if x < 12.645091f0

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   23.5
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 12.645091f0 < x

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   0.5
2. Using strategy rm
   0.5
3. Applied add-cube-cbrt to get
   \[\frac{\color{red}{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}\right)}^3}}{2}\]
   0.5
4. Applied simplify to get
   \[\frac{{\color{red}{\left(\sqrt[3]{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}\right)}}^3}{2} \leadsto \frac{{\color{blue}{\left(\sqrt[3]{\frac{\frac{1}{\varepsilon} + 1}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} - \frac{\frac{1}{\varepsilon} - 1}{e^{(\varepsilon * x + x)_*}}}\right)}}^3}{2}\]
   0.5
5. Applied taylor to get
   \[\frac{{\left(\sqrt[3]{\frac{\frac{1}{\varepsilon} + 1}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} - \frac{\frac{1}{\varepsilon} - 1}{e^{(\varepsilon * x + x)_*}}}\right)}^3}{2} \leadsto \frac{{\left(\sqrt[3]{\left(\frac{1}{\varepsilon \cdot {\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \left(\frac{1}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \frac{1}{e^{(\varepsilon * x + x)_*}}\right)\right) - \frac{1}{\varepsilon \cdot e^{(\varepsilon * x + x)_*}}}\right)}^3}{2}\]
   0.4
6. Taylor expanded around 0 to get
   \[\frac{{\color{red}{\left(\sqrt[3]{\left(\frac{1}{\varepsilon \cdot {\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \left(\frac{1}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \frac{1}{e^{(\varepsilon * x + x)_*}}\right)\right) - \frac{1}{\varepsilon \cdot e^{(\varepsilon * x + x)_*}}}\right)}}^3}{2} \leadsto \frac{{\color{blue}{\left(\sqrt[3]{\left(\frac{1}{\varepsilon \cdot {\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \left(\frac{1}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \frac{1}{e^{(\varepsilon * x + x)_*}}\right)\right) - \frac{1}{\varepsilon \cdot e^{(\varepsilon * x + x)_*}}}\right)}}^3}{2}\]
   0.4
7. Applied simplify to get
   \[\frac{{\left(\sqrt[3]{\left(\frac{1}{\varepsilon \cdot {\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \left(\frac{1}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \frac{1}{e^{(\varepsilon * x + x)_*}}\right)\right) - \frac{1}{\varepsilon \cdot e^{(\varepsilon * x + x)_*}}}\right)}^3}{2} \leadsto \frac{\left(\frac{1}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}} + \frac{\frac{1}{\varepsilon}}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}}\right) + \left(e^{-(\varepsilon * x + x)_*} - \frac{\frac{1}{\varepsilon}}{e^{(\varepsilon * x + x)_*}}\right)}{2}\]
   0.5

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8. Applied final simplification