Initial program 0.5
\[\log \left(1 + e^{x}\right) - x \cdot y\]
- Using strategy
rm Applied pow10.5
\[\leadsto \log \color{blue}{\left({\left(1 + e^{x}\right)}^{1}\right)} - x \cdot y\]
Applied log-pow0.5
\[\leadsto \color{blue}{1 \cdot \log \left(1 + e^{x}\right)} - x \cdot y\]
Applied prod-diff0.5
\[\leadsto \color{blue}{(1 \cdot \left(\log \left(1 + e^{x}\right)\right) + \left(-y \cdot x\right))_* + (\left(-y\right) \cdot x + \left(y \cdot x\right))_*}\]
Applied simplify0.5
\[\leadsto \color{blue}{\left(\log_* (1 + e^{x}) - y \cdot x\right)} + (\left(-y\right) \cdot x + \left(y \cdot x\right))_*\]
- Using strategy
rm Applied add-cube-cbrt1.6
\[\leadsto \left(\color{blue}{\left(\sqrt[3]{\log_* (1 + e^{x})} \cdot \sqrt[3]{\log_* (1 + e^{x})}\right) \cdot \sqrt[3]{\log_* (1 + e^{x})}} - y \cdot x\right) + (\left(-y\right) \cdot x + \left(y \cdot x\right))_*\]
Applied prod-diff1.6
\[\leadsto \color{blue}{\left((\left(\sqrt[3]{\log_* (1 + e^{x})} \cdot \sqrt[3]{\log_* (1 + e^{x})}\right) \cdot \left(\sqrt[3]{\log_* (1 + e^{x})}\right) + \left(-x \cdot y\right))_* + (\left(-x\right) \cdot y + \left(x \cdot y\right))_*\right)} + (\left(-y\right) \cdot x + \left(y \cdot x\right))_*\]
Applied simplify0.5
\[\leadsto \left(\color{blue}{\left(\log_* (1 + e^{x}) - y \cdot x\right)} + (\left(-x\right) \cdot y + \left(x \cdot y\right))_*\right) + (\left(-y\right) \cdot x + \left(y \cdot x\right))_*\]
