if x < 0.30789185f0

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   20.2
2. Using strategy rm
   20.2
3. Applied exp-neg to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{red}{e^{-\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{blue}{\frac{1}{e^{\left(1 + \varepsilon\right) \cdot x}}}}{2}\]
   20.2
4. Applied un-div-inv to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{\left(\frac{1}{\varepsilon} - 1\right) \cdot \frac{1}{e^{\left(1 + \varepsilon\right) \cdot x}}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{\frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}}{2}\]
   20.2
5. Applied exp-neg to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \color{red}{e^{-\left(1 - \varepsilon\right) \cdot x}} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \color{blue}{\frac{1}{e^{\left(1 - \varepsilon\right) \cdot x}}} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2}\]
   20.2
6. Applied un-div-inv to get
   \[\frac{\color{red}{\left(1 + \frac{1}{\varepsilon}\right) \cdot \frac{1}{e^{\left(1 - \varepsilon\right) \cdot x}}} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\color{blue}{\frac{1 + \frac{1}{\varepsilon}}{e^{\left(1 - \varepsilon\right) \cdot x}}} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}{2}\]
   20.2
7. Applied frac-sub to get
   \[\frac{\color{red}{\frac{1 + \frac{1}{\varepsilon}}{e^{\left(1 - \varepsilon\right) \cdot x}} - \frac{\frac{1}{\varepsilon} - 1}{e^{\left(1 + \varepsilon\right) \cdot x}}}}{2} \leadsto \frac{\color{blue}{\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{\left(1 + \varepsilon\right) \cdot x} - e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} - 1\right)}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot e^{\left(1 + \varepsilon\right) \cdot x}}}}{2}\]
   20.2
8. Applied simplify to get
   \[\frac{\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{\left(1 + \varepsilon\right) \cdot x} - e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} - 1\right)}{\color{red}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot e^{\left(1 + \varepsilon\right) \cdot x}}}}{2} \leadsto \frac{\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{\left(1 + \varepsilon\right) \cdot x} - e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} - 1\right)}{\color{blue}{e^{(x * \left(1 + 0\right) + x)_*}}}}{2}\]
   20.2
9. Applied taylor to get
   \[\frac{\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{\left(1 + \varepsilon\right) \cdot x} - e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} - 1\right)}{e^{(x * \left(1 + 0\right) + x)_*}}}{2} \leadsto \frac{\frac{3 \cdot {x}^2 + \left(2 + 4 \cdot x\right)}{e^{(x * \left(1 + 0\right) + x)_*}}}{2}\]
   0.1
10. Taylor expanded around 0 to get
    \[\frac{\frac{\color{red}{3 \cdot {x}^2 + \left(2 + 4 \cdot x\right)}}{e^{(x * \left(1 + 0\right) + x)_*}}}{2} \leadsto \frac{\frac{\color{blue}{3 \cdot {x}^2 + \left(2 + 4 \cdot x\right)}}{e^{(x * \left(1 + 0\right) + x)_*}}}{2}\]
    0.1
11. Applied simplify to get
    \[\frac{\frac{3 \cdot {x}^2 + \left(2 + 4 \cdot x\right)}{e^{(x * \left(1 + 0\right) + x)_*}}}{2} \leadsto \frac{(\left(x \cdot x\right) * 3 + \left((x * 4 + 2)_*\right))_*}{2 \cdot e^{(x * 1 + x)_*}}\]
    0.1

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12. Applied final simplification
13. Applied simplify to get
    \[\color{red}{\frac{(\left(x \cdot x\right) * 3 + \left((x * 4 + 2)_*\right))_*}{2 \cdot e^{(x * 1 + x)_*}}} \leadsto \color{blue}{\frac{(\left({x}^2\right) * 3 + \left((x * 4 + 2)_*\right))_*}{e^{(x * 1 + x)_*} \cdot 2}}\]
    0.1

if 0.30789185f0 < x

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   1.9
2. Using strategy rm
   1.9
3. Applied sub-neg to get
   \[\frac{\color{red}{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\color{blue}{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} + \left(-\left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}\right)}}{2}\]
   1.9
4. Applied simplify to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} + \color{red}{\left(-\left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}\right)}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} + \color{blue}{\frac{-\left(\frac{1}{\varepsilon} - 1\right)}{e^{(\varepsilon * x + x)_*}}}}{2}\]
   1.9