\(0.5 + {\left(\frac{1}{6} \cdot \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}\right)}^{1}\)
- 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
\[\color{red}{\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5} \leadsto \color{blue}{0.5 + \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\frac{6}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}}\]
0.5
- Using strategy
rm 0.5
- Applied div-inv to get
\[0.5 + \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\color{red}{\frac{6}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}} \leadsto 0.5 + \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\color{blue}{6 \cdot \frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}}\]
0.5
- Applied *-un-lft-identity to get
\[0.5 + \frac{\color{red}{{\left(-2 \cdot \log u1\right)}^{0.5}}}{6 \cdot \frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}} \leadsto 0.5 + \frac{\color{blue}{1 \cdot {\left(-2 \cdot \log u1\right)}^{0.5}}}{6 \cdot \frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}\]
0.5
- Applied times-frac to get
\[0.5 + \color{red}{\frac{1 \cdot {\left(-2 \cdot \log u1\right)}^{0.5}}{6 \cdot \frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}} \leadsto 0.5 + \color{blue}{\frac{1}{6} \cdot \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}}\]
0.5
- Using strategy
rm 0.5
- Applied pow1 to get
\[0.5 + \color{red}{\frac{1}{6} \cdot \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}} \leadsto 0.5 + \color{blue}{{\left(\frac{1}{6} \cdot \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\frac{1}{\cos \left(\pi \cdot \left(u2 \cdot 2\right)\right)}}\right)}^{1}}\]
0.5
