if x < 10.704295f0

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   23.7
2. Applied taylor to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2} \leadsto \frac{2}{2}\]
   0
3. Taylor expanded around 0 to get
   \[\frac{\color{red}{2}}{2} \leadsto \frac{\color{blue}{2}}{2}\]
   0
4. Applied simplify to get
   \[\color{red}{\frac{2}{2}} \leadsto \color{blue}{1}\]
   0

if 10.704295f0 < x

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   1.0
2. Using strategy rm
   1.0
3. Applied exp-neg to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{red}{e^{-\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{blue}{\frac{1}{e^{\left(1 + \varepsilon\right) \cdot x}}}}{2}\]
   0.9
4. Applied un-div-inv to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{\left(\frac{1}{\varepsilon} - 1\right) \cdot \frac{1}{e^{\left(1 + \varepsilon\right) \cdot x}}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{\frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}}{2}\]
   0.9
5. Using strategy rm
   0.9
6. Applied add-cube-cbrt to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \color{red}{e^{-\left(1 - \varepsilon\right) \cdot x}} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \color{blue}{{\left(\sqrt[3]{e^{-\left(1 - \varepsilon\right) \cdot x}}\right)}^3} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2}\]
   1.0
7. Applied add-cube-cbrt to get
   \[\frac{\color{red}{\left(1 + \frac{1}{\varepsilon}\right)} \cdot {\left(\sqrt[3]{e^{-\left(1 - \varepsilon\right) \cdot x}}\right)}^3 - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{1 + \frac{1}{\varepsilon}}\right)}^3} \cdot {\left(\sqrt[3]{e^{-\left(1 - \varepsilon\right) \cdot x}}\right)}^3 - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2}\]
   1.0
8. Applied cube-unprod to get
   \[\frac{\color{red}{{\left(\sqrt[3]{1 + \frac{1}{\varepsilon}}\right)}^3 \cdot {\left(\sqrt[3]{e^{-\left(1 - \varepsilon\right) \cdot x}}\right)}^3} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{1 + \frac{1}{\varepsilon}} \cdot \sqrt[3]{e^{-\left(1 - \varepsilon\right) \cdot x}}\right)}^3} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2}\]
   1.0