if b < -2.0638378f+09

1. Started with
   \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
   25.1
2. Applied simplify to get
   \[\color{red}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\]
   9.9
3. Using strategy rm
   9.9
4. Applied add-cube-cbrt to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \color{red}{\frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \color{blue}{{\left(\sqrt[3]{\frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\right)}^3}\]
   10.3

if -2.0638378f+09 < b < 8651331.0f0

1. Started with
   \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
   29.7
2. Applied simplify to get
   \[\color{red}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\]
   14.4
3. Using strategy rm
   14.4
4. Applied expm1-udef to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{\color{red}{(e^{b \cdot \varepsilon} - 1)^*}} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{\color{blue}{e^{b \cdot \varepsilon} - 1}}\]
   29.3
5. Applied taylor to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{e^{b \cdot \varepsilon} - 1} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \left(\left(\frac{1}{b} + \frac{1}{12} \cdot \left({\varepsilon}^2 \cdot b\right)\right) - \frac{1}{2} \cdot \varepsilon\right)\]
   7.5
6. Taylor expanded around 0 to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \color{red}{\left(\left(\frac{1}{b} + \frac{1}{12} \cdot \left({\varepsilon}^2 \cdot b\right)\right) - \frac{1}{2} \cdot \varepsilon\right)} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \color{blue}{\left(\left(\frac{1}{b} + \frac{1}{12} \cdot \left({\varepsilon}^2 \cdot b\right)\right) - \frac{1}{2} \cdot \varepsilon\right)}\]
   7.5
7. Applied simplify to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \left(\left(\frac{1}{b} + \frac{1}{12} \cdot \left({\varepsilon}^2 \cdot b\right)\right) - \frac{1}{2} \cdot \varepsilon\right) \leadsto \left(\left(b \cdot \frac{1}{12}\right) \cdot {\varepsilon}^2 + \left(\frac{1}{b} - \frac{1}{2} \cdot \varepsilon\right)\right) \cdot \frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*}\]
   7.5

---

8. Applied final simplification

if 8651331.0f0 < b

1. Started with
   \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
   24.9
2. Applied simplify to get
   \[\color{red}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\]
   9.2
3. Using strategy rm
   9.2
4. Applied add-cube-cbrt to get
   \[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{\color{red}{(e^{b \cdot \varepsilon} - 1)^*}} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{\color{blue}{{\left(\sqrt[3]{(e^{b \cdot \varepsilon} - 1)^*}\right)}^3}}\]
   9.4
5. Using strategy rm
   9.4
6. Applied pow1 to get
   \[\color{red}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*}} \cdot \frac{\varepsilon}{{\left(\sqrt[3]{(e^{b \cdot \varepsilon} - 1)^*}\right)}^3} \leadsto \color{blue}{{\left(\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*}\right)}^{1}} \cdot \frac{\varepsilon}{{\left(\sqrt[3]{(e^{b \cdot \varepsilon} - 1)^*}\right)}^3}\]
   10.1