Initial program 0.5
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
Taylor expanded around 0 0.5
\[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\color{blue}{\left(t \cdot \pi\right)} \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto \frac{\color{blue}{1 \cdot \left(1 - 5 \cdot \left(v \cdot v\right)\right)}}{\left(\left(t \cdot \pi\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{1}{\left(t \cdot \pi\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{1 - 5 \cdot \left(v \cdot v\right)}{1 - v \cdot v}}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{\frac{\frac{1}{\pi}}{t}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}}} \cdot \frac{1 - 5 \cdot \left(v \cdot v\right)}{1 - v \cdot v}\]
- Using strategy
rm Applied add-sqr-sqrt0.3
\[\leadsto \frac{\frac{\frac{1}{\pi}}{t}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}} \cdot \frac{\color{blue}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}\]
Applied associate-/l*0.3
\[\leadsto \frac{\frac{\frac{1}{\pi}}{t}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}} \cdot \color{blue}{\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\frac{1 - v \cdot v}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}}\]
Final simplification0.3
\[\leadsto \frac{\frac{\frac{1}{\pi}}{t}}{\sqrt{(-6 \cdot \left(v \cdot v\right) + 2)_*}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\frac{1 - v \cdot v}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}\]
