Initial program 0.9
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
Initial simplification0.9
\[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
- Using strategy
rm Applied log1p-expm1-u0.7
\[\leadsto \color{blue}{\log_* (1 + (e^{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} - 1)^*)}\]
- Using strategy
rm Applied log1p-expm1-u0.5
\[\leadsto \log_* (1 + \color{blue}{\log_* (1 + (e^{(e^{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} - 1)^*} - 1)^*)})\]
- Using strategy
rm Applied add-sqr-sqrt0.5
\[\leadsto \log_* (1 + \log_* (1 + (e^{(e^{\frac{\tan^{-1}_* \frac{im}{re}}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}} - 1)^*} - 1)^*))\]
Applied *-un-lft-identity0.5
\[\leadsto \log_* (1 + \log_* (1 + (e^{(e^{\frac{\color{blue}{1 \cdot \tan^{-1}_* \frac{im}{re}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}} - 1)^*} - 1)^*))\]
Applied times-frac0.5
\[\leadsto \log_* (1 + \log_* (1 + (e^{(e^{\color{blue}{\frac{1}{\sqrt{\log 10}} \cdot \frac{\tan^{-1}_* \frac{im}{re}}{\sqrt{\log 10}}}} - 1)^*} - 1)^*))\]
- Using strategy
rm Applied div-inv0.4
\[\leadsto \log_* (1 + \log_* (1 + (e^{(e^{\frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\left(\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\sqrt{\log 10}}\right)}} - 1)^*} - 1)^*))\]
Applied associate-*r*0.4
\[\leadsto \log_* (1 + \log_* (1 + (e^{(e^{\color{blue}{\left(\frac{1}{\sqrt{\log 10}} \cdot \tan^{-1}_* \frac{im}{re}\right) \cdot \frac{1}{\sqrt{\log 10}}}} - 1)^*} - 1)^*))\]
Final simplification0.4
\[\leadsto \log_* (1 + \log_* (1 + (e^{(e^{\frac{1}{\sqrt{\log 10}} \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\sqrt{\log 10}}\right)} - 1)^*} - 1)^*))\]
