if b < -6.5355834f+18

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   28.5
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto -1 \cdot \frac{b}{a}\]
   0
3. Taylor expanded around -inf to get
   \[\color{red}{-1 \cdot \frac{b}{a}} \leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
   0
4. Applied simplify to get
   \[\color{red}{-1 \cdot \frac{b}{a}} \leadsto \color{blue}{\frac{-b}{a}}\]
   0

if -6.5355834f+18 < b < -1.5102728f-36

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   3.9
2. Using strategy rm
   3.9
3. Applied pow1 to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}}{2 \cdot a}\]
   3.9

if -1.5102728f-36 < b < 1.11538095f+18

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   15.4
2. Using strategy rm
   15.4
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   17.0
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   6.6
5. Using strategy rm
   6.6
6. Applied clear-num to get
   \[\color{red}{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}}\]
   6.6
7. Applied simplify to get
   \[\frac{1}{\color{red}{\frac{2 \cdot a}{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}} \leadsto \frac{1}{\color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{\frac{2}{4}}{c}}}\]
   4.2
8. Applied simplify to get
   \[\frac{1}{\color{red}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right)} \cdot \frac{\frac{2}{4}}{c}} \leadsto \frac{1}{\color{blue}{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)} \cdot \frac{\frac{2}{4}}{c}}\]
   4.2

if 1.11538095f+18 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   30.4
2. Using strategy rm
   30.4
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   30.8
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   18.2
5. Using strategy rm
   18.2
6. Applied clear-num to get
   \[\color{red}{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}}\]
   18.2
7. Applied simplify to get
   \[\frac{1}{\color{red}{\frac{2 \cdot a}{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}} \leadsto \frac{1}{\color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{\frac{2}{4}}{c}}}\]
   18.0
8. Applied taylor to get
   \[\frac{1}{\left(\left(-b\right) - \sqrt{b \cdot b - a \cdot \left(4 \cdot c\right)}\right) \cdot \frac{\frac{2}{4}}{c}} \leadsto \frac{1}{\frac{a}{b} - \frac{b}{c}}\]
   1.1
9. Taylor expanded around inf to get
   \[\frac{1}{\color{red}{\frac{a}{b} - \frac{b}{c}}} \leadsto \frac{1}{\color{blue}{\frac{a}{b} - \frac{b}{c}}}\]
   1.1
10. Applied simplify to get
    \[\frac{1}{\frac{a}{b} - \frac{b}{c}} \leadsto \frac{1}{\frac{a}{b} - \frac{b}{c}}\]
    1.1

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11. Applied final simplification