\((\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right) * \left(\log \left(e^{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right)\right) + 0.5)_*\)
- Started with
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
0.5
- Applied simplify to get
\[\color{red}{\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5} \leadsto \color{blue}{(\left(\frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6}\right) * \left(\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)\right) + 0.5)_*}\]
0.4
- Applied taylor to get
\[(\left(\frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6}\right) * \left(\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)\right) + 0.5)_* \leadsto (\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right) * \left(\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)\right) + 0.5)_*\]
0.5
- Taylor expanded around 0 to get
\[(\color{red}{\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right)} * \left(\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)\right) + 0.5)_* \leadsto (\color{blue}{\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right)} * \left(\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)\right) + 0.5)_*\]
0.5
- Using strategy
rm 0.5
- Applied add-log-exp to get
\[(\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right) * \color{red}{\left(\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)\right)} + 0.5)_* \leadsto (\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right) * \color{blue}{\left(\log \left(e^{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right)\right)} + 0.5)_*\]
0.5
