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 *-un-lft-identity0.5
\[\leadsto \frac{\color{blue}{1 \cdot \left(1 - 5 \cdot \left(v \cdot v\right)\right)}}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{1}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{1 - 5 \cdot \left(v \cdot v\right)}{1 - v \cdot v}}\]
Simplified0.4
\[\leadsto \color{blue}{\frac{\frac{\frac{1}{t}}{\pi}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}} \cdot \frac{1 - 5 \cdot \left(v \cdot v\right)}{1 - v \cdot v}\]
- Using strategy
rm Applied add-log-exp0.4
\[\leadsto \frac{\frac{\frac{1}{t}}{\pi}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}} \cdot \frac{1 - \color{blue}{\log \left(e^{5 \cdot \left(v \cdot v\right)}\right)}}{1 - v \cdot v}\]
Final simplification0.4
\[\leadsto \frac{\frac{\frac{1}{t}}{\pi}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}} \cdot \frac{1 - \log \left(e^{\left(v \cdot v\right) \cdot 5}\right)}{1 - v \cdot v}\]
