Initial program 41.4
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
- Using strategy
rm Applied add-exp-log41.4
\[\leadsto \color{blue}{e^{\log \left(\frac{2}{1 + e^{-2 \cdot x}} - 1\right)}}\]
- Using strategy
rm Applied flip3-+41.4
\[\leadsto e^{\log \left(\frac{2}{\color{blue}{\frac{{1}^{3} + {\left(e^{-2 \cdot x}\right)}^{3}}{1 \cdot 1 + \left(e^{-2 \cdot x} \cdot e^{-2 \cdot x} - 1 \cdot e^{-2 \cdot x}\right)}}} - 1\right)}\]
Applied associate-/r/41.4
\[\leadsto e^{\log \left(\color{blue}{\frac{2}{{1}^{3} + {\left(e^{-2 \cdot x}\right)}^{3}} \cdot \left(1 \cdot 1 + \left(e^{-2 \cdot x} \cdot e^{-2 \cdot x} - 1 \cdot e^{-2 \cdot x}\right)\right)} - 1\right)}\]
Simplified41.4
\[\leadsto e^{\log \left(\frac{2}{{1}^{3} + {\left(e^{-2 \cdot x}\right)}^{3}} \cdot \color{blue}{\left(1 + \left(e^{x \cdot -4} - e^{-2 \cdot x}\right)\right)} - 1\right)}\]
- Using strategy
rm Applied add-sqr-sqrt41.4
\[\leadsto e^{\log \left(\frac{2}{{1}^{3} + {\color{blue}{\left(\sqrt{e^{-2 \cdot x}} \cdot \sqrt{e^{-2 \cdot x}}\right)}}^{3}} \cdot \left(1 + \left(e^{x \cdot -4} - e^{-2 \cdot x}\right)\right) - 1\right)}\]
Applied unpow-prod-down41.4
\[\leadsto e^{\log \left(\frac{2}{{1}^{3} + \color{blue}{{\left(\sqrt{e^{-2 \cdot x}}\right)}^{3} \cdot {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3}}} \cdot \left(1 + \left(e^{x \cdot -4} - e^{-2 \cdot x}\right)\right) - 1\right)}\]
- Using strategy
rm Applied pow141.4
\[\leadsto e^{\log \color{blue}{\left({\left(\frac{2}{{1}^{3} + {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3} \cdot {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3}} \cdot \left(1 + \left(e^{x \cdot -4} - e^{-2 \cdot x}\right)\right) - 1\right)}^{1}\right)}}\]
Applied log-pow41.4
\[\leadsto e^{\color{blue}{1 \cdot \log \left(\frac{2}{{1}^{3} + {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3} \cdot {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3}} \cdot \left(1 + \left(e^{x \cdot -4} - e^{-2 \cdot x}\right)\right) - 1\right)}}\]
Applied exp-prod41.4
\[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\frac{2}{{1}^{3} + {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3} \cdot {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3}} \cdot \left(1 + \left(e^{x \cdot -4} - e^{-2 \cdot x}\right)\right) - 1\right)\right)}}\]
Simplified41.4
\[\leadsto {\color{blue}{e}}^{\left(\log \left(\frac{2}{{1}^{3} + {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3} \cdot {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3}} \cdot \left(1 + \left(e^{x \cdot -4} - e^{-2 \cdot x}\right)\right) - 1\right)\right)}\]
Final simplification41.4
\[\leadsto {e}^{\left(\log \left(\left(1 + \left(e^{-4 \cdot x} - e^{-2 \cdot x}\right)\right) \cdot \frac{2}{1 + {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3} \cdot {\left(\sqrt{e^{-2 \cdot x}}\right)}^{3}} - 1\right)\right)}\]
