if b < -1.4516784f-11

1. Started with
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   28.2
2. Applied taylor to get
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   7.2
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a} \leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
   7.2
4. Applied simplify to get
   \[\color{red}{\frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}} \leadsto \color{blue}{\frac{c}{b} \cdot \frac{-2}{2}}\]
   0

if -1.4516784f-11 < b < 3.318237f+16

1. Started with
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   5.4
2. Using strategy rm
   5.4
3. Applied add-cube-cbrt to get
   \[\color{red}{\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\right)}^3}\]
   5.9
4. Applied taylor to get
   \[{\left(\sqrt[3]{\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\right)}^3 \leadsto {\left(\sqrt[3]{\frac{-1}{2} \cdot \left(\left(\frac{1}{b} + \sqrt{\frac{1}{{b}^2} - 4 \cdot \frac{1}{c \cdot a}}\right) \cdot a\right)}\right)}^3\]
   29.7
5. Taylor expanded around inf to get
   \[{\color{red}{\left(\sqrt[3]{\frac{-1}{2} \cdot \left(\left(\frac{1}{b} + \sqrt{\frac{1}{{b}^2} - 4 \cdot \frac{1}{c \cdot a}}\right) \cdot a\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{-1}{2} \cdot \left(\left(\frac{1}{b} + \sqrt{\frac{1}{{b}^2} - 4 \cdot \frac{1}{c \cdot a}}\right) \cdot a\right)}\right)}}^3\]
   29.7
6. Applied simplify to get
   \[\color{red}{{\left(\sqrt[3]{\frac{-1}{2} \cdot \left(\left(\frac{1}{b} + \sqrt{\frac{1}{{b}^2} - 4 \cdot \frac{1}{c \cdot a}}\right) \cdot a\right)}\right)}^3} \leadsto \color{blue}{(\left(\sqrt{\frac{1}{b \cdot b} - \frac{\frac{4}{a}}{c}}\right) * \left(\frac{-1}{2} \cdot a\right) + \left(\frac{a}{b} \cdot \frac{-1}{2}\right))_*}\]
   29.8
7. Applied taylor to get
   \[(\left(\sqrt{\frac{1}{b \cdot b} - \frac{\frac{4}{a}}{c}}\right) * \left(\frac{-1}{2} \cdot a\right) + \left(\frac{a}{b} \cdot \frac{-1}{2}\right))_* \leadsto (\left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right) * \left(\frac{\frac{-1}{2}}{a}\right) + \left(\frac{-1}{2} \cdot \frac{b}{a}\right))_*\]
   5.4
8. Taylor expanded around inf to get
   \[\color{red}{(\left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right) * \left(\frac{\frac{-1}{2}}{a}\right) + \left(\frac{-1}{2} \cdot \frac{b}{a}\right))_*} \leadsto \color{blue}{(\left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right) * \left(\frac{\frac{-1}{2}}{a}\right) + \left(\frac{-1}{2} \cdot \frac{b}{a}\right))_*}\]
   5.4
9. Applied simplify to get
   \[(\left(\sqrt{{b}^2 - 4 \cdot \left(c \cdot a\right)}\right) * \left(\frac{\frac{-1}{2}}{a}\right) + \left(\frac{-1}{2} \cdot \frac{b}{a}\right))_* \leadsto (\left(\sqrt{{b}^2 - \left(4 \cdot c\right) \cdot a}\right) * \left(\frac{\frac{-1}{2}}{a}\right) + \left(\frac{\frac{-1}{2}}{\frac{a}{b}}\right))_*\]
   5.5

---

10. Applied final simplification

if 3.318237f+16 < b

1. Started with
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   25.3
2. Applied taylor to get
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \leadsto \frac{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}{2 \cdot a}\]
   5.8
3. Taylor expanded around inf to get
   \[\frac{\color{red}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a} \leadsto \frac{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a}\]
   5.8
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