Initial program 0.4
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
Initial simplification0.4
\[\leadsto (\left(\cos \left(\pi \cdot \left(2 \cdot u2\right)\right)\right) \cdot \left({\left(-2 \cdot \log u1\right)}^{0.5} \cdot \frac{1}{6}\right) + 0.5)_*\]
Taylor expanded around inf 0.4
\[\leadsto \color{blue}{\frac{1}{6} \cdot \left(\cos \left(2 \cdot \left(u2 \cdot \pi\right)\right) \cdot {\left({-1}^{1.0} \cdot \left({-2}^{1.0} \cdot {\left(\log \left(\frac{1}{u1}\right)\right)}^{1.0}\right)\right)}^{0.5}\right) + 0.5}\]
Simplified0.4
\[\leadsto \color{blue}{(\left(\frac{1}{6} \cdot \cos \left(\left(\pi \cdot 2\right) \cdot u2\right)\right) \cdot \left({\left({\left(-\log u1\right)}^{1.0} \cdot \left({-2}^{1.0} \cdot {-1}^{1.0}\right)\right)}^{0.5}\right) + 0.5)_*}\]
- Using strategy
rm Applied unpow-prod-down0.3
\[\leadsto (\left(\frac{1}{6} \cdot \cos \left(\left(\pi \cdot 2\right) \cdot u2\right)\right) \cdot \color{blue}{\left({\left({\left(-\log u1\right)}^{1.0}\right)}^{0.5} \cdot {\left({-2}^{1.0} \cdot {-1}^{1.0}\right)}^{0.5}\right)} + 0.5)_*\]
- Using strategy
rm Applied add-sqr-sqrt0.3
\[\leadsto (\left(\frac{1}{6} \cdot \cos \color{blue}{\left(\sqrt{\left(\pi \cdot 2\right) \cdot u2} \cdot \sqrt{\left(\pi \cdot 2\right) \cdot u2}\right)}\right) \cdot \left({\left({\left(-\log u1\right)}^{1.0}\right)}^{0.5} \cdot {\left({-2}^{1.0} \cdot {-1}^{1.0}\right)}^{0.5}\right) + 0.5)_*\]
Final simplification0.3
\[\leadsto (\left(\frac{1}{6} \cdot \cos \left(\sqrt{\left(2 \cdot \pi\right) \cdot u2} \cdot \sqrt{\left(2 \cdot \pi\right) \cdot u2}\right)\right) \cdot \left({\left({-1}^{1.0} \cdot {-2}^{1.0}\right)}^{0.5} \cdot {\left({\left(-\log u1\right)}^{1.0}\right)}^{0.5}\right) + 0.5)_*\]
