if x < 859.389f0

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   21.2
2. Using strategy rm
   21.2
3. Applied flip-- to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{\left(\frac{1}{\varepsilon} - 1\right)} \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{\frac{{\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2}{\frac{1}{\varepsilon} + 1}} \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   21.6
4. Applied associate-*l/ to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{\frac{{\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2}{\frac{1}{\varepsilon} + 1} \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{\frac{\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{\frac{1}{\varepsilon} + 1}}}{2}\]
   22.0
5. Applied exp-neg to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \color{red}{e^{-\left(1 - \varepsilon\right) \cdot x}} - \frac{\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{\frac{1}{\varepsilon} + 1}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \color{blue}{\frac{1}{e^{\left(1 - \varepsilon\right) \cdot x}}} - \frac{\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{\frac{1}{\varepsilon} + 1}}{2}\]
   22.0
6. Applied un-div-inv to get
   \[\frac{\color{red}{\left(1 + \frac{1}{\varepsilon}\right) \cdot \frac{1}{e^{\left(1 - \varepsilon\right) \cdot x}}} - \frac{\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{\frac{1}{\varepsilon} + 1}}{2} \leadsto \frac{\color{blue}{\frac{1 + \frac{1}{\varepsilon}}{e^{\left(1 - \varepsilon\right) \cdot x}}} - \frac{\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{\frac{1}{\varepsilon} + 1}}{2}\]
   22.0
7. Applied frac-sub to get
   \[\frac{\color{red}{\frac{1 + \frac{1}{\varepsilon}}{e^{\left(1 - \varepsilon\right) \cdot x}} - \frac{\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{\frac{1}{\varepsilon} + 1}}}{2} \leadsto \frac{\color{blue}{\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \left(\frac{1}{\varepsilon} + 1\right) - e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}\right)}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}}{2}\]
   22.1
8. Applied simplify to get
   \[\frac{\frac{\color{red}{\left(1 + \frac{1}{\varepsilon}\right) \cdot \left(\frac{1}{\varepsilon} + 1\right) - e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\left({\left(\frac{1}{\varepsilon}\right)}^2 - {1}^2\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}\right)}}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}{2} \leadsto \frac{\frac{\color{blue}{\left(1 + \frac{1}{\varepsilon}\right) \cdot \left(1 + \frac{1}{\varepsilon}\right) - \frac{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}}{{\left(e^{x}\right)}^{\left(1 + \varepsilon\right)}} \cdot \left(\frac{1}{\varepsilon \cdot \varepsilon} - 1\right)}}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}{2}\]
   18.8
9. Applied taylor to get
   \[\frac{\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot \left(1 + \frac{1}{\varepsilon}\right) - \frac{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}}{{\left(e^{x}\right)}^{\left(1 + \varepsilon\right)}} \cdot \left(\frac{1}{\varepsilon \cdot \varepsilon} - 1\right)}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}{2} \leadsto \frac{\frac{2 + \left(2 \cdot \frac{x}{\varepsilon} + 2 \cdot \frac{1}{\varepsilon}\right)}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}{2}\]
   0.3
10. Taylor expanded around 0 to get
    \[\frac{\frac{\color{red}{2 + \left(2 \cdot \frac{x}{\varepsilon} + 2 \cdot \frac{1}{\varepsilon}\right)}}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}{2} \leadsto \frac{\frac{\color{blue}{2 + \left(2 \cdot \frac{x}{\varepsilon} + 2 \cdot \frac{1}{\varepsilon}\right)}}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}{2}\]
    0.3
11. Applied simplify to get
    \[\frac{\frac{2 + \left(2 \cdot \frac{x}{\varepsilon} + 2 \cdot \frac{1}{\varepsilon}\right)}{e^{\left(1 - \varepsilon\right) \cdot x} \cdot \left(\frac{1}{\varepsilon} + 1\right)}}{2} \leadsto \frac{\frac{\left(2 + \frac{2}{\varepsilon}\right) + \frac{x \cdot 2}{\varepsilon}}{{\left(e^{x}\right)}^{\left(1 - \varepsilon\right)}}}{2 + \frac{2}{\varepsilon}}\]
    3.7

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12. Applied final simplification

if 859.389f0 < x

1. Started with
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
   0.1
2. Using strategy rm
   0.1
3. Applied add-cube-cbrt to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{red}{e^{-\left(1 + \varepsilon\right) \cdot x}}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot \color{blue}{{\left(\sqrt[3]{e^{-\left(1 + \varepsilon\right) \cdot x}}\right)}^3}}{2}\]
   0.1
4. Applied add-cube-cbrt to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{\left(\frac{1}{\varepsilon} - 1\right)} \cdot {\left(\sqrt[3]{e^{-\left(1 + \varepsilon\right) \cdot x}}\right)}^3}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{{\left(\sqrt[3]{\frac{1}{\varepsilon} - 1}\right)}^3} \cdot {\left(\sqrt[3]{e^{-\left(1 + \varepsilon\right) \cdot x}}\right)}^3}{2}\]
   0.1
5. Applied cube-unprod to get
   \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{red}{{\left(\sqrt[3]{\frac{1}{\varepsilon} - 1}\right)}^3 \cdot {\left(\sqrt[3]{e^{-\left(1 + \varepsilon\right) \cdot x}}\right)}^3}}{2} \leadsto \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \color{blue}{{\left(\sqrt[3]{\frac{1}{\varepsilon} - 1} \cdot \sqrt[3]{e^{-\left(1 + \varepsilon\right) \cdot x}}\right)}^3}}{2}\]
   0.1