if x < 0.03150794f0

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   18.0
2. Applied taylor to get
   \[\frac{e^{x}}{e^{x} - 1} \leadsto \frac{e^{x}}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\]
   5.4
3. Taylor expanded around 0 to get
   \[\frac{e^{x}}{\color{red}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}} \leadsto \frac{e^{x}}{\color{blue}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}\]
   5.4
4. Using strategy rm
   5.4
5. Applied add-cube-cbrt to get
   \[\frac{e^{x}}{\color{red}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}} \leadsto \frac{e^{x}}{\color{blue}{{\left(\sqrt[3]{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\right)}^3}}\]
   5.9
6. Applied add-cube-cbrt to get
   \[\frac{\color{red}{e^{x}}}{{\left(\sqrt[3]{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\right)}^3} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{e^{x}}\right)}^3}}{{\left(\sqrt[3]{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\right)}^3}\]
   5.9
7. Applied cube-undiv to get
   \[\color{red}{\frac{{\left(\sqrt[3]{e^{x}}\right)}^3}{{\left(\sqrt[3]{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\right)}^3}} \leadsto \color{blue}{{\left(\frac{\sqrt[3]{e^{x}}}{\sqrt[3]{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}\right)}^3}\]
   5.9
8. Applied simplify to get
   \[{\color{red}{\left(\frac{\sqrt[3]{e^{x}}}{\sqrt[3]{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}\right)}}^3 \leadsto {\color{blue}{\left(\frac{\sqrt[3]{e^{x}}}{\sqrt[3]{{x}^2 \cdot \left(x \cdot \frac{1}{6} + \frac{1}{2}\right) + x}}\right)}}^3\]
   0.5

if 0.03150794f0 < x

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   27.6
2. Using strategy rm
   27.6
3. Applied clear-num to get
   \[\color{red}{\frac{e^{x}}{e^{x} - 1}} \leadsto \color{blue}{\frac{1}{\frac{e^{x} - 1}{e^{x}}}}\]
   27.6
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