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 simplification0.3
\[\leadsto 0.5 + \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\frac{6}{\cos \left(\left(2 \cdot u2\right) \cdot \pi\right)}}\]
- Using strategy
rm Applied div-inv0.3
\[\leadsto 0.5 + \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\color{blue}{6 \cdot \frac{1}{\cos \left(\left(2 \cdot u2\right) \cdot \pi\right)}}}\]
Applied *-un-lft-identity0.3
\[\leadsto 0.5 + \frac{\color{blue}{1 \cdot {\left(-2 \cdot \log u1\right)}^{0.5}}}{6 \cdot \frac{1}{\cos \left(\left(2 \cdot u2\right) \cdot \pi\right)}}\]
Applied times-frac0.4
\[\leadsto 0.5 + \color{blue}{\frac{1}{6} \cdot \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{\frac{1}{\cos \left(\left(2 \cdot u2\right) \cdot \pi\right)}}}\]
Simplified0.4
\[\leadsto 0.5 + \frac{1}{6} \cdot \color{blue}{\left(\cos \left(\left(u2 \cdot \pi\right) \cdot 2\right) \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right)}\]
- Using strategy
rm Applied add-sqr-sqrt0.4
\[\leadsto 0.5 + \color{blue}{\left(\sqrt{\frac{1}{6}} \cdot \sqrt{\frac{1}{6}}\right)} \cdot \left(\cos \left(\left(u2 \cdot \pi\right) \cdot 2\right) \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right)\]
Applied associate-*l*0.4
\[\leadsto 0.5 + \color{blue}{\sqrt{\frac{1}{6}} \cdot \left(\sqrt{\frac{1}{6}} \cdot \left(\cos \left(\left(u2 \cdot \pi\right) \cdot 2\right) \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right)\right)}\]
Final simplification0.4
\[\leadsto \sqrt{\frac{1}{6}} \cdot \left(\left(\cos \left(\left(u2 \cdot \pi\right) \cdot 2\right) \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \sqrt{\frac{1}{6}}\right) + 0.5\]
