if b < -2.2913476789857995e+35

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   38.0
2. Using strategy rm
   38.0
3. Applied clear-num to get
   \[\color{red}{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}\]
   38.1
4. Applied taylor to get
   \[\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}} \leadsto \frac{1}{\frac{2 \cdot a}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}\]
   10.6
5. Taylor expanded around -inf to get
   \[\frac{1}{\frac{2 \cdot a}{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}} \leadsto \frac{1}{\frac{2 \cdot a}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}\]
   10.6
6. Applied simplify to get
   \[\frac{1}{\frac{2 \cdot a}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}} \leadsto \frac{1}{\frac{\frac{a}{1}}{a \cdot \frac{c}{b} - b}}\]
   3.1

---

7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\frac{1}{\frac{\frac{a}{1}}{a \cdot \frac{c}{b} - b}}} \leadsto \color{blue}{\frac{\frac{c}{b}}{1} - \frac{b}{a}}\]
   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
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   58.3
2. Using strategy rm
   58.3
3. Applied clear-num to get
   \[\color{red}{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}\]
   58.3
4. Applied taylor to get
   \[\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}} \leadsto \frac{1}{-1 \cdot \frac{b}{c}}\]
   0.7
5. Taylor expanded around 0 to get
   \[\frac{1}{\color{red}{-1 \cdot \frac{b}{c}}} \leadsto \frac{1}{\color{blue}{-1 \cdot \frac{b}{c}}}\]
   0.7
6. Applied simplify to get
   \[\frac{1}{-1 \cdot \frac{b}{c}} \leadsto \frac{\frac{1}{-1}}{\frac{b}{c}}\]
   0.7

---

7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{-1}}{\frac{b}{c}}} \leadsto \color{blue}{\frac{c}{-b}}\]
   0