Initial program 0.3
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
- Using strategy
rm Applied add-sqr-sqrt0.3
\[\leadsto \left(\left(\log \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{x + y}\right)} + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
Applied log-prod0.3
\[\leadsto \left(\left(\color{blue}{\left(\log \left(\sqrt{x + y}\right) + \log \left(\sqrt{x + y}\right)\right)} + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
Applied associate-+l+0.3
\[\leadsto \left(\color{blue}{\left(\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \log z\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]
Applied associate--l+0.3
\[\leadsto \color{blue}{\left(\log \left(\sqrt{x + y}\right) + \left(\left(\log \left(\sqrt{x + y}\right) + \log z\right) - t\right)\right)} + \left(a - 0.5\right) \cdot \log t\]
Applied associate-+l+0.3
\[\leadsto \color{blue}{\log \left(\sqrt{x + y}\right) + \left(\left(\left(\log \left(\sqrt{x + y}\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]
- Using strategy
rm Applied add-cube-cbrt0.3
\[\leadsto \log \left(\sqrt{x + y}\right) + \left(\left(\left(\log \color{blue}{\left(\left(\sqrt[3]{\sqrt{x + y}} \cdot \sqrt[3]{\sqrt{x + y}}\right) \cdot \sqrt[3]{\sqrt{x + y}}\right)} + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
Applied log-prod0.3
\[\leadsto \log \left(\sqrt{x + y}\right) + \left(\left(\left(\color{blue}{\left(\log \left(\sqrt[3]{\sqrt{x + y}} \cdot \sqrt[3]{\sqrt{x + y}}\right) + \log \left(\sqrt[3]{\sqrt{x + y}}\right)\right)} + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
Applied associate-+l+0.3
\[\leadsto \log \left(\sqrt{x + y}\right) + \left(\left(\color{blue}{\left(\log \left(\sqrt[3]{\sqrt{x + y}} \cdot \sqrt[3]{\sqrt{x + y}}\right) + \left(\log \left(\sqrt[3]{\sqrt{x + y}}\right) + \log z\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
Applied associate--l+0.3
\[\leadsto \log \left(\sqrt{x + y}\right) + \left(\color{blue}{\left(\log \left(\sqrt[3]{\sqrt{x + y}} \cdot \sqrt[3]{\sqrt{x + y}}\right) + \left(\left(\log \left(\sqrt[3]{\sqrt{x + y}}\right) + \log z\right) - t\right)\right)} + \left(a - 0.5\right) \cdot \log t\right)\]
Applied associate-+l+0.3
\[\leadsto \log \left(\sqrt{x + y}\right) + \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{x + y}} \cdot \sqrt[3]{\sqrt{x + y}}\right) + \left(\left(\left(\log \left(\sqrt[3]{\sqrt{x + y}}\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)}\]
Applied associate-+r+0.3
\[\leadsto \color{blue}{\left(\log \left(\sqrt{x + y}\right) + \log \left(\sqrt[3]{\sqrt{x + y}} \cdot \sqrt[3]{\sqrt{x + y}}\right)\right) + \left(\left(\left(\log \left(\sqrt[3]{\sqrt{x + y}}\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]
Final simplification0.3
\[\leadsto \left(\left(\left(\log z + \log \left(\sqrt[3]{\sqrt{y + x}}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\right) + \left(\log \left(\sqrt[3]{\sqrt{y + x}} \cdot \sqrt[3]{\sqrt{y + x}}\right) + \log \left(\sqrt{y + x}\right)\right)\]
