if x < 0.1563779f0

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   18.1
2. Using strategy rm
   18.1
3. Applied add-exp-log to get
   \[\frac{e^{x}}{\color{red}{e^{x} - 1}} \leadsto \frac{e^{x}}{\color{blue}{e^{\log \left(e^{x} - 1\right)}}}\]
   29.4
4. Applied div-exp to get
   \[\color{red}{\frac{e^{x}}{e^{\log \left(e^{x} - 1\right)}}} \leadsto \color{blue}{e^{x - \log \left(e^{x} - 1\right)}}\]
   29.4
5. Applied taylor to get
   \[e^{x - \log \left(e^{x} - 1\right)} \leadsto e^{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)}\]
   22.1
6. Taylor expanded around 0 to get
   \[e^{\color{red}{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)}} \leadsto e^{\color{blue}{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)}}\]
   22.1
7. Applied simplify to get
   \[e^{\frac{1}{2} \cdot x - \left(\frac{1}{24} \cdot {x}^2 + \log x\right)} \leadsto \frac{\frac{\sqrt{e^{x}}}{{\left(e^{\frac{1}{24}}\right)}^{\left(x \cdot x\right)}}}{x}\]
   0.1

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8. Applied final simplification
9. Applied simplify to get
   \[\color{red}{\frac{\frac{\sqrt{e^{x}}}{{\left(e^{\frac{1}{24}}\right)}^{\left(x \cdot x\right)}}}{x}} \leadsto \color{blue}{\frac{\frac{\sqrt{e^{x}}}{x}}{{\left(e^{\frac{1}{24}}\right)}^{\left({x}^2\right)}}}\]
   0.1

if 0.1563779f0 < x

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   27.7
2. Using strategy rm
   27.7
3. Applied clear-num to get
   \[\color{red}{\frac{e^{x}}{e^{x} - 1}} \leadsto \color{blue}{\frac{1}{\frac{e^{x} - 1}{e^{x}}}}\]
   27.7
4. Applied simplify to get
   \[\frac{1}{\color{red}{\frac{e^{x} - 1}{e^{x}}}} \leadsto \frac{1}{\color{blue}{1 - e^{-x}}}\]
   0.0