if b < -2.2913476789857995e+35

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   38.1
2. Using strategy rm
   38.1
3. Applied clear-num to get
   \[\color{red}{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}\]
   38.2
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

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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

if 2.890760014197913e-73 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   58.4
2. Using strategy rm
   58.4
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   58.4
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{c \cdot \left(4 \cdot a\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
   34.7
5. Applied taylor to get
   \[\frac{\frac{c \cdot \left(4 \cdot a\right)}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{c \cdot \left(4 \cdot a\right)}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
   15.9
6. Taylor expanded around inf to get
   \[\frac{\frac{c \cdot \left(4 \cdot a\right)}{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}{2 \cdot a} \leadsto \frac{\frac{c \cdot \left(4 \cdot a\right)}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}{2 \cdot a}\]
   15.9
7. Applied simplify to get
   \[\color{red}{\frac{\frac{c \cdot \left(4 \cdot a\right)}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}} \leadsto \color{blue}{\frac{\frac{c}{\frac{2}{4}}}{\frac{c}{b} \cdot a - b} \cdot \frac{1}{2}}\]
   3.9
8. Applied taylor to get
   \[\frac{\frac{c}{\frac{2}{4}}}{\frac{c}{b} \cdot a - b} \cdot \frac{1}{2} \leadsto \frac{\frac{c}{\frac{2}{4}}}{\frac{c \cdot a}{b} - b} \cdot \frac{1}{2}\]
   7.4
9. Taylor expanded around 0 to get
   \[\frac{\frac{c}{\frac{2}{4}}}{\color{red}{\frac{c \cdot a}{b}} - b} \cdot \frac{1}{2} \leadsto \frac{\frac{c}{\frac{2}{4}}}{\color{blue}{\frac{c \cdot a}{b}} - b} \cdot \frac{1}{2}\]
   7.4
10. Applied simplify to get
    \[\frac{\frac{c}{\frac{2}{4}}}{\frac{c \cdot a}{b} - b} \cdot \frac{1}{2} \leadsto \frac{\frac{\frac{c}{\frac{2}{4}}}{2}}{\frac{a}{\frac{b}{c}} - b}\]
    3.9

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11. Applied final simplification