if wj < 4.117893899060259e-06

1. Started with
   \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
   13.6
2. Using strategy rm
   13.6
3. Applied div-sub to get
   \[wj - \color{red}{\frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}} \leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
   13.6
4. Applied simplify to get
   \[wj - \left(\color{red}{\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right) \leadsto wj - \left(\color{blue}{\frac{wj}{wj + 1}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)\]
   13.6
5. Applied simplify to get
   \[wj - \left(\frac{wj}{wj + 1} - \color{red}{\frac{x}{e^{wj} + wj \cdot e^{wj}}}\right) \leadsto wj - \left(\frac{wj}{wj + 1} - \color{blue}{\frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}}\right)\]
   13.6
6. Applied taylor to get
   \[wj - \left(\frac{wj}{wj + 1} - \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\right) \leadsto wj - \left(\left(\left({wj}^{3} + wj\right) - {wj}^2\right) - \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\right)\]
   13.3
7. Taylor expanded around 0 to get
   \[wj - \left(\color{red}{\left(\left({wj}^{3} + wj\right) - {wj}^2\right)} - \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\right) \leadsto wj - \left(\color{blue}{\left(\left({wj}^{3} + wj\right) - {wj}^2\right)} - \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\right)\]
   13.3
8. Applied simplify to get
   \[wj - \left(\left(\left({wj}^{3} + wj\right) - {wj}^2\right) - \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\right) \leadsto \left(\left(\left(wj - wj\right) - {wj}^3\right) + {wj}^2\right) + \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\]
   0.0

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9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{\left(\left(\left(wj - wj\right) - {wj}^3\right) + {wj}^2\right) + \frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}} \leadsto \color{blue}{(wj * \left(wj - {wj}^2\right) + \left(\frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}\right))_*}\]
    0.0

if 4.117893899060259e-06 < wj

1. Started with
   \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
   58.8
2. Using strategy rm
   58.8
3. Applied div-sub to get
   \[wj - \color{red}{\frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}} \leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
   58.8
4. Applied simplify to get
   \[wj - \left(\color{red}{\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right) \leadsto wj - \left(\color{blue}{\frac{wj}{wj + 1}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)\]
   0.1
5. Applied simplify to get
   \[wj - \left(\frac{wj}{wj + 1} - \color{red}{\frac{x}{e^{wj} + wj \cdot e^{wj}}}\right) \leadsto wj - \left(\frac{wj}{wj + 1} - \color{blue}{\frac{x}{(wj * \left(e^{wj}\right) + \left(e^{wj}\right))_*}}\right)\]
   0.1