if b < -1.2339538201069979e+148

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   58.4
2. Applied taylor to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a} & \text{otherwise} \end{cases}\]
   11.5
3. Taylor expanded around -inf to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a} & \text{otherwise} \end{cases}\]
   11.5
4. Applied simplify to get
   \[\color{red}{\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c \cdot 2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot c\right) \cdot a}} & \text{when } b \ge 0 \\ \frac{\frac{c}{b}}{1} - \frac{b}{a} & \text{otherwise} \end{cases}}\]
   0.0
5. Applied simplify to get
   \[\begin{cases} \frac{c \cdot 2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot c\right) \cdot a}} & \text{when } b \ge 0 \\ \frac{\frac{c}{b}}{1} - \frac{b}{a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c \cdot 2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot c\right) \cdot a}} & \text{when } b \ge 0 \\ \frac{c}{b} - \frac{b}{a} & \text{otherwise} \end{cases}\]
   0.0

if -1.2339538201069979e+148 < b < 2.4608343160951844e+34

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   9.5
2. Using strategy rm
   9.5
3. Applied add-cbrt-cube to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{red}{\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{blue}{\sqrt[3]{{\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^3}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   14.1

if 2.4608343160951844e+34 < b

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   28.2
2. Applied taylor to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   8.0
3. Taylor expanded around inf to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{red}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   8.0
4. Applied simplify to get
   \[\color{red}{\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c \cdot 2}{(\left(\frac{c}{\frac{b}{a}}\right) * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases}}\]
   2.1
5. Using strategy rm
   2.1
6. Applied add-cube-cbrt to get
   \[\begin{cases} \frac{c \cdot 2}{(\color{red}{\left(\frac{c}{\frac{b}{a}}\right)} * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c \cdot 2}{(\color{blue}{\left({\left(\sqrt[3]{\frac{c}{\frac{b}{a}}}\right)}^3\right)} * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases}\]
   2.2