if x < 255.52292f0

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   17.2
2. Applied simplify to get
   \[\color{red}{\frac{e^{x}}{e^{x} - 1}} \leadsto \color{blue}{\frac{e^{x}}{(e^{x} - 1)^*}}\]
   0.2

if 255.52292f0 < x

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   30.0
2. Applied simplify to get
   \[\color{red}{\frac{e^{x}}{e^{x} - 1}} \leadsto \color{blue}{\frac{e^{x}}{(e^{x} - 1)^*}}\]
   30.0
3. Applied taylor to get
   \[\frac{e^{x}}{(e^{x} - 1)^*} \leadsto \frac{1}{2} \cdot \frac{{x}^2}{(e^{x} - 1)^*} + \left(\frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{x} - 1)^*}\right)\]
   30.0
4. Taylor expanded around 0 to get
   \[\color{red}{\frac{1}{2} \cdot \frac{{x}^2}{(e^{x} - 1)^*} + \left(\frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{x} - 1)^*}\right)} \leadsto \color{blue}{\frac{1}{2} \cdot \frac{{x}^2}{(e^{x} - 1)^*} + \left(\frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{x} - 1)^*}\right)}\]
   30.0
5. Applied simplify to get
   \[\color{red}{\frac{1}{2} \cdot \frac{{x}^2}{(e^{x} - 1)^*} + \left(\frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{x} - 1)^*}\right)} \leadsto \color{blue}{\left(x \cdot \frac{1}{2} + 1\right) \cdot \frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{x} - 1)^*}}\]
   30.0
6. Applied taylor to get
   \[\left(x \cdot \frac{1}{2} + 1\right) \cdot \frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{x} - 1)^*} \leadsto \left(x \cdot \frac{1}{2} + 1\right) \cdot \frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{\frac{1}{x}} - 1)^*}\]
   28.9
7. Taylor expanded around inf to get
   \[\left(x \cdot \frac{1}{2} + 1\right) \cdot \frac{x}{(e^{x} - 1)^*} + \color{red}{\frac{1}{(e^{\frac{1}{x}} - 1)^*}} \leadsto \left(x \cdot \frac{1}{2} + 1\right) \cdot \frac{x}{(e^{x} - 1)^*} + \color{blue}{\frac{1}{(e^{\frac{1}{x}} - 1)^*}}\]
   28.9
8. Applied simplify to get
   \[\color{red}{\left(x \cdot \frac{1}{2} + 1\right) \cdot \frac{x}{(e^{x} - 1)^*} + \frac{1}{(e^{\frac{1}{x}} - 1)^*}} \leadsto \color{blue}{(\left((\frac{1}{2} * x + 1)_*\right) * \left(\frac{x}{(e^{x} - 1)^*}\right) + \left(\frac{1}{(e^{\frac{1}{x}} - 1)^*}\right))_*}\]
   28.9
9. Applied taylor to get
   \[(\left((\frac{1}{2} * x + 1)_*\right) * \left(\frac{x}{(e^{x} - 1)^*}\right) + \left(\frac{1}{(e^{\frac{1}{x}} - 1)^*}\right))_* \leadsto (\left((\frac{1}{2} * \left(\frac{1}{x}\right) + 1)_*\right) * \left(\frac{1}{(e^{\frac{1}{x}} - 1)^* \cdot x}\right) + \left(\frac{1}{(e^{x} - 1)^*}\right))_*\]
   0.2
10. Taylor expanded around inf to get
    \[\color{red}{(\left((\frac{1}{2} * \left(\frac{1}{x}\right) + 1)_*\right) * \left(\frac{1}{(e^{\frac{1}{x}} - 1)^* \cdot x}\right) + \left(\frac{1}{(e^{x} - 1)^*}\right))_*} \leadsto \color{blue}{(\left((\frac{1}{2} * \left(\frac{1}{x}\right) + 1)_*\right) * \left(\frac{1}{(e^{\frac{1}{x}} - 1)^* \cdot x}\right) + \left(\frac{1}{(e^{x} - 1)^*}\right))_*}\]
    0.2
11. Applied simplify to get
    \[(\left((\frac{1}{2} * \left(\frac{1}{x}\right) + 1)_*\right) * \left(\frac{1}{(e^{\frac{1}{x}} - 1)^* \cdot x}\right) + \left(\frac{1}{(e^{x} - 1)^*}\right))_* \leadsto (\left((\frac{1}{2} * \left(\frac{1}{x}\right) + 1)_*\right) * \left(\frac{\frac{1}{(e^{\frac{1}{x}} - 1)^*}}{x}\right) + \left(\frac{1}{(e^{x} - 1)^*}\right))_*\]
    0.2

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12. Applied final simplification