Initial program 0.0
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
Initial simplification0.0
\[\leadsto \frac{1 - v \cdot v}{\frac{4}{\sqrt{2}}} \cdot \sqrt{-3 \cdot \left(v \cdot v\right) + 1}\]
- Using strategy
rm Applied flip3-+0.0
\[\leadsto \frac{1 - v \cdot v}{\frac{4}{\sqrt{2}}} \cdot \sqrt{\color{blue}{\frac{{\left(-3 \cdot \left(v \cdot v\right)\right)}^{3} + {1}^{3}}{\left(-3 \cdot \left(v \cdot v\right)\right) \cdot \left(-3 \cdot \left(v \cdot v\right)\right) + \left(1 \cdot 1 - \left(-3 \cdot \left(v \cdot v\right)\right) \cdot 1\right)}}}\]
Applied sqrt-div0.0
\[\leadsto \frac{1 - v \cdot v}{\frac{4}{\sqrt{2}}} \cdot \color{blue}{\frac{\sqrt{{\left(-3 \cdot \left(v \cdot v\right)\right)}^{3} + {1}^{3}}}{\sqrt{\left(-3 \cdot \left(v \cdot v\right)\right) \cdot \left(-3 \cdot \left(v \cdot v\right)\right) + \left(1 \cdot 1 - \left(-3 \cdot \left(v \cdot v\right)\right) \cdot 1\right)}}}\]
Applied frac-times0.0
\[\leadsto \color{blue}{\frac{\left(1 - v \cdot v\right) \cdot \sqrt{{\left(-3 \cdot \left(v \cdot v\right)\right)}^{3} + {1}^{3}}}{\frac{4}{\sqrt{2}} \cdot \sqrt{\left(-3 \cdot \left(v \cdot v\right)\right) \cdot \left(-3 \cdot \left(v \cdot v\right)\right) + \left(1 \cdot 1 - \left(-3 \cdot \left(v \cdot v\right)\right) \cdot 1\right)}}}\]
Simplified0.0
\[\leadsto \frac{\left(1 - v \cdot v\right) \cdot \sqrt{{\left(-3 \cdot \left(v \cdot v\right)\right)}^{3} + {1}^{3}}}{\color{blue}{\sqrt{\left(3 \cdot \left(v \cdot v\right) + 1\right) - \left(-3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)} \cdot \frac{4}{\sqrt{2}}}}\]
Final simplification0.0
\[\leadsto \frac{\sqrt{{\left(-3 \cdot \left(v \cdot v\right)\right)}^{3} + 1} \cdot \left(1 - v \cdot v\right)}{\sqrt{\left(3 \cdot \left(v \cdot v\right) + 1\right) - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(-3 \cdot \left(v \cdot v\right)\right)} \cdot \frac{4}{\sqrt{2}}}\]
