Initial program 0.5
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
- Using strategy
rm Applied add-sqr-sqrt0.5
\[\leadsto \frac{\color{blue}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}}\]
Taylor expanded around 0 0.5
\[\leadsto \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\color{blue}{\left(\pi \cdot t\right)} \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}\]
Applied simplify0.4
\[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot 5\right) \cdot v}{t}}{\sqrt{2 - \left(3 \cdot v\right) \cdot \left(v + v\right)}}}{\left(1 - v \cdot v\right) \cdot \pi}}\]
- Using strategy
rm Applied flip3--0.4
\[\leadsto \frac{\frac{\frac{1 - \left(v \cdot 5\right) \cdot v}{t}}{\sqrt{\color{blue}{\frac{{2}^{3} - {\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)}^{3}}{2 \cdot 2 + \left(\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) + 2 \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)\right)}}}}}{\left(1 - v \cdot v\right) \cdot \pi}\]
Applied sqrt-div0.4
\[\leadsto \frac{\frac{\frac{1 - \left(v \cdot 5\right) \cdot v}{t}}{\color{blue}{\frac{\sqrt{{2}^{3} - {\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)}^{3}}}{\sqrt{2 \cdot 2 + \left(\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) + 2 \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)\right)}}}}}{\left(1 - v \cdot v\right) \cdot \pi}\]
Applied associate-/r/0.4
\[\leadsto \frac{\color{blue}{\frac{\frac{1 - \left(v \cdot 5\right) \cdot v}{t}}{\sqrt{{2}^{3} - {\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)}^{3}}} \cdot \sqrt{2 \cdot 2 + \left(\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) + 2 \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)\right)}}}{\left(1 - v \cdot v\right) \cdot \pi}\]
Applied times-frac0.4
\[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot 5\right) \cdot v}{t}}{\sqrt{{2}^{3} - {\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)}^{3}}}}{1 - v \cdot v} \cdot \frac{\sqrt{2 \cdot 2 + \left(\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right) + 2 \cdot \left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)\right)}}{\pi}}\]
Applied simplify0.4
\[\leadsto \frac{\frac{\frac{1 - \left(v \cdot 5\right) \cdot v}{t}}{\sqrt{{2}^{3} - {\left(\left(3 \cdot v\right) \cdot \left(v + v\right)\right)}^{3}}}}{1 - v \cdot v} \cdot \color{blue}{\frac{\sqrt{\left(2 + 2\right) + \left(\left(v \cdot v\right) \cdot \left(3 + 3\right)\right) \cdot \left(\left(v \cdot v\right) \cdot \left(3 + 3\right) + 2\right)}}{\pi}}\]
- Removed slow
pow expressions.
