if x < 0.11032443f0

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   18.3
2. Applied taylor to get
   \[\frac{e^{x}}{e^{x} - 1} \leadsto \frac{e^{x}}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\]
   5.2
3. Taylor expanded around 0 to get
   \[\frac{e^{x}}{\color{red}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}} \leadsto \frac{e^{x}}{\color{blue}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}\]
   5.2
4. Using strategy rm
   5.2
5. Applied div-inv to get
   \[\color{red}{\frac{e^{x}}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}} \leadsto \color{blue}{e^{x} \cdot \frac{1}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}\]
   5.2
6. Applied simplify to get
   \[e^{x} \cdot \color{red}{\frac{1}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}} \leadsto e^{x} \cdot \color{blue}{\frac{1}{x + \left(x \cdot x\right) \cdot \left(\frac{1}{6} \cdot x + \frac{1}{2}\right)}}\]
   0.1
7. Applied simplify to get
   \[e^{x} \cdot \frac{1}{\color{red}{x + \left(x \cdot x\right) \cdot \left(\frac{1}{6} \cdot x + \frac{1}{2}\right)}} \leadsto e^{x} \cdot \frac{1}{\color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right) \cdot {x}^2 + x}}\]
   0.1

if 0.11032443f0 < x

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   27.8
2. Using strategy rm
   27.8
3. Applied clear-num to get
   \[\color{red}{\frac{e^{x}}{e^{x} - 1}} \leadsto \color{blue}{\frac{1}{\frac{e^{x} - 1}{e^{x}}}}\]
   27.8
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