if re < -4.0233915f+09

1. Started with
   \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   23.4
2. Applied simplify to get
   \[\color{red}{\log \left(\sqrt{re \cdot re + im \cdot im}\right)} \leadsto \color{blue}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}\]
   23.4
3. Applied taylor to get
   \[\log \left(\sqrt{{re}^2 + im \cdot im}\right) \leadsto \log \left(-1 \cdot re\right)\]
   0.0
4. Taylor expanded around -inf to get
   \[\log \color{red}{\left(-1 \cdot re\right)} \leadsto \log \color{blue}{\left(-1 \cdot re\right)}\]
   0.0
5. Applied simplify to get
   \[\color{red}{\log \left(-1 \cdot re\right)} \leadsto \color{blue}{\log \left(-re\right)}\]
   0.0

if -4.0233915f+09 < re < 1.1667896f+15

1. Started with
   \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   9.5
2. Applied simplify to get
   \[\color{red}{\log \left(\sqrt{re \cdot re + im \cdot im}\right)} \leadsto \color{blue}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}\]
   9.5
3. Using strategy rm
   9.5
4. Applied pow1/2 to get
   \[\log \color{red}{\left(\sqrt{{re}^2 + im \cdot im}\right)} \leadsto \log \color{blue}{\left({\left({re}^2 + im \cdot im\right)}^{\frac{1}{2}}\right)}\]
   9.5
5. Applied log-pow to get
   \[\color{red}{\log \left({\left({re}^2 + im \cdot im\right)}^{\frac{1}{2}}\right)} \leadsto \color{blue}{\frac{1}{2} \cdot \log \left({re}^2 + im \cdot im\right)}\]
   9.5

if 1.1667896f+15 < re

1. Started with
   \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   26.1
2. Applied simplify to get
   \[\color{red}{\log \left(\sqrt{re \cdot re + im \cdot im}\right)} \leadsto \color{blue}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}\]
   26.1
3. Applied taylor to get
   \[\log \left(\sqrt{{re}^2 + im \cdot im}\right) \leadsto \log re\]
   0.0
4. Taylor expanded around inf to get
   \[\log \color{red}{re} \leadsto \log \color{blue}{re}\]
   0.0