if b < -2.2913476789857995e+35

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   38.1
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]
   10.5
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a} \leadsto \frac{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
   10.5
4. Applied simplify to get
   \[\color{red}{\frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}} \leadsto \color{blue}{\frac{\frac{c}{b}}{1} - \frac{b}{a}}\]
   0.0
5. Applied simplify to get
   \[\color{red}{\frac{\frac{c}{b}}{1}} - \frac{b}{a} \leadsto \color{blue}{\frac{c}{b}} - \frac{b}{a}\]
   0.0

if -2.2913476789857995e+35 < b < 2.890760014197913e-73

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   13.8
2. Using strategy rm
   13.8
3. Applied frac-2neg to get
   \[\color{red}{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{-\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}{-2 \cdot a}}\]
   13.8
4. Applied simplify to get
   \[\frac{\color{red}{-\left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}{-2 \cdot a} \leadsto \frac{\color{blue}{\left(-\sqrt{{b}^2 - a \cdot \left(4 \cdot c\right)}\right) + b}}{-2 \cdot a}\]
   13.9

if 2.890760014197913e-73 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   58.4
2. Using strategy rm
   58.4
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   58.4
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{c \cdot \left(4 \cdot a\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
   34.7
5. Using strategy rm
   34.7
6. Applied div-inv to get
   \[\frac{\color{red}{\frac{c \cdot \left(4 \cdot a\right)}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a} \leadsto \frac{\color{blue}{\left(c \cdot \left(4 \cdot a\right)\right) \cdot \frac{1}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   34.8
7. Applied associate-/l* to get
   \[\color{red}{\frac{\left(c \cdot \left(4 \cdot a\right)\right) \cdot \frac{1}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}} \leadsto \color{blue}{\frac{c \cdot \left(4 \cdot a\right)}{\frac{2 \cdot a}{\frac{1}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}}\]
   33.9
8. Applied taylor to get
   \[\frac{c \cdot \left(4 \cdot a\right)}{\frac{2 \cdot a}{\frac{1}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}} \leadsto \frac{c \cdot \left(4 \cdot a\right)}{\frac{2 \cdot a}{\frac{1}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}\]
   18.3
9. Taylor expanded around inf to get
   \[\frac{c \cdot \left(4 \cdot a\right)}{\frac{2 \cdot a}{\frac{1}{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}} \leadsto \frac{c \cdot \left(4 \cdot a\right)}{\frac{2 \cdot a}{\frac{1}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}}\]
   18.3
10. Applied simplify to get
    \[\color{red}{\frac{c \cdot \left(4 \cdot a\right)}{\frac{2 \cdot a}{\frac{1}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}} \leadsto \color{blue}{\frac{c}{\frac{2}{1}} \cdot \frac{\frac{4}{2}}{c \cdot \frac{a}{b} - b}}\]
    4.0
11. Applied simplify to get
    \[\color{red}{\frac{c}{\frac{2}{1}}} \cdot \frac{\frac{4}{2}}{c \cdot \frac{a}{b} - b} \leadsto \color{blue}{\frac{c}{2}} \cdot \frac{\frac{4}{2}}{c \cdot \frac{a}{b} - b}\]
    4.0