Initial program 57.5
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Initial simplification53.3
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\]
- Using strategy
rm Applied *-un-lft-identity53.3
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\color{blue}{1 \cdot \log 10}}\]
Applied add-cube-cbrt53.3
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)} \cdot \sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}\right) \cdot \sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}}}{1 \cdot \log 10}\]
Applied times-frac53.3
\[\leadsto \color{blue}{\frac{\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)} \cdot \sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}}{1} \cdot \frac{\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}}{\log 10}}\]
Simplified53.3
\[\leadsto \color{blue}{\left(\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)} \cdot \sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}\right)} \cdot \frac{\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}}{\log 10}\]
- Using strategy
rm Applied log1p-expm1-u53.3
\[\leadsto \left(\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)} \cdot \color{blue}{\log_* (1 + (e^{\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}} - 1)^*)}\right) \cdot \frac{\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}}{\log 10}\]
Final simplification53.3
\[\leadsto \left(\log_* (1 + (e^{\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}} - 1)^*) \cdot \sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}\right) \cdot \frac{\sqrt[3]{\log \left(\sqrt{re^2 + im^2}^*\right)}}{\log 10}\]
