\(\frac{\sqrt[3]{\log \left(\sqrt{im^2 + re^2}^*\right)} \cdot \sqrt[3]{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^2}}{\sqrt[3]{\log base}}\)
- Started with
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
14.9
- Applied simplify to get
\[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}}\]
0.4
- Using strategy
rm 0.4
- Applied add-cbrt-cube to get
\[\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\color{red}{\log base}} \leadsto \frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\color{blue}{\sqrt[3]{{\left(\log base\right)}^3}}}\]
0.4
- Applied add-cbrt-cube to get
\[\frac{\color{red}{\log \left(\sqrt{im^2 + re^2}^*\right)}}{\sqrt[3]{{\left(\log base\right)}^3}} \leadsto \frac{\color{blue}{\sqrt[3]{{\left(\log \left(\sqrt{im^2 + re^2}^*\right)\right)}^3}}}{\sqrt[3]{{\left(\log base\right)}^3}}\]
0.4
- Applied cbrt-undiv to get
\[\color{red}{\frac{\sqrt[3]{{\left(\log \left(\sqrt{im^2 + re^2}^*\right)\right)}^3}}{\sqrt[3]{{\left(\log base\right)}^3}}} \leadsto \color{blue}{\sqrt[3]{\frac{{\left(\log \left(\sqrt{im^2 + re^2}^*\right)\right)}^3}{{\left(\log base\right)}^3}}}\]
0.4
- Applied simplify to get
\[\sqrt[3]{\color{red}{\frac{{\left(\log \left(\sqrt{im^2 + re^2}^*\right)\right)}^3}{{\left(\log base\right)}^3}}} \leadsto \sqrt[3]{\color{blue}{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^3}}\]
0.4
- Using strategy
rm 0.4
- Applied cube-mult to get
\[\sqrt[3]{\color{red}{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^3}} \leadsto \sqrt[3]{\color{blue}{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base} \cdot \left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base} \cdot \frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}}\]
0.4
- Applied cbrt-prod to get
\[\color{red}{\sqrt[3]{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base} \cdot \left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base} \cdot \frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}} \leadsto \color{blue}{\sqrt[3]{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}} \cdot \sqrt[3]{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base} \cdot \frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}}}\]
0.5
- Applied simplify to get
\[\sqrt[3]{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}} \cdot \color{red}{\sqrt[3]{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base} \cdot \frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}}} \leadsto \sqrt[3]{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}} \cdot \color{blue}{\sqrt[3]{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^2}}\]
0.5
- Using strategy
rm 0.5
- Applied cbrt-div to get
\[\color{red}{\sqrt[3]{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}}} \cdot \sqrt[3]{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^2} \leadsto \color{blue}{\frac{\sqrt[3]{\log \left(\sqrt{im^2 + re^2}^*\right)}}{\sqrt[3]{\log base}}} \cdot \sqrt[3]{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^2}\]
0.6
- Applied associate-*l/ to get
\[\color{red}{\frac{\sqrt[3]{\log \left(\sqrt{im^2 + re^2}^*\right)}}{\sqrt[3]{\log base}} \cdot \sqrt[3]{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^2}} \leadsto \color{blue}{\frac{\sqrt[3]{\log \left(\sqrt{im^2 + re^2}^*\right)} \cdot \sqrt[3]{{\left(\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}\right)}^2}}{\sqrt[3]{\log base}}}\]
0.6
- Removed slow pow expressions
