if b < -1.8967889f+12

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   21.7
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]
   5.7
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a} \leadsto \frac{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
   5.7
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 -1.8967889f+12 < b < -5.8884015f-31

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   3.9

if -5.8884015f-31 < b < 1.5915723f+15

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
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   15.1
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 *-un-lft-identity to get
   \[\frac{\frac{\left(4 \cdot a\right) \cdot c}{\color{red}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a} \leadsto \frac{\frac{\left(4 \cdot a\right) \cdot c}{\color{blue}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a}\]
   7.0
7. Applied times-frac to get
   \[\frac{\color{red}{\frac{\left(4 \cdot a\right) \cdot c}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   4.5

if 1.5915723f+15 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   29.6
2. Using strategy rm
   29.6
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   30.7
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   17.3
5. Using strategy rm
   17.3
6. Applied *-un-lft-identity to get
   \[\frac{\frac{\left(4 \cdot a\right) \cdot c}{\color{red}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a} \leadsto \frac{\frac{\left(4 \cdot a\right) \cdot c}{\color{blue}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a}\]
   17.3
7. Applied times-frac to get
   \[\frac{\color{red}{\frac{\left(4 \cdot a\right) \cdot c}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   17.0
8. Using strategy rm
   17.0
9. Applied add-exp-log to get
   \[\frac{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - \color{red}{\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a} \leadsto \frac{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - \color{blue}{e^{\log \left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}}{2 \cdot a}\]
   17.2
10. Applied taylor to get
    \[\frac{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - e^{\log \left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a} \leadsto \frac{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - e^{\log \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}{2 \cdot a}\]
    5.7
11. Taylor expanded around inf to get
    \[\frac{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - e^{\log \color{red}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}}{2 \cdot a} \leadsto \frac{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - e^{\log \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}}{2 \cdot a}\]
    5.7
12. Applied simplify to get
    \[\frac{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - e^{\log \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}{2 \cdot a} \leadsto \frac{\frac{c}{a}}{\left(\left(-b\right) - b\right) + \frac{2 \cdot c}{\frac{b}{a}}} \cdot \frac{a}{\frac{2}{4}}\]
    8.2

---

13. Applied final simplification
14. Applied simplify to get
    \[\color{red}{\frac{\frac{c}{a}}{\left(\left(-b\right) - b\right) + \frac{2 \cdot c}{\frac{b}{a}}} \cdot \frac{a}{\frac{2}{4}}} \leadsto \color{blue}{\frac{\frac{c}{2} \cdot 4}{\left(\left(-b\right) - b\right) + \frac{c \cdot 2}{\frac{b}{a}}}}\]
    0.7