if b < -7.1884515f+13

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   23.2
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]
   6.1
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a} \leadsto \frac{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
   6.1
4. Applied simplify to get
   \[\color{red}{\frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}} \leadsto \color{blue}{\frac{\frac{c}{b}}{1} - \frac{b}{a}}\]
   0.0
5. Applied simplify to get
   \[\color{red}{\frac{\frac{c}{b}}{1}} - \frac{b}{a} \leadsto \color{blue}{\frac{c}{b}} - \frac{b}{a}\]
   0.0

if -7.1884515f+13 < b < 3.5037975f0

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   7.1
2. Using strategy rm
   7.1
3. Applied add-cube-cbrt to get
   \[\color{red}{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\right)}^3}\]
   7.5
4. Applied taylor to get
   \[{\left(\sqrt[3]{\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\right)}^3 \leadsto {\left(\sqrt[3]{\frac{1}{2} \cdot \frac{\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)} - b}{a}}\right)}^3\]
   7.5
5. Taylor expanded around 0 to get
   \[{\color{red}{\left(\sqrt[3]{\frac{1}{2} \cdot \frac{\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)} - b}{a}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{1}{2} \cdot \frac{\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)} - b}{a}}\right)}}^3\]
   7.5
6. Applied simplify to get
   \[{\left(\sqrt[3]{\frac{1}{2} \cdot \frac{\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)} - b}{a}}\right)}^3 \leadsto \frac{\frac{1}{2}}{a} \cdot \left(\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b\right)\]
   7.2

---

7. Applied final simplification

if 3.5037975f0 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   28.2
2. Using strategy rm
   28.2
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   29.9
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{c \cdot \left(4 \cdot a\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
   15.2
5. Applied taylor to get
   \[\frac{\frac{c \cdot \left(4 \cdot a\right)}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{c \cdot \left(4 \cdot a\right)}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
   7.6
6. Taylor expanded around inf to get
   \[\frac{\frac{c \cdot \left(4 \cdot a\right)}{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}{2 \cdot a} \leadsto \frac{\frac{c \cdot \left(4 \cdot a\right)}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}}{2 \cdot a}\]
   7.6
7. Applied simplify to get
   \[\color{red}{\frac{\frac{c \cdot \left(4 \cdot a\right)}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}} \leadsto \color{blue}{\frac{\frac{c}{\frac{2}{4}}}{\frac{c}{b} \cdot a - b} \cdot \frac{1}{2}}\]
   1.5