if b/2 < -1.102640798064626e+96

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   47.2
2. Using strategy rm
   47.2
3. Applied div-inv to get
   \[\color{red}{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}} \leadsto \color{blue}{\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right) \cdot \frac{1}{a}}\]
   47.2
4. Applied taylor to get
   \[\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right) \cdot \frac{1}{a} \leadsto \frac{1}{2} \cdot \frac{c}{b/2} - 2 \cdot \frac{b/2}{a}\]
   0.0
5. Taylor expanded around -inf to get
   \[\color{red}{\frac{1}{2} \cdot \frac{c}{b/2} - 2 \cdot \frac{b/2}{a}} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{c}{b/2} - 2 \cdot \frac{b/2}{a}}\]
   0.0

if -1.102640798064626e+96 < b/2 < -4.180861961583105e-193

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   7.2
2. Using strategy rm
   7.2
3. Applied add-sqr-sqrt to get
   \[\frac{\left(-b/2\right) + \color{red}{\sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\left(-b/2\right) + \color{blue}{{\left(\sqrt{\sqrt{{b/2}^2 - a \cdot c}}\right)}^2}}{a}\]
   7.4

if -4.180861961583105e-193 < b/2 < 2.2608845850534584e+29

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   25.6
2. Using strategy rm
   25.6
3. Applied div-inv to get
   \[\color{red}{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}} \leadsto \color{blue}{\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right) \cdot \frac{1}{a}}\]
   25.6
4. Using strategy rm
   25.6
5. Applied flip-+ to get
   \[\color{red}{\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right)} \cdot \frac{1}{a} \leadsto \color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}} \cdot \frac{1}{a}\]
   25.9
6. Applied associate-*l/ to get
   \[\color{red}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \cdot \frac{1}{a}} \leadsto \color{blue}{\frac{\left({\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2\right) \cdot \frac{1}{a}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}\]
   26.0
7. Applied simplify to get
   \[\frac{\color{red}{\left({\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2\right) \cdot \frac{1}{a}}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \leadsto \frac{\color{blue}{\frac{a \cdot c}{a}}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}\]
   16.5

if 2.2608845850534584e+29 < b/2

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   58.1
2. Using strategy rm
   58.1
3. Applied div-inv to get
   \[\color{red}{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}} \leadsto \color{blue}{\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right) \cdot \frac{1}{a}}\]
   58.1
4. Using strategy rm
   58.1
5. Applied flip-+ to get
   \[\color{red}{\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right)} \cdot \frac{1}{a} \leadsto \color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}} \cdot \frac{1}{a}\]
   58.2
6. Applied associate-*l/ to get
   \[\color{red}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \cdot \frac{1}{a}} \leadsto \color{blue}{\frac{\left({\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2\right) \cdot \frac{1}{a}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}\]
   58.2
7. Applied simplify to get
   \[\frac{\color{red}{\left({\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2\right) \cdot \frac{1}{a}}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \leadsto \frac{\color{blue}{\frac{a \cdot c}{a}}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}\]
   30.0
8. Applied taylor to get
   \[\frac{\frac{a \cdot c}{a}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \leadsto \frac{\frac{a \cdot c}{a}}{\left(-b/2\right) - \left(b/2 - \frac{1}{2} \cdot \frac{c \cdot a}{b/2}\right)}\]
   10.5
9. Taylor expanded around inf to get
   \[\frac{\frac{a \cdot c}{a}}{\left(-b/2\right) - \color{red}{\left(b/2 - \frac{1}{2} \cdot \frac{c \cdot a}{b/2}\right)}} \leadsto \frac{\frac{a \cdot c}{a}}{\left(-b/2\right) - \color{blue}{\left(b/2 - \frac{1}{2} \cdot \frac{c \cdot a}{b/2}\right)}}\]
   10.5
10. Applied simplify to get
    \[\frac{\frac{a \cdot c}{a}}{\left(-b/2\right) - \left(b/2 - \frac{1}{2} \cdot \frac{c \cdot a}{b/2}\right)} \leadsto \frac{1 \cdot c}{\left(\left(-b/2\right) - b/2\right) + \frac{\frac{1}{2} \cdot c}{\frac{b/2}{a}}}\]
    2.2

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11. Applied final simplification
12. Applied simplify to get
    \[\color{red}{\frac{1 \cdot c}{\left(\left(-b/2\right) - b/2\right) + \frac{\frac{1}{2} \cdot c}{\frac{b/2}{a}}}} \leadsto \color{blue}{\frac{c}{\left(\left(-b/2\right) - b/2\right) + \frac{c}{b/2} \cdot \left(a \cdot \frac{1}{2}\right)}}\]
    2.2