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 flip--0.5
\[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \color{blue}{\frac{1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)}{1 + 3 \cdot \left(v \cdot v\right)}}}\right) \cdot \left(1 - v \cdot v\right)}\]
Applied associate-*r/0.5
\[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{\color{blue}{\frac{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}{1 + 3 \cdot \left(v \cdot v\right)}}}\right) \cdot \left(1 - v \cdot v\right)}\]
Applied sqrt-div0.5
\[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \color{blue}{\frac{\sqrt{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}}{\sqrt{1 + 3 \cdot \left(v \cdot v\right)}}}\right) \cdot \left(1 - v \cdot v\right)}\]
Applied associate-*r/0.5
\[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\frac{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}}{\sqrt{1 + 3 \cdot \left(v \cdot v\right)}}} \cdot \left(1 - v \cdot v\right)}\]
Taylor expanded around 0 0.6
\[\leadsto \color{blue}{\left(9 \cdot \frac{{v}^{4}}{\pi \cdot \left(t \cdot {\left(\sqrt{2}\right)}^{3}\right)} + \frac{1}{\pi \cdot \left(t \cdot \sqrt{2}\right)}\right) - \left(\frac{89}{8} \cdot \frac{{v}^{4}}{\pi \cdot \left(t \cdot \sqrt{2}\right)} + \frac{5}{2} \cdot \frac{{v}^{2}}{\pi \cdot \left(t \cdot \sqrt{2}\right)}\right)}\]
Applied simplify0.5
\[\leadsto \color{blue}{\left(\frac{\frac{1}{t}}{\sqrt{2} \cdot \pi} - \frac{\frac{\frac{5}{2} \cdot v}{\frac{\pi}{v}}}{t \cdot \sqrt{2}}\right) - \frac{{v}^{4}}{t \cdot \pi} \cdot \left(\frac{\frac{89}{8}}{\sqrt{2}} - \frac{\frac{9}{2}}{\sqrt{2}}\right)}\]
- Using strategy
rm Applied div-inv0.5
\[\leadsto \left(\color{blue}{\frac{1}{t} \cdot \frac{1}{\sqrt{2} \cdot \pi}} - \frac{\frac{\frac{5}{2} \cdot v}{\frac{\pi}{v}}}{t \cdot \sqrt{2}}\right) - \frac{{v}^{4}}{t \cdot \pi} \cdot \left(\frac{\frac{89}{8}}{\sqrt{2}} - \frac{\frac{9}{2}}{\sqrt{2}}\right)\]
