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-7.1
\[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
Taylor expanded around 0 1.1
\[\leadsto \color{blue}{\left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Simplified1.1
\[\leadsto \color{blue}{\left({wj}^{4} - \left(wj \cdot wj - wj\right) \cdot wj\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
- Using strategy
rm Applied add-cube-cbrt1.2
\[\leadsto \left({wj}^{4} - \color{blue}{\left(\sqrt[3]{\left(wj \cdot wj - wj\right) \cdot wj} \cdot \sqrt[3]{\left(wj \cdot wj - wj\right) \cdot wj}\right) \cdot \sqrt[3]{\left(wj \cdot wj - wj\right) \cdot wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Final simplification1.2
\[\leadsto \frac{x}{e^{wj} \cdot wj + e^{wj}} + \left({wj}^{4} - \left(\sqrt[3]{\left(wj \cdot wj - wj\right) \cdot wj} \cdot \sqrt[3]{\left(wj \cdot wj - wj\right) \cdot wj}\right) \cdot \sqrt[3]{\left(wj \cdot wj - wj\right) \cdot wj}\right)\]
