if im < -2.2638177f+14

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
   25.7
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base}}\]
   25.7
3. Using strategy rm
   25.7
4. Applied add-cbrt-cube to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \color{red}{\log base}} \leadsto \frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \color{blue}{\sqrt[3]{{\left(\log base\right)}^3}}}\]
   25.7
5. Applied add-cbrt-cube to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{red}{\log base} \cdot \sqrt[3]{{\left(\log base\right)}^3}} \leadsto \frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{blue}{\sqrt[3]{{\left(\log base\right)}^3}} \cdot \sqrt[3]{{\left(\log base\right)}^3}}\]
   25.7
6. Applied cbrt-unprod to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{red}{\sqrt[3]{{\left(\log base\right)}^3} \cdot \sqrt[3]{{\left(\log base\right)}^3}}} \leadsto \frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{blue}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}}\]
   25.7
7. Applied add-cbrt-cube to get
   \[\frac{\color{red}{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}} \leadsto \frac{\color{blue}{\sqrt[3]{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}}}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}\]
   25.7
8. Applied cbrt-undiv to get
   \[\color{red}{\frac{\sqrt[3]{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}} \leadsto \color{blue}{\sqrt[3]{\frac{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}}\]
   25.7
9. Applied simplify to get
   \[\sqrt[3]{\color{red}{\frac{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}} \leadsto \sqrt[3]{\color{blue}{\frac{{\left(\log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)}^3}{{\left(\log base\right)}^3}}}\]
   25.7
10. Applied taylor to get
    \[\sqrt[3]{\frac{{\left(\log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)}^3}{{\left(\log base\right)}^3}} \leadsto \sqrt[3]{\frac{{\left(\log \left(-1 \cdot im\right)\right)}^3}{{\left(\log base\right)}^3}}\]
    0.4
11. Taylor expanded around -inf to get
    \[\sqrt[3]{\frac{{\left(\log \color{red}{\left(-1 \cdot im\right)}\right)}^3}{{\left(\log base\right)}^3}} \leadsto \sqrt[3]{\frac{{\left(\log \color{blue}{\left(-1 \cdot im\right)}\right)}^3}{{\left(\log base\right)}^3}}\]
    0.4
12. Applied simplify to get
    \[\color{red}{\sqrt[3]{\frac{{\left(\log \left(-1 \cdot im\right)\right)}^3}{{\left(\log base\right)}^3}}} \leadsto \color{blue}{\frac{\log \left(-im\right)}{\log base}}\]
    0.4

if -2.2638177f+14 < im < 5.397122f+09

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
   9.7
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base}}\]
   9.7
3. Using strategy rm
   9.7
4. Applied add-cbrt-cube to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \color{red}{\log base}} \leadsto \frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \color{blue}{\sqrt[3]{{\left(\log base\right)}^3}}}\]
   9.7
5. Applied add-cbrt-cube to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{red}{\log base} \cdot \sqrt[3]{{\left(\log base\right)}^3}} \leadsto \frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{blue}{\sqrt[3]{{\left(\log base\right)}^3}} \cdot \sqrt[3]{{\left(\log base\right)}^3}}\]
   9.7
6. Applied cbrt-unprod to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{red}{\sqrt[3]{{\left(\log base\right)}^3} \cdot \sqrt[3]{{\left(\log base\right)}^3}}} \leadsto \frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\color{blue}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}}\]
   9.7
7. Applied add-cbrt-cube to get
   \[\frac{\color{red}{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}} \leadsto \frac{\color{blue}{\sqrt[3]{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}}}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}\]
   9.8
8. Applied cbrt-undiv to get
   \[\color{red}{\frac{\sqrt[3]{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}}{\sqrt[3]{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}} \leadsto \color{blue}{\sqrt[3]{\frac{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}}\]
   9.7
9. Applied simplify to get
   \[\sqrt[3]{\color{red}{\frac{{\left(\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0\right)}^3}{{\left(\log base\right)}^3 \cdot {\left(\log base\right)}^3}}} \leadsto \sqrt[3]{\color{blue}{\frac{{\left(\log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)}^3}{{\left(\log base\right)}^3}}}\]
   9.7
10. Applied simplify to get
    \[\sqrt[3]{\frac{\color{red}{{\left(\log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)}^3}}{{\left(\log base\right)}^3}} \leadsto \sqrt[3]{\frac{\color{blue}{{\left(\log \left(\sqrt{{im}^2 + re \cdot re}\right)\right)}^3}}{{\left(\log base\right)}^3}}\]
    9.7

if 5.397122f+09 < im

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
   22.8
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base}}\]
   22.8
3. Applied taylor to get
   \[\frac{\log base \cdot \log \left(\sqrt{{re}^2 + im \cdot im}\right) + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log im + 0}{\log base \cdot \log base}\]
   0.4
4. Taylor expanded around 0 to get
   \[\frac{\log base \cdot \log \color{red}{im} + 0}{\log base \cdot \log base} \leadsto \frac{\log base \cdot \log \color{blue}{im} + 0}{\log base \cdot \log base}\]
   0.4
5. Applied simplify to get
   \[\color{red}{\frac{\log base \cdot \log im + 0}{\log base \cdot \log base}} \leadsto \color{blue}{\frac{\log im}{\log base}}\]
   0.4