if wj < -3.1807354f-05 or 8.293655f-05 < wj

1. Started with
   \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
   21.1
2. Using strategy rm
   21.1
3. Applied distribute-rgt1-in to get
   \[wj - \frac{wj \cdot e^{wj} - x}{\color{red}{e^{wj} + wj \cdot e^{wj}}} \leadsto wj - \frac{wj \cdot e^{wj} - x}{\color{blue}{\left(wj + 1\right) \cdot e^{wj}}}\]
   21.6
4. Applied *-un-lft-identity to get
   \[wj - \frac{\color{red}{wj \cdot e^{wj} - x}}{\left(wj + 1\right) \cdot e^{wj}} \leadsto wj - \frac{\color{blue}{1 \cdot \left(wj \cdot e^{wj} - x\right)}}{\left(wj + 1\right) \cdot e^{wj}}\]
   21.6
5. Applied times-frac to get
   \[wj - \color{red}{\frac{1 \cdot \left(wj \cdot e^{wj} - x\right)}{\left(wj + 1\right) \cdot e^{wj}}} \leadsto wj - \color{blue}{\frac{1}{wj + 1} \cdot \frac{wj \cdot e^{wj} - x}{e^{wj}}}\]
   21.7
6. Applied simplify to get
   \[wj - \frac{1}{wj + 1} \cdot \color{red}{\frac{wj \cdot e^{wj} - x}{e^{wj}}} \leadsto wj - \frac{1}{wj + 1} \cdot \color{blue}{\left(wj - \frac{x}{e^{wj}}\right)}\]
   0.6
7. Using strategy rm
   0.6
8. Applied flip-+ to get
   \[wj - \frac{1}{\color{red}{wj + 1}} \cdot \left(wj - \frac{x}{e^{wj}}\right) \leadsto wj - \frac{1}{\color{blue}{\frac{{wj}^2 - {1}^2}{wj - 1}}} \cdot \left(wj - \frac{x}{e^{wj}}\right)\]
   0.6
9. Applied associate-/r/ to get
   \[wj - \color{red}{\frac{1}{\frac{{wj}^2 - {1}^2}{wj - 1}}} \cdot \left(wj - \frac{x}{e^{wj}}\right) \leadsto wj - \color{blue}{\left(\frac{1}{{wj}^2 - {1}^2} \cdot \left(wj - 1\right)\right)} \cdot \left(wj - \frac{x}{e^{wj}}\right)\]
   0.6
10. Applied associate-*l* to get
    \[wj - \color{red}{\left(\frac{1}{{wj}^2 - {1}^2} \cdot \left(wj - 1\right)\right) \cdot \left(wj - \frac{x}{e^{wj}}\right)} \leadsto wj - \color{blue}{\frac{1}{{wj}^2 - {1}^2} \cdot \left(\left(wj - 1\right) \cdot \left(wj - \frac{x}{e^{wj}}\right)\right)}\]
    0.6

if -3.1807354f-05 < wj < 8.293655f-05

1. Started with
   \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
   1.0
2. Applied taylor to get
   \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}} \leadsto \left({wj}^2 + x\right) - 2 \cdot \left(wj \cdot x\right)\]
   0.0
3. 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
4. Applied simplify to get
   \[\color{red}{\left({wj}^2 + x\right) - 2 \cdot \left(wj \cdot x\right)} \leadsto \color{blue}{(\left(wj - 2 \cdot x\right) * wj + x)_*}\]
   0.2