if a < -1639.1333f0 or 3.581931f-06 < a

1. Started with
   \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
   25.6
2. Applied simplify to get
   \[\color{red}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\]
   8.7
3. Using strategy rm
   8.7
4. Applied add-cube-cbrt to get
   \[\color{red}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*}} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*}}\right)}^3} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}\]
   8.8

if -1639.1333f0 < a < 3.581931f-06

1. Started with
   \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
   30.0
2. Applied simplify to get
   \[\color{red}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\]
   15.2
3. Using strategy rm
   15.2
4. Applied expm1-udef to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{\color{red}{(e^{a \cdot \varepsilon} - 1)^*}} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{\color{blue}{e^{a \cdot \varepsilon} - 1}} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}\]
   29.8
5. Applied taylor to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{e^{a \cdot \varepsilon} - 1} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{a \cdot (e^{\varepsilon \cdot b} - 1)^*} - \frac{1}{2} \cdot \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot b} - 1)^*}\]
   7.2
6. Taylor expanded around 0 to get
   \[\color{red}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{a \cdot (e^{\varepsilon \cdot b} - 1)^*} - \frac{1}{2} \cdot \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot b} - 1)^*}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{a \cdot (e^{\varepsilon \cdot b} - 1)^*} - \frac{1}{2} \cdot \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot b} - 1)^*}}\]
   7.2
7. Applied simplify to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{a \cdot (e^{\varepsilon \cdot b} - 1)^*} - \frac{1}{2} \cdot \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot b} - 1)^*} \leadsto \frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{(e^{b \cdot \varepsilon} - 1)^* \cdot a} - \frac{1}{2} \cdot \frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}\]
   7.2

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8. Applied final simplification