Initial program 1.0
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
Initial simplification0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
- Using strategy
rm Applied flip3--0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{\color{blue}{\frac{{1}^{3} - {\left(v \cdot v\right)}^{3}}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
Applied associate-/r/0.0
\[\leadsto \frac{\color{blue}{\frac{\frac{\frac{4}{3}}{\pi}}{{1}^{3} - {\left(v \cdot v\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)\right)}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
Simplified0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{{1}^{3} - {\left(v \cdot v\right)}^{3}} \cdot \color{blue}{(\left((v \cdot v + 1)_*\right) \cdot \left(v \cdot v\right) + 1)_*}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
Final simplification0.0
\[\leadsto \frac{(\left((v \cdot v + 1)_*\right) \cdot \left(v \cdot v\right) + 1)_* \cdot \frac{\frac{\frac{4}{3}}{\pi}}{1 - {\left(v \cdot v\right)}^{3}}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
