if b < -1.3462214f+10

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   20.7
2. Using strategy rm
   20.7
3. Applied flip3-- to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{\color{red}{{b}^2 - \left(4 \cdot a\right) \cdot c}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{\color{blue}{\frac{{\left({b}^2\right)}^{3} - {\left(\left(4 \cdot a\right) \cdot c\right)}^{3}}{{\left({b}^2\right)}^2 + \left({\left(\left(4 \cdot a\right) \cdot c\right)}^2 + {b}^2 \cdot \left(\left(4 \cdot a\right) \cdot c\right)\right)}}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   20.7
4. Applied sqrt-div to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{red}{\sqrt{\frac{{\left({b}^2\right)}^{3} - {\left(\left(4 \cdot a\right) \cdot c\right)}^{3}}{{\left({b}^2\right)}^2 + \left({\left(\left(4 \cdot a\right) \cdot c\right)}^2 + {b}^2 \cdot \left(\left(4 \cdot a\right) \cdot c\right)\right)}}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \color{blue}{\frac{\sqrt{{\left({b}^2\right)}^{3} - {\left(\left(4 \cdot a\right) \cdot c\right)}^{3}}}{\sqrt{{\left({b}^2\right)}^2 + \left({\left(\left(4 \cdot a\right) \cdot c\right)}^2 + {b}^2 \cdot \left(\left(4 \cdot a\right) \cdot c\right)\right)}}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   20.7
5. Applied simplify to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\color{red}{\sqrt{{\left({b}^2\right)}^{3} - {\left(\left(4 \cdot a\right) \cdot c\right)}^{3}}}}{\sqrt{{\left({b}^2\right)}^2 + \left({\left(\left(4 \cdot a\right) \cdot c\right)}^2 + {b}^2 \cdot \left(\left(4 \cdot a\right) \cdot c\right)\right)}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\color{blue}{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}}{\sqrt{{\left({b}^2\right)}^2 + \left({\left(\left(4 \cdot a\right) \cdot c\right)}^2 + {b}^2 \cdot \left(\left(4 \cdot a\right) \cdot c\right)\right)}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   20.7
6. Applied simplify to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}{\color{red}{\sqrt{{\left({b}^2\right)}^2 + \left({\left(\left(4 \cdot a\right) \cdot c\right)}^2 + {b}^2 \cdot \left(\left(4 \cdot a\right) \cdot c\right)\right)}}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}{\color{blue}{\sqrt{(\left(a \cdot \left(c \cdot 4\right)\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   20.7
7. Applied taylor to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}{\sqrt{(\left(a \cdot \left(c \cdot 4\right)\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}{\sqrt{(\left(a \cdot \left(c \cdot 4\right)\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a} & \text{otherwise} \end{cases}\]
   5.8
8. Taylor expanded around -inf to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}{\sqrt{(\left(a \cdot \left(c \cdot 4\right)\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}{\sqrt{(\left(a \cdot \left(c \cdot 4\right)\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a} & \text{otherwise} \end{cases}\]
   5.8
9. Applied simplify to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{\left({b}^3\right)}^2 - {\left(a \cdot \left(c \cdot 4\right)\right)}^3}}{\sqrt{(\left(a \cdot \left(c \cdot 4\right)\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c \cdot 2}{\left(-b\right) - \frac{\sqrt{{b}^3 \cdot {b}^3 - {\left(\left(a \cdot c\right) \cdot 4\right)}^3}}{\sqrt{(\left(\left(a \cdot c\right) \cdot 4\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ \frac{\frac{c \cdot 2}{\frac{b}{a}} - \left(b - \left(-b\right)\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]
   1.6

---

10. Applied final simplification
11. Applied simplify to get
    \[\color{red}{\begin{cases} \frac{c \cdot 2}{\left(-b\right) - \frac{\sqrt{{b}^3 \cdot {b}^3 - {\left(\left(a \cdot c\right) \cdot 4\right)}^3}}{\sqrt{(\left(\left(a \cdot c\right) \cdot 4\right) * \left((c * \left(a \cdot 4\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ \frac{\frac{c \cdot 2}{\frac{b}{a}} - \left(b - \left(-b\right)\right)}{a \cdot 2} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \frac{\sqrt{{b}^3 \cdot {b}^3 - {\left(c \cdot \left(4 \cdot a\right)\right)}^3}}{\sqrt{(\left(c \cdot \left(4 \cdot a\right)\right) * \left((c * \left(4 \cdot a\right) + \left({b}^2\right))_*\right) + \left({b}^2 \cdot {b}^2\right))_*}}} & \text{when } b \ge 0 \\ 1 \cdot \frac{c}{b} - \frac{b - \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}}\]
    0.3

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

if 1.6720318f+16 < b

1. Started with
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   17.0
2. Applied taylor to get
   \[\begin{cases} \frac{2 \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.0
3. Taylor expanded around inf to get
   \[\begin{cases} \frac{2 \cdot c}{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{2 \cdot c}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}\]
   4.0
4. Applied simplify to get
   \[\color{red}{\begin{cases} \frac{2 \cdot c}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b} & \text{when } b \ge 0 \\ \frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c}{\frac{c}{b} \cdot a - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}}\]
   0.4
5. Using strategy rm
   0.4
6. Applied add-cube-cbrt to get
   \[\begin{cases} \frac{c}{\color{red}{\frac{c}{b} \cdot a} - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{c}{\color{blue}{{\left(\sqrt[3]{\frac{c}{b} \cdot a}\right)}^3} - b} & \text{when } b \ge 0 \\ \frac{\sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4} + \left(-b\right)}{a \cdot 2} & \text{otherwise} \end{cases}\]
   0.4