if b < -1.6844219f+10

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   21.2
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]
   6.1
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a} \leadsto \frac{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
   6.1
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 -1.6844219f+10 < b < 3.426723f-06

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   6.5
2. Using strategy rm
   6.5
3. Applied pow1 to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}}{2 \cdot a}\]
   6.5
4. Using strategy rm
   6.5
5. Applied *-un-lft-identity to get
   \[\frac{{\color{red}{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}^{1}}{2 \cdot a} \leadsto \frac{{\color{blue}{\left(1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)\right)}}^{1}}{2 \cdot a}\]
   6.5
6. Applied unpow-prod-down to get
   \[\frac{\color{red}{{\left(1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)\right)}^{1}}}{2 \cdot a} \leadsto \frac{\color{blue}{{1}^{1} \cdot {\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}}{2 \cdot a}\]
   6.5
7. Applied times-frac to get
   \[\color{red}{\frac{{1}^{1} \cdot {\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{2 \cdot a}} \leadsto \color{blue}{\frac{{1}^{1}}{2} \cdot \frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a}}\]
   6.5
8. Applied simplify to get
   \[\color{red}{\frac{{1}^{1}}{2}} \cdot \frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a} \leadsto \color{blue}{\frac{1}{2}} \cdot \frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a}\]
   6.5
9. Applied simplify to get
   \[\frac{1}{2} \cdot \color{red}{\frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a}} \leadsto \frac{1}{2} \cdot \color{blue}{\frac{\left(-b\right) + \sqrt{{b}^2 - a \cdot \left(c \cdot 4\right)}}{a}}\]
   6.6

if 3.426723f-06 < b < 2.2299319f+17

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   20.6
2. Using strategy rm
   20.6
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   23.4
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   4.9

if 2.2299319f+17 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   30.2
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   7.3
3. Taylor expanded around inf to get
   \[\frac{\color{red}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a} \leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
   7.3
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