if re < -5.2596218f+17

1. Started with
   \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   28.3
2. Applied simplify to get
   \[\color{red}{\log \left(\sqrt{re \cdot re + im \cdot im}\right)} \leadsto \color{blue}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}\]
   28.3
3. Applied taylor to get
   \[\log \left(\sqrt{{re}^2 + im \cdot im}\right) \leadsto \log \left(-1 \cdot re\right)\]
   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
5. Applied simplify to get
   \[\color{red}{\log \left(-1 \cdot re\right)} \leadsto \color{blue}{\log \left(-re\right)}\]
   0

if -5.2596218f+17 < re < 9.018499f+07

1. Started with
   \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   9.6
2. Applied simplify to get
   \[\color{red}{\log \left(\sqrt{re \cdot re + im \cdot im}\right)} \leadsto \color{blue}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}\]
   9.6
3. Using strategy rm
   9.6
4. Applied add-exp-log to get
   \[\log \left(\sqrt{\color{red}{{re}^2 + im \cdot im}}\right) \leadsto \log \left(\sqrt{\color{blue}{e^{\log \left({re}^2 + im \cdot im\right)}}}\right)\]
   9.6

if 9.018499f+07 < re

1. Started with
   \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   21.6
2. Applied simplify to get
   \[\color{red}{\log \left(\sqrt{re \cdot re + im \cdot im}\right)} \leadsto \color{blue}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}\]
   21.6
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