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 *-un-lft-identity0.5
\[\leadsto \cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{1 \cdot \left(v \cdot v - 1\right)}}\right)\]
Applied add-sqr-sqrt0.6
\[\leadsto \cos^{-1} \left(\frac{\color{blue}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}{1 \cdot \left(v \cdot v - 1\right)}\right)\]
Applied times-frac0.6
\[\leadsto \cos^{-1} \color{blue}{\left(\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{v \cdot v - 1}\right)}\]
Simplified0.6
\[\leadsto \cos^{-1} \left(\color{blue}{\sqrt{1 - \left(v \cdot v\right) \cdot 5}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{v \cdot v - 1}\right)\]
- Using strategy
rm Applied add-exp-log0.6
\[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\sqrt{1 - \left(v \cdot v\right) \cdot 5} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{v \cdot v - 1}\right)\right)}}\]
Final simplification0.6
\[\leadsto e^{\log \left(\cos^{-1} \left(\frac{\sqrt{1 - \left(v \cdot v\right) \cdot 5}}{v \cdot v - 1} \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 5}\right)\right)}\]
