Initial program 13.5
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
- Using strategy
rm Applied div-sub13.5
\[\leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
Applied associate--r-7.5
\[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
Applied simplify6.9
\[\leadsto \color{blue}{\left(wj - \frac{wj}{1 + wj}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Taylor expanded around 0 1.2
\[\leadsto \color{blue}{\left(\left({wj}^{4} + {wj}^{2}\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Applied simplify1.2
\[\leadsto \color{blue}{\frac{x}{(wj \cdot \left(e^{wj}\right) + \left(e^{wj}\right))_*} + (\left(wj \cdot wj\right) \cdot \left(1 - wj\right) + \left({wj}^{4}\right))_*}\]
- Using strategy
rm Applied add-exp-log1.8
\[\leadsto \frac{x}{(wj \cdot \left(e^{wj}\right) + \left(e^{wj}\right))_*} + \color{blue}{e^{\log \left((\left(wj \cdot wj\right) \cdot \left(1 - wj\right) + \left({wj}^{4}\right))_*\right)}}\]
Taylor expanded around 0 32.4
\[\leadsto \frac{x}{(wj \cdot \left(e^{wj}\right) + \left(e^{wj}\right))_*} + e^{\color{blue}{\left(\frac{1}{2} \cdot {wj}^{2} + 2 \cdot \log wj\right) - wj}}\]
Applied simplify1.3
\[\leadsto \color{blue}{(\left({\left(e^{wj}\right)}^{\left(\frac{1}{2} \cdot wj\right)}\right) \cdot \left(\frac{wj \cdot wj}{e^{wj}}\right) + \left(\frac{x}{(\left(e^{wj}\right) \cdot wj + \left(e^{wj}\right))_*}\right))_*}\]
