if re < -8.533487505443716e+145

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   57.1
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   57.1
3. Applied taylor to get
   \[\sqrt{{re}^2 + im \cdot im} \leadsto -1 \cdot re\]
   0
4. Taylor expanded around -inf to get
   \[\color{red}{-1 \cdot re} \leadsto \color{blue}{-1 \cdot re}\]
   0
5. Applied simplify to get
   \[\color{red}{-1 \cdot re} \leadsto \color{blue}{-re}\]
   0

if -8.533487505443716e+145 < re < 3.751610550051807e+91

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   19.6
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   19.6

if 3.751610550051807e+91 < re

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   46.7
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   46.7
3. Using strategy rm
   46.7
4. Applied add-exp-log to get
   \[\color{red}{\sqrt{{re}^2 + im \cdot im}} \leadsto \color{blue}{e^{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}}\]
   47.9
5. Using strategy rm
   47.9
6. Applied pow1/2 to get
   \[e^{\log \color{red}{\left(\sqrt{{re}^2 + im \cdot im}\right)}} \leadsto e^{\log \color{blue}{\left({\left({re}^2 + im \cdot im\right)}^{\frac{1}{2}}\right)}}\]
   47.9
7. Applied log-pow to get
   \[e^{\color{red}{\log \left({\left({re}^2 + im \cdot im\right)}^{\frac{1}{2}}\right)}} \leadsto e^{\color{blue}{\frac{1}{2} \cdot \log \left({re}^2 + im \cdot im\right)}}\]
   47.9
8. Applied exp-prod to get
   \[\color{red}{e^{\frac{1}{2} \cdot \log \left({re}^2 + im \cdot im\right)}} \leadsto \color{blue}{{\left(e^{\frac{1}{2}}\right)}^{\left(\log \left({re}^2 + im \cdot im\right)\right)}}\]
   48.1
9. Using strategy rm
   48.1
10. Applied add-cube-cbrt to get
    \[{\left(e^{\frac{1}{2}}\right)}^{\color{red}{\left(\log \left({re}^2 + im \cdot im\right)\right)}} \leadsto {\left(e^{\frac{1}{2}}\right)}^{\color{blue}{\left({\left(\sqrt[3]{\log \left({re}^2 + im \cdot im\right)}\right)}^3\right)}}\]
    48.5
11. Applied taylor to get
    \[{\left(e^{\frac{1}{2}}\right)}^{\left({\left(\sqrt[3]{\log \left({re}^2 + im \cdot im\right)}\right)}^3\right)} \leadsto {\left({re}^2\right)}^{\frac{1}{2}} + \frac{1}{2} \cdot \frac{{im}^2}{re}\]
    45.3
12. Taylor expanded around 0 to get
    \[\color{red}{{\left({re}^2\right)}^{\frac{1}{2}} + \frac{1}{2} \cdot \frac{{im}^2}{re}} \leadsto \color{blue}{{\left({re}^2\right)}^{\frac{1}{2}} + \frac{1}{2} \cdot \frac{{im}^2}{re}}\]
    45.3
13. Applied simplify to get
    \[{\left({re}^2\right)}^{\frac{1}{2}} + \frac{1}{2} \cdot \frac{{im}^2}{re} \leadsto \left|re\right| + \frac{im \cdot \frac{1}{2}}{\frac{re}{im}}\]
    0.0

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14. Applied final simplification