Initial program 0.0
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
- Using strategy
rm Applied flip--0.0
\[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \color{blue}{\frac{1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)}{1 + v \cdot v}}\]
Applied associate-*l/0.0
\[\leadsto \color{blue}{\frac{\sqrt{2} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}{4}} \cdot \frac{1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)}{1 + v \cdot v}\]
Applied frac-times0.0
\[\leadsto \color{blue}{\frac{\left(\sqrt{2} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)}{4 \cdot \left(1 + v \cdot v\right)}}\]
Simplified0.0
\[\leadsto \frac{\color{blue}{\left(\sqrt{2} \cdot \left(1 - {v}^{4}\right)\right) \cdot \sqrt{(\left(v \cdot v\right) \cdot -3 + 1)_*}}}{4 \cdot \left(1 + v \cdot v\right)}\]
Simplified0.0
\[\leadsto \frac{\left(\sqrt{2} \cdot \left(1 - {v}^{4}\right)\right) \cdot \sqrt{(\left(v \cdot v\right) \cdot -3 + 1)_*}}{\color{blue}{(\left(v \cdot v\right) \cdot 4 + 4)_*}}\]
Final simplification0.0
\[\leadsto \frac{\sqrt{(\left(v \cdot v\right) \cdot -3 + 1)_*} \cdot \left(\left(1 - {v}^{4}\right) \cdot \sqrt{2}\right)}{(\left(v \cdot v\right) \cdot 4 + 4)_*}\]
