Initial program 0.6
\[\log \left(1 + e^{x}\right) - x \cdot y\]
- Using strategy
rm Applied flip3-+0.6
\[\leadsto \log \color{blue}{\left(\frac{{1}^{3} + {\left(e^{x}\right)}^{3}}{1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)}\right)} - x \cdot y\]
Applied log-div0.6
\[\leadsto \color{blue}{\left(\log \left({1}^{3} + {\left(e^{x}\right)}^{3}\right) - \log \left(1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)\right)\right)} - x \cdot y\]
Simplified0.6
\[\leadsto \left(\color{blue}{\log \left(e^{\left(x + x\right) + x} + 1\right)} - \log \left(1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)\right)\right) - x \cdot y\]
- Using strategy
rm Applied add-sqr-sqrt1.4
\[\leadsto \left(\log \color{blue}{\left(\sqrt{e^{\left(x + x\right) + x} + 1} \cdot \sqrt{e^{\left(x + x\right) + x} + 1}\right)} - \log \left(1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)\right)\right) - x \cdot y\]
Applied log-prod1.1
\[\leadsto \left(\color{blue}{\left(\log \left(\sqrt{e^{\left(x + x\right) + x} + 1}\right) + \log \left(\sqrt{e^{\left(x + x\right) + x} + 1}\right)\right)} - \log \left(1 \cdot 1 + \left(e^{x} \cdot e^{x} - 1 \cdot e^{x}\right)\right)\right) - x \cdot y\]
Final simplification1.1
\[\leadsto \left(\left(\log \left(\sqrt{e^{\left(x + x\right) + x} + 1}\right) + \log \left(\sqrt{e^{\left(x + x\right) + x} + 1}\right)\right) - \log \left(1 + \left(e^{x} \cdot e^{x} - e^{x}\right)\right)\right) - x \cdot y\]
