Initial program 13.9
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
Initial simplification7.0
\[\leadsto \left(wj - \frac{wj}{wj + 1}\right) + \frac{\frac{x}{e^{wj}}}{wj + 1}\]
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 flip3-+1.1
\[\leadsto \left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right) + \frac{\frac{x}{e^{wj}}}{\color{blue}{\frac{{wj}^{3} + {1}^{3}}{wj \cdot wj + \left(1 \cdot 1 - wj \cdot 1\right)}}}\]
Applied associate-/r/1.1
\[\leadsto \left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right) + \color{blue}{\frac{\frac{x}{e^{wj}}}{{wj}^{3} + {1}^{3}} \cdot \left(wj \cdot wj + \left(1 \cdot 1 - wj \cdot 1\right)\right)}\]
Simplified1.1
\[\leadsto \left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right) + \frac{\frac{x}{e^{wj}}}{{wj}^{3} + {1}^{3}} \cdot \color{blue}{\left(\left(1 - wj\right) + wj \cdot wj\right)}\]
- Using strategy
rm Applied associate--l+1.1
\[\leadsto \color{blue}{\left({wj}^{2} + \left({wj}^{4} - {wj}^{3}\right)\right)} + \frac{\frac{x}{e^{wj}}}{{wj}^{3} + {1}^{3}} \cdot \left(\left(1 - wj\right) + wj \cdot wj\right)\]
- Using strategy
rm Applied flip-+1.1
\[\leadsto \left({wj}^{2} + \left({wj}^{4} - {wj}^{3}\right)\right) + \frac{\frac{x}{e^{wj}}}{{wj}^{3} + {1}^{3}} \cdot \color{blue}{\frac{\left(1 - wj\right) \cdot \left(1 - wj\right) - \left(wj \cdot wj\right) \cdot \left(wj \cdot wj\right)}{\left(1 - wj\right) - wj \cdot wj}}\]
Applied frac-times1.1
\[\leadsto \left({wj}^{2} + \left({wj}^{4} - {wj}^{3}\right)\right) + \color{blue}{\frac{\frac{x}{e^{wj}} \cdot \left(\left(1 - wj\right) \cdot \left(1 - wj\right) - \left(wj \cdot wj\right) \cdot \left(wj \cdot wj\right)\right)}{\left({wj}^{3} + {1}^{3}\right) \cdot \left(\left(1 - wj\right) - wj \cdot wj\right)}}\]
Simplified1.1
\[\leadsto \left({wj}^{2} + \left({wj}^{4} - {wj}^{3}\right)\right) + \frac{\frac{x}{e^{wj}} \cdot \left(\left(1 - wj\right) \cdot \left(1 - wj\right) - \left(wj \cdot wj\right) \cdot \left(wj \cdot wj\right)\right)}{\color{blue}{\left(\left(1 - wj\right) - wj \cdot wj\right) \cdot \left(1 + {wj}^{3}\right)}}\]
Final simplification1.1
\[\leadsto \left(\left({wj}^{4} - {wj}^{3}\right) + {wj}^{2}\right) + \frac{\frac{x}{e^{wj}} \cdot \left(\left(1 - wj\right) \cdot \left(1 - wj\right) - \left(wj \cdot wj\right) \cdot \left(wj \cdot wj\right)\right)}{\left(\left(1 - wj\right) - wj \cdot wj\right) \cdot \left(1 + {wj}^{3}\right)}\]
