Initial program 0.5
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
Initial simplification0.3
\[\leadsto \frac{\frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}{\sqrt{\left(-3 \cdot v\right) \cdot \left(v \cdot 2\right) + 2} \cdot \left(t \cdot \left(1 - v \cdot v\right)\right)}\]
- Using strategy
rm Applied *-un-lft-identity0.3
\[\leadsto \frac{\color{blue}{1 \cdot \frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}}{\sqrt{\left(-3 \cdot v\right) \cdot \left(v \cdot 2\right) + 2} \cdot \left(t \cdot \left(1 - v \cdot v\right)\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{1}{\sqrt{\left(-3 \cdot v\right) \cdot \left(v \cdot 2\right) + 2}} \cdot \frac{\frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}{t \cdot \left(1 - v \cdot v\right)}}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{1}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}} \cdot \frac{\frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}{t \cdot \left(1 - v \cdot v\right)}\]
- Using strategy
rm Applied associate-*r/0.1
\[\leadsto \color{blue}{\frac{\frac{1}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}} \cdot \frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}{t \cdot \left(1 - v \cdot v\right)}}\]
- Using strategy
rm Applied flip3-+0.1
\[\leadsto \frac{\frac{1}{\sqrt{\color{blue}{\frac{{2}^{3} + {\left(\left(v \cdot v\right) \cdot -6\right)}^{3}}{2 \cdot 2 + \left(\left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right) - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right)}}}} \cdot \frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}{t \cdot \left(1 - v \cdot v\right)}\]
Applied sqrt-div0.1
\[\leadsto \frac{\frac{1}{\color{blue}{\frac{\sqrt{{2}^{3} + {\left(\left(v \cdot v\right) \cdot -6\right)}^{3}}}{\sqrt{2 \cdot 2 + \left(\left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right) - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right)}}}} \cdot \frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}{t \cdot \left(1 - v \cdot v\right)}\]
Applied associate-/r/0.1
\[\leadsto \frac{\color{blue}{\left(\frac{1}{\sqrt{{2}^{3} + {\left(\left(v \cdot v\right) \cdot -6\right)}^{3}}} \cdot \sqrt{2 \cdot 2 + \left(\left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right) - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right)}\right)} \cdot \frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}}{t \cdot \left(1 - v \cdot v\right)}\]
Applied associate-*l*0.1
\[\leadsto \frac{\color{blue}{\frac{1}{\sqrt{{2}^{3} + {\left(\left(v \cdot v\right) \cdot -6\right)}^{3}}} \cdot \left(\sqrt{2 \cdot 2 + \left(\left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right) - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right)} \cdot \frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}\right)}}{t \cdot \left(1 - v \cdot v\right)}\]
Simplified0.1
\[\leadsto \frac{\color{blue}{\frac{1}{\sqrt{8 + {v}^{5} \cdot \left(-216 \cdot v\right)}}} \cdot \left(\sqrt{2 \cdot 2 + \left(\left(\left(v \cdot v\right) \cdot -6\right) \cdot \left(\left(v \cdot v\right) \cdot -6\right) - 2 \cdot \left(\left(v \cdot v\right) \cdot -6\right)\right)} \cdot \frac{1 + \left(-5 \cdot v\right) \cdot v}{\pi}\right)}{t \cdot \left(1 - v \cdot v\right)}\]
Final simplification0.1
\[\leadsto \frac{\frac{1}{\sqrt{\left(v \cdot -216\right) \cdot {v}^{5} + 8}} \cdot \left(\frac{v \cdot \left(v \cdot -5\right) + 1}{\pi} \cdot \sqrt{\left(\left(-6 \cdot \left(v \cdot v\right)\right) \cdot \left(-6 \cdot \left(v \cdot v\right)\right) - 2 \cdot \left(-6 \cdot \left(v \cdot v\right)\right)\right) + 4}\right)}{\left(1 - v \cdot v\right) \cdot t}\]
