if b < -1.2890155f+19

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   28.7
2. Using strategy rm
   28.7
3. Applied *-un-lft-identity to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a}\]
   28.7
4. Applied times-frac to get
   \[\color{red}{\frac{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{a}}\]
   28.7
5. Applied taylor to get
   \[\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{a} \leadsto \frac{1}{2} \cdot \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{a}\]
   5.8
6. Taylor expanded around -inf to get
   \[\frac{1}{2} \cdot \frac{\left(-b\right) + \color{red}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}}{a} \leadsto \frac{1}{2} \cdot \frac{\left(-b\right) + \color{blue}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}}{a}\]
   5.8
7. Applied simplify to get
   \[\frac{1}{2} \cdot \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{a} \leadsto \frac{\frac{1}{2}}{a} \cdot \left(\frac{c \cdot 2}{\frac{b}{a}} - \left(b - \left(-b\right)\right)\right)\]
   1.3

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8. Applied final simplification
9. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{2}}{a} \cdot \left(\frac{c \cdot 2}{\frac{b}{a}} - \left(b - \left(-b\right)\right)\right)} \leadsto \color{blue}{\frac{\frac{c \cdot 2}{\frac{b}{a}} - \left(b - \left(-b\right)\right)}{a \cdot 2}}\]
   1.2

if -1.2890155f+19 < b < 1.048583f-06

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   5.8
2. Using strategy rm
   5.8
3. Applied *-un-lft-identity to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}}{2 \cdot a}\]
   5.8
4. Applied times-frac to get
   \[\color{red}{\frac{1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}{2 \cdot a}} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{a}}\]
   5.8

if 1.048583f-06 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   28.3
2. Using strategy rm
   28.3
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   29.7
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{c \cdot \left(4 \cdot a\right)}}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
   16.1
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
   \[\frac{\frac{c \cdot \left(4 \cdot a\right)}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}{2 \cdot a} \leadsto \frac{\frac{a \cdot \left(4 \cdot c\right)}{2}}{\left(2 \cdot a\right) \cdot \left(\frac{c}{b} \cdot a - b\right)}\]
   9.0

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8. Applied final simplification
9. Applied simplify to get
   \[\color{red}{\frac{\frac{a \cdot \left(4 \cdot c\right)}{2}}{\left(2 \cdot a\right) \cdot \left(\frac{c}{b} \cdot a - b\right)}} \leadsto \color{blue}{\frac{c}{\frac{2}{1}} \cdot \frac{\frac{4}{2}}{\frac{a}{b} \cdot c - b}}\]
   2.0