Initial program 0.4
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
- Using strategy
rm Applied add-sqr-sqrt0.4
\[\leadsto \frac{\color{blue}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
Applied times-frac0.4
\[\leadsto \color{blue}{\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}}\]
Taylor expanded around 0 0.5
\[\leadsto \color{blue}{\left(\frac{1}{t \cdot \left(\sqrt{2} \cdot \pi\right)} - \left(\frac{7}{2} \cdot \frac{{v}^{4}}{t \cdot \left(\sqrt{2} \cdot \pi\right)} + \frac{{v}^{2}}{t \cdot \left(\sqrt{2} \cdot \pi\right)}\right)\right)} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}\]
Simplified0.3
\[\leadsto \color{blue}{\left(\left(\frac{\frac{\frac{1}{\pi}}{\sqrt{2}}}{t} - \frac{v \cdot \frac{v}{t}}{\sqrt{2} \cdot \pi}\right) - \frac{\left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \frac{7}{2}\right)}{\left(\sqrt{2} \cdot \pi\right) \cdot t}\right)} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}\]
Final simplification0.3
\[\leadsto \frac{\sqrt{1 - \left(v \cdot v\right) \cdot 5}}{1 - v \cdot v} \cdot \left(\left(\frac{\frac{\frac{1}{\pi}}{\sqrt{2}}}{t} - \frac{\frac{v}{t} \cdot v}{\pi \cdot \sqrt{2}}\right) - \frac{\left(v \cdot v\right) \cdot \left(\frac{7}{2} \cdot \left(v \cdot v\right)\right)}{\left(\pi \cdot \sqrt{2}\right) \cdot t}\right)\]
