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-*l*0.5
\[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)} \cdot \left(1 - v \cdot v\right)}\]
Taylor expanded around 0 0.6
\[\leadsto \color{blue}{\frac{1}{t \cdot \left(\sqrt{2} \cdot \pi\right)} - \left(\frac{53}{8} \cdot \frac{{v}^{4}}{t \cdot \left(\sqrt{2} \cdot \pi\right)} + \frac{5}{2} \cdot \frac{{v}^{2}}{t \cdot \left(\sqrt{2} \cdot \pi\right)}\right)}\]
Simplified0.6
\[\leadsto \color{blue}{\frac{v \cdot v}{\left(\sqrt{2} \cdot \pi\right) \cdot t} \cdot \frac{-5}{2} + \left(\frac{1}{\left(\sqrt{2} \cdot \pi\right) \cdot t} + \frac{\frac{v \cdot v}{\sqrt{2} \cdot \pi} \cdot \left(v \cdot v\right)}{t} \cdot \frac{-53}{8}\right)}\]
- Using strategy
rm Applied associate-/r*0.3
\[\leadsto \frac{v \cdot v}{\left(\sqrt{2} \cdot \pi\right) \cdot t} \cdot \frac{-5}{2} + \left(\color{blue}{\frac{\frac{1}{\sqrt{2} \cdot \pi}}{t}} + \frac{\frac{v \cdot v}{\sqrt{2} \cdot \pi} \cdot \left(v \cdot v\right)}{t} \cdot \frac{-53}{8}\right)\]
Final simplification0.3
\[\leadsto \left(\frac{\left(v \cdot v\right) \cdot \frac{v \cdot v}{\sqrt{2} \cdot \pi}}{t} \cdot \frac{-53}{8} + \frac{\frac{1}{\sqrt{2} \cdot \pi}}{t}\right) + \frac{-5}{2} \cdot \frac{v \cdot v}{\left(\sqrt{2} \cdot \pi\right) \cdot t}\]
