Initial program 1.0
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
Simplified0.0
\[\leadsto \color{blue}{\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto \frac{\color{blue}{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}} \cdot \sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}\]
Applied associate-/l*0.0
\[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}{\frac{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}}\]
- Using strategy
rm Applied *-un-lft-identity0.0
\[\leadsto \frac{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}{\frac{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}{\color{blue}{1 \cdot \sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}}\]
Applied add-sqr-sqrt1.0
\[\leadsto \frac{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}{\frac{\color{blue}{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}} \cdot \sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}}{1 \cdot \sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}\]
Applied times-frac1.0
\[\leadsto \frac{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}{\color{blue}{\frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{1} \cdot \frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}}\]
Applied flip--1.0
\[\leadsto \frac{\sqrt{\frac{\frac{4}{3}}{\color{blue}{\frac{\pi \cdot \pi - \left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right)}{\pi + \left(v \cdot v\right) \cdot \pi}}}}}{\frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{1} \cdot \frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}\]
Applied associate-/r/1.6
\[\leadsto \frac{\sqrt{\color{blue}{\frac{\frac{4}{3}}{\pi \cdot \pi - \left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right)} \cdot \left(\pi + \left(v \cdot v\right) \cdot \pi\right)}}}{\frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{1} \cdot \frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}\]
Applied sqrt-prod1.0
\[\leadsto \frac{\color{blue}{\sqrt{\frac{\frac{4}{3}}{\pi \cdot \pi - \left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right)}} \cdot \sqrt{\pi + \left(v \cdot v\right) \cdot \pi}}}{\frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{1} \cdot \frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}\]
Applied times-frac0.0
\[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{4}{3}}{\pi \cdot \pi - \left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right)}}}{\frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{1}} \cdot \frac{\sqrt{\pi + \left(v \cdot v\right) \cdot \pi}}{\frac{\sqrt{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}}{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}}}\]
Final simplification0.0
\[\leadsto \frac{\sqrt{\frac{\frac{4}{3}}{\pi \cdot \pi - \left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right)}}}{\sqrt{\sqrt{\left(v \cdot -6\right) \cdot v + 2}}} \cdot \frac{\sqrt{\pi + \pi \cdot \left(v \cdot v\right)}}{\frac{\sqrt{\sqrt{\left(v \cdot -6\right) \cdot v + 2}}}{\sqrt{\frac{\frac{4}{3}}{\pi - \pi \cdot \left(v \cdot v\right)}}}}\]
