if x < -8.61646249982272e-12

1. Started with
   \[\frac{e^{x} - 1}{x}\]
   0.5
2. Using strategy rm
   0.5
3. Applied flip3-- to get
   \[\frac{\color{red}{e^{x} - 1}}{x} \leadsto \frac{\color{blue}{\frac{{\left(e^{x}\right)}^{3} - {1}^{3}}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}}{x}\]
   0.5
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(e^{x}\right)}^{3} - {1}^{3}}}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}{x} \leadsto \frac{\frac{\color{blue}{{\left(e^{x}\right)}^3 - 1}}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}{x}\]
   0.5
5. Applied simplify to get
   \[\frac{\frac{{\left(e^{x}\right)}^3 - 1}{\color{red}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}}{x} \leadsto \frac{\frac{{\left(e^{x}\right)}^3 - 1}{\color{blue}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}}{x}\]
   0.5
6. Using strategy rm
   0.5
7. Applied flip3-- to get
   \[\frac{\frac{\color{red}{{\left(e^{x}\right)}^3 - 1}}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}{x} \leadsto \frac{\frac{\color{blue}{\frac{{\left({\left(e^{x}\right)}^3\right)}^{3} - {1}^{3}}{{\left({\left(e^{x}\right)}^3\right)}^2 + \left({1}^2 + {\left(e^{x}\right)}^3 \cdot 1\right)}}}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}{x}\]
   0.5
8. Applied simplify to get
   \[\frac{\frac{\frac{\color{red}{{\left({\left(e^{x}\right)}^3\right)}^{3} - {1}^{3}}}{{\left({\left(e^{x}\right)}^3\right)}^2 + \left({1}^2 + {\left(e^{x}\right)}^3 \cdot 1\right)}}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}{x} \leadsto \frac{\frac{\frac{\color{blue}{{\left({\left(e^{x}\right)}^3\right)}^3 - 1}}{{\left({\left(e^{x}\right)}^3\right)}^2 + \left({1}^2 + {\left(e^{x}\right)}^3 \cdot 1\right)}}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}{x}\]
   0.5
9. Applied simplify to get
   \[\frac{\frac{\frac{{\left({\left(e^{x}\right)}^3\right)}^3 - 1}{\color{red}{{\left({\left(e^{x}\right)}^3\right)}^2 + \left({1}^2 + {\left(e^{x}\right)}^3 \cdot 1\right)}}}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}{x} \leadsto \frac{\frac{\frac{{\left({\left(e^{x}\right)}^3\right)}^3 - 1}{\color{blue}{{\left({\left(e^{x}\right)}^3\right)}^2 + \left(1 + {\left(e^{x}\right)}^3\right)}}}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}{x}\]
   0.5

if -8.61646249982272e-12 < x

1. Started with
   \[\frac{e^{x} - 1}{x}\]
   60.8
2. Applied taylor to get
   \[\frac{e^{x} - 1}{x} \leadsto \frac{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}{x}\]
   3.9
3. Taylor expanded around 0 to get
   \[\frac{\color{red}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}{x} \leadsto \frac{\color{blue}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}{x}\]
   3.9
4. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}{x}} \leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{6} + \frac{1}{2}\right) + x}{x}}\]
   3.9
5. Applied simplify to get
   \[\frac{\color{red}{\left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{6} + \frac{1}{2}\right) + x}}{x} \leadsto \frac{\color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right) \cdot {x}^2 + x}}{x}\]
   3.9