if re < -1.5511732f+19

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   27.4
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   27.4
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 -1.5511732f+19 < re < 7.052067f+15

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   8.9
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   8.9

if 7.052067f+15 < re

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   24.0
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   24.0
3. Using strategy rm
   24.0
4. Applied add-cube-cbrt to get
   \[\color{red}{\sqrt{{re}^2 + im \cdot im}} \leadsto \color{blue}{{\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3}\]
   24.1
5. Using strategy rm
   24.1
6. Applied add-sqr-sqrt to get
   \[{\color{red}{\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}}^3 \leadsto {\color{blue}{\left({\left(\sqrt{\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}}\right)}^2\right)}}^3\]
   24.1
7. Using strategy rm
   24.1
8. Applied add-log-exp to get
   \[{\left({\color{red}{\left(\sqrt{\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}}\right)}}^2\right)}^3 \leadsto {\left({\color{blue}{\left(\log \left(e^{\sqrt{\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}}}\right)\right)}}^2\right)}^3\]
   27.7
9. Applied taylor to get
   \[{\left({\left(\log \left(e^{\sqrt{\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}}}\right)\right)}^2\right)}^3 \leadsto re + \frac{1}{2} \cdot \frac{{im}^2}{re}\]
   5.0
10. Taylor expanded around 0 to get
    \[\color{red}{re + \frac{1}{2} \cdot \frac{{im}^2}{re}} \leadsto \color{blue}{re + \frac{1}{2} \cdot \frac{{im}^2}{re}}\]
    5.0
11. Applied simplify to get
    \[re + \frac{1}{2} \cdot \frac{{im}^2}{re} \leadsto re + \frac{\frac{1}{2} \cdot im}{\frac{re}{im}}\]
    0.0

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12. Applied final simplification