if b < -1.6844219f+10

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   21.2
2. Applied taylor to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a} & \text{otherwise} \end{cases}\]
   6.1
3. Taylor expanded around -inf to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a} & \text{otherwise} \end{cases}\]
   6.1
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 -1.6844219f+10 < b < 2.2299319f+17

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.2
2. Using strategy rm
   4.2
3. Applied add-sqr-sqrt to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{red}{\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{blue}{{\left(\sqrt{\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}\right)}^2}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.3

if 2.2299319f+17 < b

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   18.3
2. Applied taylor to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.0
3. Taylor expanded around inf to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{red}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.0
4. Applied simplify to get
   \[\color{red}{\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c \cdot 2}{(\left(\frac{c}{\frac{b}{a}}\right) * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases}}\]
   0.7
5. Using strategy rm
   0.7
6. Applied add-cube-cbrt to get
   \[\begin{cases} \frac{c \cdot 2}{(\color{red}{\left(\frac{c}{\frac{b}{a}}\right)} * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c \cdot 2}{(\color{blue}{\left({\left(\sqrt[3]{\frac{c}{\frac{b}{a}}}\right)}^3\right)} * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases}\]
   0.8
7. Using strategy rm
   0.8
8. Applied associate-/r/ to get
   \[\begin{cases} \frac{c \cdot 2}{(\left({\left(\sqrt[3]{\color{red}{\frac{c}{\frac{b}{a}}}}\right)}^3\right) * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c \cdot 2}{(\left({\left(\sqrt[3]{\color{blue}{\frac{c}{b} \cdot a}}\right)}^3\right) * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases}\]
   0.8
9. Applied cbrt-prod to get
   \[\begin{cases} \frac{c \cdot 2}{(\left({\color{red}{\left(\sqrt[3]{\frac{c}{b} \cdot a}\right)}}^3\right) * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c \cdot 2}{(\left({\color{blue}{\left(\sqrt[3]{\frac{c}{b}} \cdot \sqrt[3]{a}\right)}}^3\right) * 2 + \left(\left(-b\right) - b\right))_*} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(a \cdot c\right) \cdot 4} + \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases}\]
   0.8