Initial program 0.5
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
Simplified0.5
\[\leadsto \color{blue}{\cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{v \cdot v - 1}\right)}\]
- Using strategy
rm Applied flip--0.5
\[\leadsto \cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{\color{blue}{\frac{\left(v \cdot v\right) \cdot \left(v \cdot v\right) - 1 \cdot 1}{v \cdot v + 1}}}\right)\]
Applied associate-/r/0.5
\[\leadsto \cos^{-1} \color{blue}{\left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{\left(v \cdot v\right) \cdot \left(v \cdot v\right) - 1 \cdot 1} \cdot \left(v \cdot v + 1\right)\right)}\]
- Using strategy
rm Applied add-exp-log0.5
\[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{\left(v \cdot v\right) \cdot \left(v \cdot v\right) - 1 \cdot 1} \cdot \left(v \cdot v + 1\right)\right)\right)}}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto e^{\color{blue}{1 \cdot \log \left(\cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{\left(v \cdot v\right) \cdot \left(v \cdot v\right) - 1 \cdot 1} \cdot \left(v \cdot v + 1\right)\right)\right)}}\]
Applied exp-prod0.5
\[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{\left(v \cdot v\right) \cdot \left(v \cdot v\right) - 1 \cdot 1} \cdot \left(v \cdot v + 1\right)\right)\right)\right)}}\]
Simplified0.5
\[\leadsto {\color{blue}{e}}^{\left(\log \left(\cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{\left(v \cdot v\right) \cdot \left(v \cdot v\right) - 1 \cdot 1} \cdot \left(v \cdot v + 1\right)\right)\right)\right)}\]
Final simplification0.5
\[\leadsto {e}^{\left(\log \left(\cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{\left(v \cdot v\right) \cdot \left(v \cdot v\right) - 1} \cdot \left(v \cdot v + 1\right)\right)\right)\right)}\]
