if b < -3.840384f-10

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   17.3
2. Using strategy rm
   17.3
3. Applied *-un-lft-identity to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a}\]
   17.3
4. Applied times-frac to get
   \[\color{red}{\frac{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{a}}\]
   17.3
5. Applied taylor to get
   \[\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{a} \leadsto \frac{1}{2} \cdot \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{a}\]
   4.6
6. Taylor expanded around -inf to get
   \[\frac{1}{2} \cdot \frac{\left(-b\right) + \color{red}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}}{a} \leadsto \frac{1}{2} \cdot \frac{\left(-b\right) + \color{blue}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}}{a}\]
   4.6
7. Applied simplify to get
   \[\color{red}{\frac{1}{2} \cdot \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{a}} \leadsto \color{blue}{\frac{\frac{c \cdot 2}{\frac{b}{a}} + \left(\left(-b\right) - b\right)}{a \cdot 2}}\]
   2.5

if -3.840384f-10 < b < 1.7973414f+17

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   12.4
2. Using strategy rm
   12.4
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   14.6
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{c \cdot \left(4 \cdot a\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
   7.6
5. Using strategy rm
   7.6
6. Applied *-un-lft-identity to get
   \[\frac{\frac{c \cdot \left(4 \cdot a\right)}{\color{red}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a} \leadsto \frac{\frac{c \cdot \left(4 \cdot a\right)}{\color{blue}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}}{2 \cdot a}\]
   7.6
7. Applied times-frac to get
   \[\frac{\color{red}{\frac{c \cdot \left(4 \cdot a\right)}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{c}{1} \cdot \frac{4 \cdot a}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   5.7
8. Applied times-frac to get
   \[\color{red}{\frac{\frac{c}{1} \cdot \frac{4 \cdot a}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}} \leadsto \color{blue}{\frac{\frac{c}{1}}{2} \cdot \frac{\frac{4 \cdot a}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a}}\]
   5.7
9. Applied simplify to get
   \[\color{red}{\frac{\frac{c}{1}}{2}} \cdot \frac{\frac{4 \cdot a}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a} \leadsto \color{blue}{\frac{c}{2}} \cdot \frac{\frac{4 \cdot a}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a}\]
   5.7
10. Applied simplify to get
    \[\frac{c}{2} \cdot \color{red}{\frac{\frac{4 \cdot a}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{a}} \leadsto \frac{c}{2} \cdot \color{blue}{\frac{4}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}}\]
    5.7
11. Applied simplify to get
    \[\frac{c}{2} \cdot \frac{4}{\color{red}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}} \leadsto \frac{c}{2} \cdot \frac{4}{\color{blue}{\left(-b\right) - \sqrt{{b}^2 - \left(c \cdot a\right) \cdot 4}}}\]
    5.6

if 1.7973414f+17 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   30.0
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   7.4
3. Taylor expanded around inf to get
   \[\frac{\color{red}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a} \leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
   7.4
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