- Started with
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
28.2
- Using strategy
rm 28.2
- Applied distribute-rgt1-in to get
\[wj - \frac{wj \cdot e^{wj} - x}{\color{red}{e^{wj} + wj \cdot e^{wj}}} \leadsto wj - \frac{wj \cdot e^{wj} - x}{\color{blue}{\left(wj + 1\right) \cdot e^{wj}}}\]
28.4
- Applied *-un-lft-identity to get
\[wj - \frac{\color{red}{wj \cdot e^{wj} - x}}{\left(wj + 1\right) \cdot e^{wj}} \leadsto wj - \frac{\color{blue}{1 \cdot \left(wj \cdot e^{wj} - x\right)}}{\left(wj + 1\right) \cdot e^{wj}}\]
28.4
- Applied times-frac to get
\[wj - \color{red}{\frac{1 \cdot \left(wj \cdot e^{wj} - x\right)}{\left(wj + 1\right) \cdot e^{wj}}} \leadsto wj - \color{blue}{\frac{1}{wj + 1} \cdot \frac{wj \cdot e^{wj} - x}{e^{wj}}}\]
28.4
- Applied simplify to get
\[wj - \frac{1}{wj + 1} \cdot \color{red}{\frac{wj \cdot e^{wj} - x}{e^{wj}}} \leadsto wj - \frac{1}{wj + 1} \cdot \color{blue}{\left(wj - \frac{x}{e^{wj}}\right)}\]
28.3
- Applied taylor to get
\[wj - \frac{1}{wj + 1} \cdot \left(wj - \frac{x}{e^{wj}}\right) \leadsto \left({wj}^2 + x\right) - 2 \cdot \left(wj \cdot x\right)\]
0.0
- Taylor expanded around 0 to get
\[\color{red}{\left({wj}^2 + x\right) - 2 \cdot \left(wj \cdot x\right)} \leadsto \color{blue}{\left({wj}^2 + x\right) - 2 \cdot \left(wj \cdot x\right)}\]
0.0
- Applied simplify to get
\[\color{red}{\left({wj}^2 + x\right) - 2 \cdot \left(wj \cdot x\right)} \leadsto \color{blue}{(\left(wj - 2 \cdot x\right) * wj + x)_*}\]
0.0
