if b < -1.9477068539312885e+142

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   57.1
2. Applied taylor to get
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \leadsto -1 \cdot \frac{b}{a}\]
   0
3. Taylor expanded around -inf to get
   \[\color{red}{-1 \cdot \frac{b}{a}} \leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
   0
4. Applied simplify to get
   \[\color{red}{-1 \cdot \frac{b}{a}} \leadsto \color{blue}{\frac{-b}{a}}\]
   0

if -1.9477068539312885e+142 < b < 4.025974820008425e-237

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   9.7

if 4.025974820008425e-237 < b < 1.487068810053394e+69

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   35.3
2. Using strategy rm
   35.3
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   35.4
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   17.1
5. Using strategy rm
   17.1
6. Applied *-un-lft-identity to get
   \[\frac{\frac{\left(4 \cdot a\right) \cdot c}{\color{red}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a} \leadsto \frac{\frac{\left(4 \cdot a\right) \cdot c}{\color{blue}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a}\]
   17.1
7. Applied times-frac to get
   \[\frac{\color{red}{\frac{\left(4 \cdot a\right) \cdot c}{1 \cdot \left(\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{4 \cdot a}{1} \cdot \frac{c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   13.7

if 1.487068810053394e+69 < b

1. Started with
   \[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
   58.3
2. Using strategy rm
   58.3
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
   58.3
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^2}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{\left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
   32.1
5. Using strategy rm
   32.1
6. Applied add-sqr-sqrt to get
   \[\color{red}{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}} \leadsto \color{blue}{{\left(\sqrt{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}}\right)}^2}\]
   38.1
7. Applied simplify to get
   \[{\color{red}{\left(\sqrt{\frac{\frac{\left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}}\right)}}^2 \leadsto {\color{blue}{\left(\sqrt{\frac{\frac{c}{2} \cdot \left(1 \cdot 4\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}}\right)}}^2\]
   37.0
8. Applied taylor to get
   \[{\left(\sqrt{\frac{\frac{c}{2} \cdot \left(1 \cdot 4\right)}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}}\right)}^2 \leadsto {\left(\sqrt{\frac{\frac{c}{2} \cdot \left(1 \cdot 4\right)}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}\right)}^2\]
   26.4
9. Taylor expanded around inf to get
   \[{\left(\sqrt{\frac{\frac{c}{2} \cdot \left(1 \cdot 4\right)}{\left(-b\right) - \color{red}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}\right)}^2 \leadsto {\left(\sqrt{\frac{\frac{c}{2} \cdot \left(1 \cdot 4\right)}{\left(-b\right) - \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}}\right)}^2\]
   26.4
10. Applied simplify to get
    \[{\left(\sqrt{\frac{\frac{c}{2} \cdot \left(1 \cdot 4\right)}{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}\right)}^2 \leadsto \frac{4 \cdot \frac{c}{2}}{(\left(\frac{c}{b} \cdot a\right) * 2 + \left(\left(-b\right) - b\right))_*}\]
    1.4

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11. Applied final simplification