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
\[\leadsto \color{blue}{\frac{\frac{x}{e^{wj}}}{1 + wj} + \left({wj}^{4} + \left(1 - wj\right) \cdot \left(wj \cdot wj\right)\right)}\]
- Using strategy
rm Applied add-cube-cbrt1.2
\[\leadsto \frac{\frac{x}{e^{wj}}}{1 + wj} + \left({wj}^{4} + \color{blue}{\left(\left(\sqrt[3]{1 - wj} \cdot \sqrt[3]{1 - wj}\right) \cdot \sqrt[3]{1 - wj}\right)} \cdot \left(wj \cdot wj\right)\right)\]
Applied associate-*l*1.2
\[\leadsto \frac{\frac{x}{e^{wj}}}{1 + wj} + \left({wj}^{4} + \color{blue}{\left(\sqrt[3]{1 - wj} \cdot \sqrt[3]{1 - wj}\right) \cdot \left(\sqrt[3]{1 - wj} \cdot \left(wj \cdot wj\right)\right)}\right)\]
