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
\[\leadsto (\left(\cos \left(\pi \cdot \left(2 \cdot u2\right)\right)\right) \cdot \left({\left(-2 \cdot \log u1\right)}^{0.5} \cdot \frac{1}{6}\right) + 0.5)_*\]
- Using strategy
rm Applied add-cbrt-cube0.6
\[\leadsto (\left(\cos \left(\pi \cdot \left(2 \cdot u2\right)\right)\right) \cdot \color{blue}{\left(\sqrt[3]{\left(\left({\left(-2 \cdot \log u1\right)}^{0.5} \cdot \frac{1}{6}\right) \cdot \left({\left(-2 \cdot \log u1\right)}^{0.5} \cdot \frac{1}{6}\right)\right) \cdot \left({\left(-2 \cdot \log u1\right)}^{0.5} \cdot \frac{1}{6}\right)}\right)} + 0.5)_*\]
Taylor expanded around 0 0.5
\[\leadsto (\left(\cos \left(\pi \cdot \left(2 \cdot u2\right)\right)\right) \cdot \left(\sqrt[3]{\color{blue}{\left(\frac{1}{36} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{1.0}\right)} \cdot \left({\left(-2 \cdot \log u1\right)}^{0.5} \cdot \frac{1}{6}\right)}\right) + 0.5)_*\]
- Using strategy
rm Applied associate-*r*0.5
\[\leadsto (\left(\cos \left(\pi \cdot \left(2 \cdot u2\right)\right)\right) \cdot \left(\sqrt[3]{\color{blue}{\left(\left(\frac{1}{36} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{1.0}\right) \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \frac{1}{6}}}\right) + 0.5)_*\]
Final simplification0.5
\[\leadsto (\left(\cos \left(\left(u2 \cdot 2\right) \cdot \pi\right)\right) \cdot \left(\sqrt[3]{\left({\left(\log u1 \cdot -2\right)}^{0.5} \cdot \left({\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{1.0} \cdot \frac{1}{36}\right)\right) \cdot \frac{1}{6}}\right) + 0.5)_*\]
