if b < -1.3462214f+10 or 1.6720318f+16 < b

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   18.7
2. Applied taylor to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   11.6
3. Taylor expanded around inf to get
   \[\begin{cases} \frac{2 \cdot c}{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   11.6
4. Applied simplify to get
   \[\color{red}{\begin{cases} \frac{2 \cdot c}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c}{\frac{c}{b} \cdot a - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}}\]
   9.7
5. Using strategy rm
   9.7
6. Applied add-cube-cbrt to get
   \[\begin{cases} \frac{c}{\color{red}{\frac{c}{b} \cdot a} - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c}{\color{blue}{{\left(\sqrt[3]{\frac{c}{b} \cdot a}\right)}^3} - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]
   9.7
7. Using strategy rm
   9.7
8. Applied add-log-exp to get
   \[\begin{cases} \frac{c}{{\color{red}{\left(\sqrt[3]{\frac{c}{b} \cdot a}\right)}}^3 - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c}{{\color{blue}{\left(\log \left(e^{\sqrt[3]{\frac{c}{b} \cdot a}}\right)\right)}}^3 - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]
   12.1
9. Applied taylor to get
   \[\begin{cases} \frac{c}{{\left(\log \left(e^{\sqrt[3]{\frac{c}{b} \cdot a}}\right)\right)}^3 - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c}{{\left(\log \left(e^{\sqrt[3]{\frac{c}{b} \cdot a}}\right)\right)}^3 - b} & \text{when } b \ge 0 \\ \frac{\left(2 \cdot \frac{c \cdot a}{b} - b\right) + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]
   5.3
10. Taylor expanded around -inf to get
    \[\begin{cases} \frac{c}{{\left(\log \left(e^{\sqrt[3]{\frac{c}{b} \cdot a}}\right)\right)}^3 - b} & \text{when } b \ge 0 \\ \frac{\left(2 \cdot \frac{c \cdot a}{b} - b\right) + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c}{{\left(\log \left(e^{\sqrt[3]{\frac{c}{b} \cdot a}}\right)\right)}^3 - b} & \text{when } b \ge 0 \\ \frac{\left(2 \cdot \frac{c \cdot a}{b} - b\right) + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]
    5.3
11. Applied simplify to get
    \[\begin{cases} \frac{c}{{\left(\log \left(e^{\sqrt[3]{\frac{c}{b} \cdot a}}\right)\right)}^3 - b} & \text{when } b \ge 0 \\ \frac{\left(2 \cdot \frac{c \cdot a}{b} - b\right) + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c}{\frac{a}{b} \cdot c - b} & \text{when } b \ge 0 \\ \frac{\frac{c \cdot 2}{\frac{b}{a}} - \left(b - \left(-b\right)\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]
    1.0

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12. Applied final simplification
13. Applied simplify to get
    \[\color{red}{\begin{cases} \frac{c}{\frac{a}{b} \cdot c - b} & \text{when } b \ge 0 \\ \frac{\frac{c \cdot 2}{\frac{b}{a}} - \left(b - \left(-b\right)\right)}{a \cdot 2} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c}{\frac{a}{\frac{b}{c}} - b} & \text{when } b \ge 0 \\ \frac{c}{b} - \frac{b - \left(-b\right)}{2 \cdot a} & \text{otherwise} \end{cases}}\]
    0.4

if -1.3462214f+10 < b < 1.6720318f+16

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.0
2. Using strategy rm
   4.0
3. Applied add-sqr-sqrt to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{red}{\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{blue}{{\left(\sqrt{\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}\right)}^2}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.1