if b < -1.0189882f+17

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   25.5
2. Using strategy rm
   25.5
3. Applied add-exp-log to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{e^{\log \left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a}\]
   25.9
4. Applied taylor to get
   \[\frac{e^{\log \left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}{2 \cdot a} \leadsto \frac{e^{\log \left(\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)\right)}}{2 \cdot a}\]
   8.9
5. Taylor expanded around -inf to get
   \[\frac{e^{\log \left(\left(-b\right) + \color{red}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}\right)}}{2 \cdot a} \leadsto \frac{e^{\log \left(\left(-b\right) + \color{blue}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}\right)}}{2 \cdot a}\]
   8.9
6. Applied simplify to get
   \[\frac{e^{\log \left(\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)\right)}}{2 \cdot a} \leadsto \frac{\frac{2 \cdot c}{\frac{b}{a}} - \left(b - \left(-b\right)\right)}{a \cdot 2}\]
   1.0

---

7. Applied final simplification

if -1.0189882f+17 < b < 4.7617268f-36

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   4.4
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}}{2 \cdot a}\]
   4.3
3. Taylor expanded around 0 to get
   \[\frac{\left(-b\right) + \sqrt{\color{red}{{b}^2 - 4 \cdot \left(c \cdot a\right)}}}{2 \cdot a} \leadsto \frac{\left(-b\right) + \sqrt{\color{blue}{{b}^2 - 4 \cdot \left(c \cdot a\right)}}}{2 \cdot a}\]
   4.3

if 4.7617268f-36 < b < 6.8314427f+10

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   14.7
2. Using strategy rm
   14.7
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   15.3
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   7.1
5. Using strategy rm
   7.1
6. Applied *-un-lft-identity to get
   \[\frac{\color{red}{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a} \leadsto \frac{\color{blue}{1 \cdot \frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   7.1
7. Applied times-frac to get
   \[\color{red}{\frac{1 \cdot \frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{a}}\]
   7.1
8. Applied simplify to get
   \[\frac{1}{2} \cdot \color{red}{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{a}} \leadsto \frac{1}{2} \cdot \color{blue}{\frac{4 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}}\]
   4.2
9. Applied simplify to get
   \[\frac{1}{2} \cdot \frac{4 \cdot c}{\color{red}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}} \leadsto \frac{1}{2} \cdot \frac{4 \cdot c}{\color{blue}{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4}}}\]
   4.3

if 6.8314427f+10 < b

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
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   6.9
3. Taylor expanded around inf to get
   \[\frac{\color{red}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a} \leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
   6.9
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