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 0.6
\[\leadsto \color{blue}{\left(\frac{27}{2} \cdot \frac{{v}^{4}}{\pi \cdot \left(t \cdot {\left(\sqrt{2}\right)}^{5}\right)} + \left(3 \cdot \frac{{v}^{2}}{\pi \cdot \left(t \cdot {\left(\sqrt{2}\right)}^{3}\right)} + \frac{1}{\pi \cdot \left(t \cdot \sqrt{2}\right)}\right)\right) - \left(12 \cdot \frac{{v}^{4}}{\pi \cdot \left(t \cdot {\left(\sqrt{2}\right)}^{3}\right)} + \left(4 \cdot \frac{{v}^{4}}{\pi \cdot \left(t \cdot \sqrt{2}\right)} + 4 \cdot \frac{{v}^{2}}{\pi \cdot \left(t \cdot \sqrt{2}\right)}\right)\right)}\]
Applied simplify0.5
\[\leadsto \color{blue}{(\left(\frac{\frac{3}{2}}{t \cdot \sqrt{2}}\right) \cdot \left(\frac{v}{\frac{\pi}{v}}\right) + \left((\left(\frac{\frac{27}{2}}{\pi}\right) \cdot \left(\frac{\frac{{v}^{4}}{t}}{{\left(\sqrt{2}\right)}^{5}}\right) + \left(\frac{\frac{1}{\pi}}{t \cdot \sqrt{2}}\right))_*\right))_* - (12 \cdot \left(\frac{\frac{{v}^{4}}{\pi}}{\left(2 \cdot t\right) \cdot \sqrt{2}}\right) + \left(\frac{\frac{4}{t}}{\sqrt{2}} \cdot \left(\frac{{v}^{4}}{\pi} + \frac{v}{\frac{\pi}{v}}\right)\right))_*}\]
Taylor expanded around 0 0.5
\[\leadsto (\left(\frac{\frac{3}{2}}{t \cdot \sqrt{2}}\right) \cdot \left(\frac{v}{\frac{\pi}{v}}\right) + \left((\left(\frac{\frac{27}{2}}{\pi}\right) \cdot \left(\frac{\frac{{v}^{4}}{t}}{{\left(\sqrt{2}\right)}^{5}}\right) + \left(\frac{\frac{1}{\pi}}{t \cdot \sqrt{2}}\right))_*\right))_* - (12 \cdot \left(\frac{\frac{{v}^{4}}{\pi}}{\left(2 \cdot t\right) \cdot \sqrt{2}}\right) + \color{blue}{\left(4 \cdot \frac{{v}^{4}}{\pi \cdot \left(t \cdot \sqrt{2}\right)} + 4 \cdot \frac{{v}^{2}}{\pi \cdot \left(t \cdot \sqrt{2}\right)}\right)})_*\]
Applied simplify0.6
\[\leadsto \color{blue}{(\left(\frac{\frac{\frac{3}{t}}{\sqrt{2}}}{2}\right) \cdot \left(v \cdot \frac{v}{\pi}\right) + \left((\left(\frac{\frac{27}{2}}{\pi}\right) \cdot \left(\frac{\frac{{v}^{4}}{t}}{{\left(\sqrt{2}\right)}^{5}}\right) + \left(\frac{\frac{\frac{1}{t}}{\pi}}{\sqrt{2}}\right))_*\right))_* - (\left(\frac{\frac{{v}^{4}}{2 \cdot \pi}}{t \cdot \sqrt{2}}\right) \cdot 12 + \left(\frac{\frac{4}{t}}{\pi} \cdot \left(\frac{v \cdot v}{\sqrt{2}} + \frac{{v}^{4}}{\sqrt{2}}\right)\right))_*}\]
Taylor expanded around 0 0.6
\[\leadsto (\left(\frac{\frac{\frac{3}{t}}{\sqrt{2}}}{2}\right) \cdot \left(v \cdot \frac{v}{\pi}\right) + \left((\left(\frac{\frac{27}{2}}{\pi}\right) \cdot \left(\frac{\frac{{v}^{4}}{t}}{{\left(\sqrt{2}\right)}^{5}}\right) + \left(\frac{\frac{\frac{1}{t}}{\pi}}{\sqrt{2}}\right))_*\right))_* - (\color{blue}{\left(\frac{1}{2} \cdot \frac{{v}^{4}}{\pi \cdot \left(t \cdot \sqrt{2}\right)}\right)} \cdot 12 + \left(\frac{\frac{4}{t}}{\pi} \cdot \left(\frac{v \cdot v}{\sqrt{2}} + \frac{{v}^{4}}{\sqrt{2}}\right)\right))_*\]
Applied simplify0.5
\[\leadsto \color{blue}{(\left(\frac{\frac{3}{\sqrt{2}}}{2 \cdot t}\right) \cdot \left(\frac{v}{\frac{\pi}{v}}\right) + \left((\left(\frac{\frac{{v}^{4}}{t}}{{\left(\sqrt{2}\right)}^{5}}\right) \cdot \left(\frac{\frac{27}{2}}{\pi}\right) + \left(\frac{\frac{1}{t}}{\pi \cdot \sqrt{2}}\right))_* - (\left((\left(\frac{v}{\sqrt{2}}\right) \cdot v + \left(\frac{{v}^{4}}{\sqrt{2}}\right))_*\right) \cdot \left(\frac{4}{t \cdot \pi}\right) + \left(\frac{{v}^{4} \cdot \left(\frac{1}{2} \cdot 12\right)}{\left(t \cdot \pi\right) \cdot \sqrt{2}}\right))_*\right))_*}\]
