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 associate-/r*0.5
\[\leadsto \color{blue}{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}}\]
- Using strategy
rm Applied associate-/r*0.5
\[\leadsto \frac{\color{blue}{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\pi \cdot t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}}{1 - v \cdot v}\]
- Using strategy
rm Applied sqrt-prod0.5
\[\leadsto \frac{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\pi \cdot t}}{\color{blue}{\sqrt{2} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}}{1 - v \cdot v}\]
Applied add-sqr-sqrt0.5
\[\leadsto \frac{\frac{\frac{\color{blue}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}{\pi \cdot t}}{\sqrt{2} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}\]
Applied times-frac0.4
\[\leadsto \frac{\frac{\color{blue}{\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\pi} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{t}}}{\sqrt{2} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}\]
Applied times-frac0.3
\[\leadsto \frac{\color{blue}{\frac{\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\pi}}{\sqrt{2}} \cdot \frac{\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{t}}{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}}{1 - v \cdot v}\]
Final simplification0.3
\[\leadsto \frac{\frac{\frac{\sqrt{1 - \left(v \cdot v\right) \cdot 5}}{\pi}}{\sqrt{2}} \cdot \frac{\frac{\sqrt{1 - \left(v \cdot v\right) \cdot 5}}{t}}{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}\]
