Initial program 31.7
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Initial simplification0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\]
- Using strategy
rm Applied add-sqr-sqrt0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\]
Applied *-un-lft-identity0.6
\[\leadsto \frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{1}{\sqrt{\log 10}} \cdot \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\sqrt{\log 10}}}\]
- Using strategy
rm Applied div-inv0.4
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{1}{\sqrt{\log 10}}\right)}\]
- Using strategy
rm Applied add-cbrt-cube0.4
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \color{blue}{\sqrt[3]{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}}}\right)\]
Applied add-cbrt-cube0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \left(\color{blue}{\sqrt[3]{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}} \cdot \sqrt[3]{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}}\right)\]
Applied cbrt-unprod0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\sqrt[3]{\left(\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \left(\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\right)}}\]
Applied add-cbrt-cube0.6
\[\leadsto \color{blue}{\sqrt[3]{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}}} \cdot \sqrt[3]{\left(\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \left(\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\right)}\]
Applied cbrt-unprod0.6
\[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \left(\left(\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \left(\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\right)\right)}}\]
Simplified0.6
\[\leadsto \sqrt[3]{\color{blue}{\left(\frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}} \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right)\right) \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\right)}}\]
- Using strategy
rm Applied add-cube-cbrt0.6
\[\leadsto \sqrt[3]{\left(\frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}} \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}\right)\right) \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\right)}\]
Applied log-prod0.6
\[\leadsto \sqrt[3]{\left(\frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}} \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) + \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)\right)}\right)\right) \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\right)}\]
Applied distribute-lft-in0.5
\[\leadsto \sqrt[3]{\left(\frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}} \cdot \color{blue}{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) + \log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)\right)}\right) \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\right)}\]
Final simplification0.5
\[\leadsto \sqrt[3]{\left(\frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}} \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right) + \log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)\right)\right) \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\right)}\]
