if b < -431232863.47265303

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   38.7
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 -431232863.47265303 < b < 1.4445095675228828e-303

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   9.3

if 1.4445095675228828e-303 < b < 1.3336442321324732e+29

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   26.2
2. Using strategy rm
   26.2
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   26.3
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   16.4

if 1.3336442321324732e+29 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   58.2
2. Using strategy rm
   58.2
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   58.2
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   31.7
5. Applied taylor to get
   \[\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}{2 \cdot a}\]
   14.8
6. Taylor expanded around inf to get
   \[\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \color{red}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}{2 \cdot a} \leadsto \frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}{2 \cdot a}\]
   14.8
7. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{\frac{\frac{c}{1}}{2} \cdot 4}{\left(\left(-b\right) - b\right) + \left(a \cdot 2\right) \cdot \frac{c}{b}}}\]
   2.2
8. Applied simplify to get
   \[\frac{\color{red}{\frac{\frac{c}{1}}{2} \cdot 4}}{\left(\left(-b\right) - b\right) + \left(a \cdot 2\right) \cdot \frac{c}{b}} \leadsto \frac{\color{blue}{\frac{4}{\frac{2}{c}}}}{\left(\left(-b\right) - b\right) + \left(a \cdot 2\right) \cdot \frac{c}{b}}\]
   2.3