Initial program 0.9
\[\lambda_1 + \tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{\cos \phi_1 + \cos \phi_2 \cdot \cos \left(\lambda_1 - \lambda_2\right)}\]
Applied simplify0.9
\[\leadsto \color{blue}{\tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \left(\lambda_1 - \lambda_2\right)}{(\left(\cos \phi_2\right) \cdot \left(\cos \left(\lambda_1 - \lambda_2\right)\right) + \left(\cos \phi_1\right))_*} + \lambda_1}\]
- Using strategy
rm Applied sub-neg0.9
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \sin \color{blue}{\left(\lambda_1 + \left(-\lambda_2\right)\right)}}{(\left(\cos \phi_2\right) \cdot \left(\cos \left(\lambda_1 - \lambda_2\right)\right) + \left(\cos \phi_1\right))_*} + \lambda_1\]
Applied sin-sum0.8
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \color{blue}{\left(\sin \lambda_1 \cdot \cos \left(-\lambda_2\right) + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}}{(\left(\cos \phi_2\right) \cdot \left(\cos \left(\lambda_1 - \lambda_2\right)\right) + \left(\cos \phi_1\right))_*} + \lambda_1\]
Applied simplify0.8
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\color{blue}{\sin \lambda_1 \cdot \cos \lambda_2} + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}{(\left(\cos \phi_2\right) \cdot \left(\cos \left(\lambda_1 - \lambda_2\right)\right) + \left(\cos \phi_1\right))_*} + \lambda_1\]
- Using strategy
rm Applied sub-neg0.8
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \cos \lambda_2 + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}{(\left(\cos \phi_2\right) \cdot \left(\cos \color{blue}{\left(\lambda_1 + \left(-\lambda_2\right)\right)}\right) + \left(\cos \phi_1\right))_*} + \lambda_1\]
Applied cos-sum0.2
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \cos \lambda_2 + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}{(\left(\cos \phi_2\right) \cdot \color{blue}{\left(\cos \lambda_1 \cdot \cos \left(-\lambda_2\right) - \sin \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)} + \left(\cos \phi_1\right))_*} + \lambda_1\]
Applied simplify0.2
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \cos \lambda_2 + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}{(\left(\cos \phi_2\right) \cdot \left(\color{blue}{\cos \lambda_1 \cdot \cos \lambda_2} - \sin \lambda_1 \cdot \sin \left(-\lambda_2\right)\right) + \left(\cos \phi_1\right))_*} + \lambda_1\]
- Using strategy
rm Applied log1p-expm1-u0.2
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \cos \lambda_2 + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}{\color{blue}{\log_* (1 + (e^{(\left(\cos \phi_2\right) \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2 - \sin \lambda_1 \cdot \sin \left(-\lambda_2\right)\right) + \left(\cos \phi_1\right))_*} - 1)^*)}} + \lambda_1\]
Applied simplify0.2
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \cos \lambda_2 + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}{\log_* (1 + \color{blue}{(e^{(\left((\left(\cos \lambda_2\right) \cdot \left(\cos \lambda_1\right) + \left(\sin \lambda_2 \cdot \sin \lambda_1\right))_*\right) \cdot \left(\cos \phi_2\right) + \left(\cos \phi_1\right))_*} - 1)^*})} + \lambda_1\]
- Using strategy
rm Applied add-log-exp0.3
\[\leadsto \tan^{-1}_* \frac{\cos \phi_2 \cdot \left(\sin \lambda_1 \cdot \cos \lambda_2 + \cos \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)}{\log_* (1 + \color{blue}{\log \left(e^{(e^{(\left((\left(\cos \lambda_2\right) \cdot \left(\cos \lambda_1\right) + \left(\sin \lambda_2 \cdot \sin \lambda_1\right))_*\right) \cdot \left(\cos \phi_2\right) + \left(\cos \phi_1\right))_*} - 1)^*}\right)})} + \lambda_1\]
