplify to get
   \[\frac{1}{\color{red}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right)} \cdot \frac{\frac{2}{4}}{c}} \leadsto \frac{1}{\color{blue}{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)} \cdot \frac{\frac{2}{4}}{c}}\]
   4.5

if 8.01392f+14 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   29.5
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   7.4
3. Taylor expanded around inf to get
   \[\frac{\color{red}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a} \leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
   7.4
4. Applied simplify to get
   \[\color{red}{\frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}} \leadsto \color{blue}{\frac{c}{b} \cdot \frac{-2}{2}}\]
   0