Initial program 13.6
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
- Using strategy
rm Applied div-sub13.6
\[\leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
Applied associate--r-7.2
\[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
Applied simplify6.6
\[\leadsto \color{blue}{\left(wj - \frac{wj}{1 + wj}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Taylor expanded around 0 1.0
\[\leadsto \color{blue}{\left(\left({wj}^{4} + {wj}^{2}\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Applied simplify1.0
\[\leadsto \color{blue}{\frac{x}{(wj \cdot \left(e^{wj}\right) + \left(e^{wj}\right))_*} + (\left(wj \cdot wj\right) \cdot \left(1 - wj\right) + \left({wj}^{4}\right))_*}\]
- Using strategy
rm Applied fma-udef1.0
\[\leadsto \frac{x}{(wj \cdot \left(e^{wj}\right) + \left(e^{wj}\right))_*} + \color{blue}{\left(\left(wj \cdot wj\right) \cdot \left(1 - wj\right) + {wj}^{4}\right)}\]
Applied associate-+r+1.0
\[\leadsto \color{blue}{\left(\frac{x}{(wj \cdot \left(e^{wj}\right) + \left(e^{wj}\right))_*} + \left(wj \cdot wj\right) \cdot \left(1 - wj\right)\right) + {wj}^{4}}\]
Applied simplify1.0
\[\leadsto \color{blue}{(wj \cdot \left(wj - wj \cdot wj\right) + \left(\frac{x}{(\left(e^{wj}\right) \cdot wj + \left(e^{wj}\right))_*}\right))_*} + {wj}^{4}\]
