if wj < 5.534257467944305e-10

1. Started with
   \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
   14.4
2. Using strategy rm
   14.4
3. Applied div-sub to get
   \[wj - \color{red}{\frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}} \leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
   14.4
4. Applied simplify to get
   \[wj - \left(\color{red}{\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right) \leadsto wj - \left(\color{blue}{\frac{wj}{wj + 1}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)\]
   14.4
5. Applied simplify to get
   \[wj - \left(\frac{wj}{wj + 1} - \color{red}{\frac{x}{e^{wj} + wj \cdot e^{wj}}}\right) \leadsto wj - \left(\frac{wj}{wj + 1} - \color{blue}{\frac{\frac{x}{1 + wj}}{e^{wj}}}\right)\]
   14.4
6. Applied taylor to get
   \[wj - \left(\frac{wj}{wj + 1} - \frac{\frac{x}{1 + wj}}{e^{wj}}\right) \leadsto wj - \left(\left(\left({wj}^{3} + wj\right) - {wj}^2\right) - \frac{\frac{x}{1 + wj}}{e^{wj}}\right)\]
   14.1
7. Taylor expanded around 0 to get
   \[wj - \left(\color{red}{\left(\left({wj}^{3} + wj\right) - {wj}^2\right)} - \frac{\frac{x}{1 + wj}}{e^{wj}}\right) \leadsto wj - \left(\color{blue}{\left(\left({wj}^{3} + wj\right) - {wj}^2\right)} - \frac{\frac{x}{1 + wj}}{e^{wj}}\right)\]
   14.1
8. Applied simplify to get
   \[\color{red}{wj - \left(\left(\left({wj}^{3} + wj\right) - {wj}^2\right) - \frac{\frac{x}{1 + wj}}{e^{wj}}\right)} \leadsto \color{blue}{\left({wj}^2 - {wj}^3\right) + \frac{x}{\left(wj + 1\right) \cdot e^{wj}}}\]
   0.0

if 5.534257467944305e-10 < wj

1. Started with
   \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
   58.5
2. Using strategy rm
   58.5
3. Applied div-sub to get
   \[wj - \color{red}{\frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}} \leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
   58.5
4. Applied simplify to get
   \[wj - \left(\color{red}{\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right) \leadsto wj - \left(\color{blue}{\frac{wj}{wj + 1}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)\]
   0.3
5. Applied simplify to get
   \[wj - \left(\frac{wj}{wj + 1} - \color{red}{\frac{x}{e^{wj} + wj \cdot e^{wj}}}\right) \leadsto wj - \left(\frac{wj}{wj + 1} - \color{blue}{\frac{\frac{x}{1 + wj}}{e^{wj}}}\right)\]
   0.3