Initial program 14.1
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
Initial simplification7.2
\[\leadsto \left(wj - \frac{wj}{wj + 1}\right) + \frac{\frac{x}{e^{wj}}}{wj + 1}\]
Taylor expanded around 0 1.1
\[\leadsto \color{blue}{\left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right)} + \frac{\frac{x}{e^{wj}}}{wj + 1}\]
- Using strategy
rm Applied add-sqr-sqrt1.1
\[\leadsto \color{blue}{\sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}} \cdot \sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}}} + \frac{\frac{x}{e^{wj}}}{wj + 1}\]
- Using strategy
rm Applied associate-/l/1.1
\[\leadsto \sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}} \cdot \sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}} + \color{blue}{\frac{x}{\left(wj + 1\right) \cdot e^{wj}}}\]
- Using strategy
rm Applied add-cbrt-cube1.1
\[\leadsto \sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}} \cdot \sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}} + \frac{x}{\color{blue}{\sqrt[3]{\left(\left(\left(wj + 1\right) \cdot e^{wj}\right) \cdot \left(\left(wj + 1\right) \cdot e^{wj}\right)\right) \cdot \left(\left(wj + 1\right) \cdot e^{wj}\right)}}}\]
Final simplification1.1
\[\leadsto \frac{x}{\sqrt[3]{\left(e^{wj} \cdot \left(1 + wj\right)\right) \cdot \left(\left(e^{wj} \cdot \left(1 + wj\right)\right) \cdot \left(e^{wj} \cdot \left(1 + wj\right)\right)\right)}} + \sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}} \cdot \sqrt{\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}}\]
