if b/2 < -5.215706425974793e+89

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   44.2
2. Applied taylor to get
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a} \leadsto \frac{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}{a}\]
   12.2
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a} \leadsto \frac{\color{blue}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}\]
   12.2
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 -5.215706425974793e+89 < b/2 < 3.664277580957564e-136

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   11.6
2. Using strategy rm
   11.6
3. Applied div-inv to get
   \[\color{red}{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}} \leadsto \color{blue}{\left(\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}\right) \cdot \frac{1}{a}}\]
   11.7

if 3.664277580957564e-136 < b/2 < 2.993431952201985e+83

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   39.4
2. Using strategy rm
   39.4
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   39.5
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   15.0
5. Using strategy rm
   15.0
6. Applied add-cube-cbrt to get
   \[\color{red}{\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}}\right)}^3}\]
   15.7
7. Applied simplify to get
   \[{\color{red}{\left(\sqrt[3]{\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{c}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - c \cdot a}}}\right)}}^3\]
   6.8

if 2.993431952201985e+83 < b/2

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   58.4
2. Using strategy rm
   58.4
3. Applied add-cube-cbrt to get
   \[\color{red}{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}}\right)}^3}\]
   58.4
4. Applied taylor to get
   \[{\left(\sqrt[3]{\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}}\right)}^3 \leadsto {\left(\sqrt[3]{\frac{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}{a}}\right)}^3\]
   15.6
5. Taylor expanded around inf to get
   \[{\left(\sqrt[3]{\frac{\color{red}{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}}{a}}\right)}^3 \leadsto {\left(\sqrt[3]{\frac{\color{blue}{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}}{a}}\right)}^3\]
   15.6
6. Applied simplify to get
   \[{\left(\sqrt[3]{\frac{\frac{-1}{2} \cdot \frac{c \cdot a}{b/2}}{a}}\right)}^3 \leadsto \frac{\frac{-1}{2}}{a} \cdot \left(\frac{c}{b/2} \cdot a\right)\]
   9.3

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7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\frac{\frac{-1}{2}}{a} \cdot \left(\frac{c}{b/2} \cdot a\right)} \leadsto \color{blue}{\left(1 \cdot \frac{-1}{2}\right) \cdot \frac{c}{b/2}}\]
   0.0