if b/2 < -2.326207163052239e+115

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   48.8
2. Applied taylor to get
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a} \leadsto \frac{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}{a}\]
   11.7
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a} \leadsto \frac{\color{blue}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}\]
   11.7
4. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}{a}} \leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{b/2}{c}} - \frac{b/2}{a} \cdot 2}\]
   0.0

if -2.326207163052239e+115 < b/2 < -1.9116038778178358e-274

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   8.9

if -1.9116038778178358e-274 < b/2 < 4.449432714488087e+57

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   28.9
2. Using strategy rm
   28.9
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   29.1
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   16.9
5. Using strategy rm
   16.9
6. Applied div-inv to get
   \[\color{red}{\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}} \leadsto \color{blue}{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \cdot \frac{1}{a}}\]
   16.9
7. Using strategy rm
   16.9
8. Applied pow1 to get
   \[\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \cdot \color{red}{\frac{1}{a}} \leadsto \frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \cdot \color{blue}{{\left(\frac{1}{a}\right)}^{1}}\]
   16.9
9. Applied pow1 to get
   \[\color{red}{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}} \cdot {\left(\frac{1}{a}\right)}^{1} \leadsto \color{blue}{{\left(\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}\right)}^{1}} \cdot {\left(\frac{1}{a}\right)}^{1}\]
   16.9
10. Applied pow-prod-down to get
    \[\color{red}{{\left(\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}\right)}^{1} \cdot {\left(\frac{1}{a}\right)}^{1}} \leadsto \color{blue}{{\left(\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \cdot \frac{1}{a}\right)}^{1}}\]
    16.9
11. Applied simplify to get
    \[{\color{red}{\left(\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}} \cdot \frac{1}{a}\right)}}^{1} \leadsto {\color{blue}{\left(\frac{c}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - c \cdot a}}\right)}}^{1}\]
    10.2
12. Applied simplify to get
    \[{\left(\frac{c}{\color{red}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - c \cdot a}}}\right)}^{1} \leadsto {\left(\frac{c}{\color{blue}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}\right)}^{1}\]
    10.2

if 4.449432714488087e+57 < b/2

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   58.3
2. Using strategy rm
   58.3
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   58.3
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   32.4
5. Applied taylor to get
   \[\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{a \cdot c}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}\]
   15.2
6. Taylor expanded around inf to get
   \[\frac{\frac{a \cdot c}{\color{red}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}}{a} \leadsto \frac{\frac{a \cdot c}{\color{blue}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}}{a}\]
   15.2
7. Applied simplify to get
   \[\color{red}{\frac{\frac{a \cdot c}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}} \leadsto \color{blue}{\frac{c}{\left(\frac{1}{2} \cdot c\right) \cdot \frac{a}{b/2} - 2 \cdot b/2}}\]
   1.6