\((\frac{1}{6} * \left({\left({\left(\log u1\right)}^{1.0} \cdot {-2}^{1.0}\right)}^{0.5} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right)\right) + 0.5)_*\)
- Started with
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
0.4
- 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
- Using strategy
rm 0.4
- Applied fma-udef to get
\[\color{red}{(\left(\frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6}\right) * \left(\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)\right) + 0.5)_*} \leadsto \color{blue}{\frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6} \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right) + 0.5}\]
0.4
- Using strategy
rm 0.4
- Applied add-log-exp to get
\[\color{red}{\frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6} \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)} + 0.5 \leadsto \color{blue}{\log \left(e^{\frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6} \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right)} + 0.5\]
0.7
- Applied taylor to get
\[\log \left(e^{\frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6} \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right) + 0.5 \leadsto \log \left(e^{\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right) \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right) + 0.5\]
0.7
- Taylor expanded around 0 to get
\[\log \left(e^{\color{red}{\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right)} \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right) + 0.5 \leadsto \log \left(e^{\color{blue}{\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right)} \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right) + 0.5\]
0.7
- Applied simplify to get
\[\log \left(e^{\left(\frac{1}{6} \cdot {\left({-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}\right)}^{0.5}\right) \cdot \cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}\right) + 0.5 \leadsto (\frac{1}{6} * \left({\left({\left(\log u1\right)}^{1.0} \cdot {-2}^{1.0}\right)}^{0.5} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right)\right) + 0.5)_*\]
0.4
- Applied final simplification
