Initial program 0.5
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
- Using strategy
rm Applied flip3--0.5
\[\leadsto \cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\frac{{\left(v \cdot v\right)}^{3} - {1}^{3}}{\left(v \cdot v\right) \cdot \left(v \cdot v\right) + \left(1 \cdot 1 + \left(v \cdot v\right) \cdot 1\right)}}}\right)\]
Applied associate-/r/0.5
\[\leadsto \cos^{-1} \color{blue}{\left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{{\left(v \cdot v\right)}^{3} - {1}^{3}} \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + \left(1 \cdot 1 + \left(v \cdot v\right) \cdot 1\right)\right)\right)}\]
Simplified0.5
\[\leadsto \cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{{\left(v \cdot v\right)}^{3} - {1}^{3}} \cdot \color{blue}{\left(\left(1 + \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) + v \cdot v\right)}\right)\]
- Using strategy
rm Applied add-exp-log0.5
\[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{{\left(v \cdot v\right)}^{3} - {1}^{3}} \cdot \left(\left(1 + \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) + v \cdot v\right)\right)\right)}}\]
Final simplification0.5
\[\leadsto e^{\log \left(\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{{\left(v \cdot v\right)}^{3} - 1} \cdot \left(v \cdot v + \left(1 + \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right)\right)\right)}\]
