Initial program 17.0
\[\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)\right) \cdot R\]
Initial simplification17.0
\[\leadsto R \cdot \cos^{-1} \left((\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\cos \left(\lambda_1 - \lambda_2\right)\right) + \left(\sin \phi_2 \cdot \sin \phi_1\right))_*\right)\]
- Using strategy
rm Applied cos-diff3.7
\[\leadsto R \cdot \cos^{-1} \left((\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \color{blue}{\left(\cos \lambda_1 \cdot \cos \lambda_2 + \sin \lambda_1 \cdot \sin \lambda_2\right)} + \left(\sin \phi_2 \cdot \sin \phi_1\right))_*\right)\]
Taylor expanded around inf 3.7
\[\leadsto \color{blue}{R \cdot \cos^{-1} \left((\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\sin \lambda_2 \cdot \sin \lambda_1 + \cos \lambda_1 \cdot \cos \lambda_2\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)}\]
Simplified3.7
\[\leadsto \color{blue}{R \cdot \cos^{-1} \left((\left((\left(\cos \lambda_2\right) \cdot \left(\cos \lambda_1\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_2 \cdot \cos \phi_1\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)}\]
- Using strategy
rm Applied add-cbrt-cube3.8
\[\leadsto R \cdot \cos^{-1} \left((\left((\left(\cos \lambda_2\right) \cdot \left(\cos \lambda_1\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_2 \cdot \cos \phi_1\right) + \color{blue}{\left(\sqrt[3]{\left(\left(\sin \phi_1 \cdot \sin \phi_2\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_2\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_2\right)}\right)})_*\right)\]
- Using strategy
rm Applied log1p-expm1-u3.8
\[\leadsto R \cdot \cos^{-1} \left((\left((\left(\cos \lambda_2\right) \cdot \left(\cos \lambda_1\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_2 \cdot \cos \phi_1\right) + \color{blue}{\left(\log_* (1 + (e^{\sqrt[3]{\left(\left(\sin \phi_1 \cdot \sin \phi_2\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_2\right)\right) \cdot \left(\sin \phi_1 \cdot \sin \phi_2\right)}} - 1)^*)\right)})_*\right)\]
Final simplification3.8
\[\leadsto \cos^{-1} \left((\left((\left(\cos \lambda_2\right) \cdot \left(\cos \lambda_1\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\log_* (1 + (e^{\sqrt[3]{\left(\sin \phi_2 \cdot \sin \phi_1\right) \cdot \left(\left(\sin \phi_2 \cdot \sin \phi_1\right) \cdot \left(\sin \phi_2 \cdot \sin \phi_1\right)\right)}} - 1)^*)\right))_*\right) \cdot R\]
