if re < -1.8009657f+17

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   25.6
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   25.6
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 -1.8009657f+17 < re < 8.580638f+12

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   8.8
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   8.8

if 8.580638f+12 < re

1. Started with
   \[\sqrt{re \cdot re + im \cdot im}\]
   22.6
2. Applied simplify to get
   \[\color{red}{\sqrt{re \cdot re + im \cdot im}} \leadsto \color{blue}{\sqrt{{re}^2 + im \cdot im}}\]
   22.6
3. Using strategy rm
   22.6
4. Applied add-cube-cbrt to get
   \[\color{red}{\sqrt{{re}^2 + im \cdot im}} \leadsto \color{blue}{{\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3}\]
   22.7
5. Applied taylor to get
   \[{\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3 \leadsto re + \frac{1}{2} \cdot \frac{{im}^2}{re}\]
   4.9
6. Taylor expanded around 0 to get
   \[\color{red}{re + \frac{1}{2} \cdot \frac{{im}^2}{re}} \leadsto \color{blue}{re + \frac{1}{2} \cdot \frac{{im}^2}{re}}\]
   4.9
7. 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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8. Applied final simplification