if re < -1.6640371f+08

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
   22.7
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base}}\]
   22.7
3. Applied taylor to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \left(-1 \cdot re\right) + 0}{\log base \cdot \log base}\]
   0.4
4. Taylor expanded around -inf to get
   \[\frac{\log base \cdot \log \color{red}{\left(-1 \cdot re\right)} + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \color{blue}{\left(-1 \cdot re\right)} + 0}{\log base \cdot \log base}\]
   0.4
5. Applied simplify to get
   \[\color{red}{\frac{\log base \cdot \log \left(-1 \cdot re\right) + 0}{\log base \cdot \log base}} \leadsto \color{blue}{\frac{\log \left(-re\right)}{\log base}}\]
   0.4

if -1.6640371f+08 < re < 2.6814642f+12

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
   9.9
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base}}\]
   9.9
3. Using strategy rm
   9.9
4. Applied add-cube-cbrt to get
   \[\frac{\log base \cdot \log \color{red}{\left(\sqrt{{re}^2 + im \cdot im}\right)} + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \color{blue}{\left({\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3\right)} + 0}{\log base \cdot \log base}\]
   9.9
5. Using strategy rm
   9.9
6. Applied cube-mult to get
   \[\frac{\log base \cdot \log \color{red}{\left({\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3\right)} + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)\right)} + 0}{\log base \cdot \log base}\]
   9.9
7. Applied log-prod to get
   \[\frac{\log base \cdot \color{red}{\log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)\right)} + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right) + \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)\right)} + 0}{\log base \cdot \log base}\]
   9.9
8. Applied distribute-lft-in to get
   \[\frac{\color{red}{\log base \cdot \left(\log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right) + \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)\right)} + 0}{\log base \cdot \log base} \leadsto \frac{\color{blue}{\left(\log base \cdot \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right) + \log base \cdot \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)\right)} + 0}{\log base \cdot \log base}\]
   9.9
9. Applied simplify to get
   \[\frac{\left(\log base \cdot \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right) + \color{red}{\log base \cdot \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}} \cdot \sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}\right) + 0}{\log base \cdot \log base} \leadsto \frac{\left(\log base \cdot \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right) + \color{blue}{\log \left(\sqrt[3]{\sqrt{im \cdot im + re \cdot re}}\right) \cdot \left(\log base + \log base\right)}\right) + 0}{\log base \cdot \log base}\]
   9.9
10. Applied simplify to get
    \[\frac{\left(\log base \cdot \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right) + \color{red}{\log \left(\sqrt[3]{\sqrt{im \cdot im + re \cdot re}}\right)} \cdot \left(\log base + \log base\right)\right) + 0}{\log base \cdot \log base} \leadsto \frac{\left(\log base \cdot \log \left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right) + \color{blue}{\log \left(\sqrt[3]{\sqrt{{im}^2 + re \cdot re}}\right)} \cdot \left(\log base + \log base\right)\right) + 0}{\log base \cdot \log base}\]
    9.9

if 2.6814642f+12 < re

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
   25.1
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base}}\]
   25.1
3. Applied taylor to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log re + 0}{\log base \cdot \log base}\]
   0.4
4. Taylor expanded around inf to get
   \[\frac{\log base \cdot \log \color{red}{re} + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \color{blue}{re} + 0}{\log base \cdot \log base}\]
   0.4
5. Applied simplify to get
   \[\color{red}{\frac{\log base \cdot \log re + 0}{\log base \cdot \log base}} \leadsto \color{blue}{\frac{\log re}{\log base}}\]
   0.4