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 *-un-lft-identity0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\sqrt{\color{blue}{1 \cdot (-6 \cdot \left(v \cdot v\right) + 2)_*}}}\]
Applied sqrt-prod0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\color{blue}{\sqrt{1} \cdot \sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}}\]
Applied add-sqr-sqrt0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{\color{blue}{\sqrt{1 - v \cdot v} \cdot \sqrt{1 - v \cdot v}}}}{\sqrt{1} \cdot \sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
Applied div-inv0.0
\[\leadsto \frac{\frac{\color{blue}{\frac{4}{3} \cdot \frac{1}{\pi}}}{\sqrt{1 - v \cdot v} \cdot \sqrt{1 - v \cdot v}}}{\sqrt{1} \cdot \sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
Applied times-frac0.0
\[\leadsto \frac{\color{blue}{\frac{\frac{4}{3}}{\sqrt{1 - v \cdot v}} \cdot \frac{\frac{1}{\pi}}{\sqrt{1 - v \cdot v}}}}{\sqrt{1} \cdot \sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
Applied times-frac0.0
\[\leadsto \color{blue}{\frac{\frac{\frac{4}{3}}{\sqrt{1 - v \cdot v}}}{\sqrt{1}} \cdot \frac{\frac{\frac{1}{\pi}}{\sqrt{1 - v \cdot v}}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}}\]
Simplified0.0
\[\leadsto \color{blue}{\frac{\frac{4}{3}}{\sqrt{1 - v \cdot v}}} \cdot \frac{\frac{\frac{1}{\pi}}{\sqrt{1 - v \cdot v}}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}\]
Final simplification0.0
\[\leadsto \frac{\frac{\frac{1}{\pi}}{\sqrt{1 - v \cdot v}}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}} \cdot \frac{\frac{4}{3}}{\sqrt{1 - v \cdot v}}\]
