if re < -1.04118355f+09

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   22.9
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}}\]
   22.9
3. Applied taylor to get
   \[\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10} \leadsto \frac{\log \left(-1 \cdot re\right)}{\log 10}\]
   0.3
4. Taylor expanded around -inf to get
   \[\frac{\log \color{red}{\left(-1 \cdot re\right)}}{\log 10} \leadsto \frac{\log \color{blue}{\left(-1 \cdot re\right)}}{\log 10}\]
   0.3
5. Applied simplify to get
   \[\color{red}{\frac{\log \left(-1 \cdot re\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(-re\right)}{\log 10}}\]
   0.3

if -1.04118355f+09 < re < 1212733.4f0

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   9.9
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}}\]
   9.9
3. Using strategy rm
   9.9
4. Applied add-cbrt-cube to get
   \[\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\color{red}{\log 10}} \leadsto \frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\color{blue}{\sqrt[3]{{\left(\log 10\right)}^3}}}\]
   9.9
5. Applied add-cbrt-cube to get
   \[\frac{\color{red}{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}}{\sqrt[3]{{\left(\log 10\right)}^3}} \leadsto \frac{\color{blue}{\sqrt[3]{{\left(\log \left(\sqrt{{re}^2 + im \cdot im}\right)\right)}^3}}}{\sqrt[3]{{\left(\log 10\right)}^3}}\]
   9.9
6. Applied cbrt-undiv to get
   \[\color{red}{\frac{\sqrt[3]{{\left(\log \left(\sqrt{{re}^2 + im \cdot im}\right)\right)}^3}}{\sqrt[3]{{\left(\log 10\right)}^3}}} \leadsto \color{blue}{\sqrt[3]{\frac{{\left(\log \left(\sqrt{{re}^2 + im \cdot im}\right)\right)}^3}{{\left(\log 10\right)}^3}}}\]
   10.0
7. Applied simplify to get
   \[\sqrt[3]{\color{red}{\frac{{\left(\log \left(\sqrt{{re}^2 + im \cdot im}\right)\right)}^3}{{\left(\log 10\right)}^3}}} \leadsto \sqrt[3]{\color{blue}{{\left(\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}\right)}^3}}\]
   10.0

if 1212733.4f0 < re

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   22.3
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}}\]
   22.3
3. Applied taylor to get
   \[\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10} \leadsto \frac{\log re}{\log 10}\]
   0.3
4. Taylor expanded around inf to get
   \[\frac{\log \color{red}{re}}{\log 10} \leadsto \frac{\log \color{blue}{re}}{\log 10}\]
   0.3