if b < -3.840384f-10

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   17.3
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a}\]
   4.6
3. Taylor expanded around -inf to get
   \[\frac{\left(-b\right) + \color{red}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}}{2 \cdot a} \leadsto \frac{\left(-b\right) + \color{blue}{\left(2 \cdot \frac{c \cdot a}{b} - b\right)}}{2 \cdot a}\]
   4.6
4. Applied taylor to get
   \[\frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a} \leadsto \frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a}\]
   4.6
5. Taylor expanded around 0 to get
   \[\frac{\left(-b\right) + \left(2 \cdot \color{red}{\frac{c \cdot a}{b}} - b\right)}{2 \cdot a} \leadsto \frac{\left(-b\right) + \left(2 \cdot \color{blue}{\frac{c \cdot a}{b}} - b\right)}{2 \cdot a}\]
   4.6
6. Applied simplify to get
   \[\frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a} \leadsto \frac{\frac{2 \cdot c}{\frac{b}{a}} - \left(b - \left(-b\right)\right)}{a \cdot 2}\]
   2.5

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7. Applied final simplification

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

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

if 1.7973414f+17 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   30.0
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   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