if (- (sqr b) (* (* 4 a) c)) < 2.6680062f+38

1. Started with
   \[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases}\]
   1.0
2. Using strategy rm
   1.0
3. Applied pow1 to get
   \[\begin{cases} \frac{\color{red}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\color{blue}{{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases}\]
   1.1

if 2.6680062f+38 < (- (sqr b) (* (* 4 a) c))

1. Started with
   \[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases}\]
   23.0
2. Using strategy rm
   23.0
3. Applied pow1 to get
   \[\begin{cases} \frac{\color{red}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\color{blue}{{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases}\]
   23.0
4. Applied taylor to get
   \[\begin{cases} \frac{{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases}\]
   15.2
5. Taylor expanded around -inf to get
   \[\begin{cases} \frac{{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\color{red}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\color{blue}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}} & \text{otherwise} \end{cases}\]
   15.2
6. Applied simplify to get
   \[\color{red}{\begin{cases} \frac{{\left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{\left(c \cdot 2\right) \cdot \frac{a}{b} - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}}\]
   13.1
7. Using strategy rm
   13.1
8. Applied add-sqr-sqrt to get
   \[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{c \cdot \color{red}{2}}{\left(c \cdot 2\right) \cdot \frac{a}{b} - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{c \cdot \color{blue}{2}}{\left(c \cdot 2\right) \cdot {\left(\sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}\]
   19.1
9. Applied add-sqr-sqrt to get
   \[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{\color{red}{c} \cdot 2}{\left(c \cdot 2\right) \cdot {\left(\sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{\color{blue}{c} \cdot 2}{{\left(\sqrt{c \cdot 2}\right)}^2 \cdot {\left(\sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}\]
   23.7
10. Applied square-unprod to get
    \[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{\color{red}{c \cdot 2}}{{\left(\sqrt{c \cdot 2}\right)}^2 \cdot {\left(\sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{\color{blue}{c \cdot 2}}{{\left(\sqrt{c \cdot 2} \cdot \sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}\]
    23.7
11. Applied taylor to get
    \[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot 4\right) \cdot a}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{{\left(\sqrt{c \cdot 2} \cdot \sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} -1 \cdot \frac{b}{a} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{{\left(\sqrt{c \cdot 2} \cdot \sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}\]
    12.3
12. Taylor expanded around inf to get
    \[\begin{cases} \color{red}{-1 \cdot \frac{b}{a}} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{{\left(\sqrt{c \cdot 2} \cdot \sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} \color{blue}{-1 \cdot \frac{b}{a}} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{{\left(\sqrt{c \cdot 2} \cdot \sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}\]
    12.3
13. Applied simplify to get
    \[\begin{cases} -1 \cdot \frac{b}{a} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{{\left(\sqrt{c \cdot 2} \cdot \sqrt{\frac{a}{b}}\right)}^2 - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{-b}{a} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{\left(c \cdot 2\right) \cdot \frac{a}{b} - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}\]
    1.7

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14. Applied final simplification
15. Applied simplify to get
    \[\color{red}{\begin{cases} \frac{-b}{a} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{\left(c \cdot 2\right) \cdot \frac{a}{b} - \left(b - \left(-b\right)\right)} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} -\frac{b}{a} & \text{when } b \ge 0 \\ \frac{c \cdot 2}{(\left(c \cdot 2\right) * \left(\frac{a}{b}\right) + \left(-b\right))_* - b} & \text{otherwise} \end{cases}}\]
    1.6