if x < 0.8279971f0

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   23.6
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 0.8279971f0 < x

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   1.5
2. Using strategy rm
   1.5
3. Applied pow1 to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{red}{e^{-\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{blue}{{\left(e^{-\left(1 + \varepsilon\right) \cdot x}\right)}^{1}}}{2}\]
   1.5
4. Applied pow1 to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{\left(\frac{1}{\varepsilon} - 1\right)} \cdot {\left(e^{-\left(1 + \varepsilon\right) \cdot x}\right)}^{1}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{{\left(\frac{1}{\varepsilon} - 1\right)}^{1}} \cdot {\left(e^{-\left(1 + \varepsilon\right) \cdot x}\right)}^{1}}{2}\]
   1.5
5. Applied pow-prod-down to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{{\left(\frac{1}{\varepsilon} - 1\right)}^{1} \cdot {\left(e^{-\left(1 + \varepsilon\right) \cdot x}\right)}^{1}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{{\left(\left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}\right)}^{1}}}{2}\]
   1.5
6. Applied simplify to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - {\color{red}{\left(\left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}\right)}}^{1}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - {\color{blue}{\left(\frac{\frac{1}{\varepsilon} - 1}{e^{(\varepsilon * x + x)_*}}\right)}}^{1}}{2}\]
   1.5
7. Applied taylor to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - {\left(\frac{\frac{1}{\varepsilon} - 1}{e^{(\varepsilon * x + x)_*}}\right)}^{1}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - {\left(\frac{1}{e^{(\varepsilon * x + x)_*} \cdot \varepsilon} - \frac{1}{e^{(\varepsilon * x + x)_*}}\right)}^{1}}{2}\]
   1.5
8. Taylor expanded around 0 to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - {\color{red}{\left(\frac{1}{e^{(\varepsilon * x + x)_*} \cdot \varepsilon} - \frac{1}{e^{(\varepsilon * x + x)_*}}\right)}}^{1}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - {\color{blue}{\left(\frac{1}{e^{(\varepsilon * x + x)_*} \cdot \varepsilon} - \frac{1}{e^{(\varepsilon * x + x)_*}}\right)}}^{1}}{2}\]
   1.5
9. Applied simplify to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - {\left(\frac{1}{e^{(\varepsilon * x + x)_*} \cdot \varepsilon} - \frac{1}{e^{(\varepsilon * x + x)_*}}\right)}^{1}}{2} \leadsto \left(\frac{e^{\left(1 - \varepsilon\right) \cdot \left(-x\right)}}{\frac{2}{1 + \frac{1}{\varepsilon}}} - \frac{e^{-(\varepsilon * x + x)_*}}{2 \cdot \varepsilon}\right) + \frac{e^{-(\varepsilon * x + x)_*}}{2}\]
   1.3

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10. Applied final simplification