Initial program 0.4
\[\log \left(1 + e^{x}\right) - x \cdot y\]
- Using strategy
rm Applied flip3-+0.5
\[\leadsto \log \color{blue}{\left(\frac{{1}^{3} + {\left(e^{x}\right)}^{3}}{1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)}\right)} - x \cdot y\]
Applied log-div0.5
\[\leadsto \color{blue}{\left(\log \left({1}^{3} + {\left(e^{x}\right)}^{3}\right) - \log \left(1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)\right)\right)} - x \cdot y\]
Applied simplify0.5
\[\leadsto \left(\color{blue}{\log \left(1 + {\left(e^{x}\right)}^{3}\right)} - \log \left(1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)\right)\right) - x \cdot y\]
Applied simplify0.5
\[\leadsto \left(\log \left(1 + {\left(e^{x}\right)}^{3}\right) - \color{blue}{\log \left(\left(1 - e^{x}\right) + e^{x} \cdot e^{x}\right)}\right) - x \cdot y\]
- Using strategy
rm Applied add-cube-cbrt0.5
\[\leadsto \left(\log \left(1 + {\left(e^{x}\right)}^{3}\right) - \log \color{blue}{\left(\left(\sqrt[3]{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}} \cdot \sqrt[3]{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}\right) \cdot \sqrt[3]{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}\right)}\right) - x \cdot y\]
Applied log-prod0.5
\[\leadsto \left(\log \left(1 + {\left(e^{x}\right)}^{3}\right) - \color{blue}{\left(\log \left(\sqrt[3]{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}} \cdot \sqrt[3]{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}\right) + \log \left(\sqrt[3]{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}\right)\right)}\right) - x \cdot y\]
Applied simplify0.5
\[\leadsto \left(\log \left(1 + {\left(e^{x}\right)}^{3}\right) - \left(\color{blue}{\log \left(\sqrt[3]{\left(1 - e^{x}\right) + e^{x + x}} \cdot \sqrt[3]{\left(1 - e^{x}\right) + e^{x + x}}\right)} + \log \left(\sqrt[3]{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}\right)\right)\right) - x \cdot y\]
Applied simplify0.5
\[\leadsto \left(\log \left(1 + {\left(e^{x}\right)}^{3}\right) - \left(\log \left(\sqrt[3]{\left(1 - e^{x}\right) + e^{x + x}} \cdot \sqrt[3]{\left(1 - e^{x}\right) + e^{x + x}}\right) + \color{blue}{\log \left(\sqrt[3]{\left(1 - e^{x}\right) + e^{x + x}}\right)}\right)\right) - x \cdot y\]
