Initial program 31.0
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Initial simplification0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\]
- Using strategy
rm Applied add-cube-cbrt0.6
\[\leadsto \frac{\log \color{blue}{\left(\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}}{\log 10}\]
- Using strategy
rm Applied expm1-log1p-u0.6
\[\leadsto \frac{\log \left(\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot \color{blue}{(e^{\log_* (1 + \sqrt[3]{\sqrt{re^2 + im^2}^*})} - 1)^*}\right)}{\log 10}\]
- Using strategy
rm Applied clear-num0.6
\[\leadsto \color{blue}{\frac{1}{\frac{\log 10}{\log \left(\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot (e^{\log_* (1 + \sqrt[3]{\sqrt{re^2 + im^2}^*})} - 1)^*\right)}}}\]
- Using strategy
rm Applied clear-num0.6
\[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\log \left(\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot (e^{\log_* (1 + \sqrt[3]{\sqrt{re^2 + im^2}^*})} - 1)^*\right)}{\log 10}}}}\]
Final simplification0.6
\[\leadsto \frac{1}{\frac{1}{\frac{\log \left((e^{\log_* (1 + \sqrt[3]{\sqrt{re^2 + im^2}^*})} - 1)^* \cdot \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)\right)}{\log 10}}}\]
