if re < -5.2596218f+17

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   28.3
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}}\]
   28.3
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 -5.2596218f+17 < re < 9.018499f+07

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

if 9.018499f+07 < re

1. Started with
   \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   21.6
2. Applied simplify to get
   \[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}} \leadsto \color{blue}{\frac{\log \left(\sqrt{{re}^2 + im \cdot im}\right)}{\log 10}}\]
   21.6
3. Using strategy rm
   21.6
4. Applied add-cube-cbrt to get
   \[\frac{\log \color{red}{\left(\sqrt{{re}^2 + im \cdot im}\right)}}{\log 10} \leadsto \frac{\log \color{blue}{\left({\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3\right)}}{\log 10}\]
   21.6
5. Applied taylor to get
   \[\frac{\log \left({\left(\sqrt[3]{\sqrt{{re}^2 + im \cdot im}}\right)}^3\right)}{\log 10} \leadsto \frac{\log \left(re + \frac{1}{2} \cdot \frac{{im}^2}{re}\right)}{\log 10}\]
   7.6
6. Taylor expanded around 0 to get
   \[\frac{\log \color{red}{\left(re + \frac{1}{2} \cdot \frac{{im}^2}{re}\right)}}{\log 10} \leadsto \frac{\log \color{blue}{\left(re + \frac{1}{2} \cdot \frac{{im}^2}{re}\right)}}{\log 10}\]
   7.6
7. Applied simplify to get
   \[\frac{\log \left(re + \frac{1}{2} \cdot \frac{{im}^2}{re}\right)}{\log 10} \leadsto \frac{\log \left(re + \frac{\frac{1}{2} \cdot im}{\frac{re}{im}}\right)}{\log 10}\]
   3.1

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8. Applied final simplification