if (* a x) < -7.260081363831148e-07

1. Started with
   \[e^{a \cdot x} - 1\]
   0.2
2. Using strategy rm
   0.2
3. Applied add-log-exp to get
   \[\color{red}{e^{a \cdot x} - 1} \leadsto \color{blue}{\log \left(e^{e^{a \cdot x} - 1}\right)}\]
   0.2

if -7.260081363831148e-07 < (* a x)

1. Started with
   \[e^{a \cdot x} - 1\]
   46.8
2. Using strategy rm
   46.8
3. Applied add-exp-log to get
   \[\color{red}{e^{a \cdot x} - 1} \leadsto \color{blue}{e^{\log \left(e^{a \cdot x} - 1\right)}}\]
   47.3
4. Applied taylor to get
   \[e^{\log \left(e^{a \cdot x} - 1\right)} \leadsto \frac{1}{2} \cdot \left(e^{\log x + \log a} \cdot \left(a \cdot x\right)\right) + \left(\frac{1}{6} \cdot \left(e^{\log x + \log a} \cdot \left({a}^2 \cdot {x}^2\right)\right) + e^{\log x + \log a}\right)\]
   49.9
5. Taylor expanded around 0 to get
   \[\color{red}{\frac{1}{2} \cdot \left(e^{\log x + \log a} \cdot \left(a \cdot x\right)\right) + \left(\frac{1}{6} \cdot \left(e^{\log x + \log a} \cdot \left({a}^2 \cdot {x}^2\right)\right) + e^{\log x + \log a}\right)} \leadsto \color{blue}{\frac{1}{2} \cdot \left(e^{\log x + \log a} \cdot \left(a \cdot x\right)\right) + \left(\frac{1}{6} \cdot \left(e^{\log x + \log a} \cdot \left({a}^2 \cdot {x}^2\right)\right) + e^{\log x + \log a}\right)}\]
   49.9
6. Applied simplify to get
   \[\frac{1}{2} \cdot \left(e^{\log x + \log a} \cdot \left(a \cdot x\right)\right) + \left(\frac{1}{6} \cdot \left(e^{\log x + \log a} \cdot \left({a}^2 \cdot {x}^2\right)\right) + e^{\log x + \log a}\right) \leadsto \left(\frac{1}{2} \cdot {\left(a \cdot x\right)}^2 + a \cdot x\right) + {\left(a \cdot x\right)}^2 \cdot \left(\left(a \cdot x\right) \cdot \frac{1}{6}\right)\]
   0.1

---

7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\left(\frac{1}{2} \cdot {\left(a \cdot x\right)}^2 + a \cdot x\right) + {\left(a \cdot x\right)}^2 \cdot \left(\left(a \cdot x\right) \cdot \frac{1}{6}\right)} \leadsto \color{blue}{a \cdot x + \left(\left(a \cdot x\right) \cdot \left(a \cdot x\right)\right) \cdot \left(\left(a \cdot x\right) \cdot \frac{1}{6} + \frac{1}{2}\right)}\]
   0.1