Initial program 58.8
\[e^{x} - 1\]
Taylor expanded around 0 0.4
\[\leadsto \color{blue}{x + \left(\frac{1}{6} \cdot {x}^{3} + \frac{1}{2} \cdot {x}^{2}\right)}\]
Simplified0.4
\[\leadsto \color{blue}{x + \left(x \cdot \frac{1}{6} + \frac{1}{2}\right) \cdot \left(x \cdot x\right)}\]
- Using strategy
rm Applied add-exp-log34.9
\[\leadsto \color{blue}{e^{\log \left(x + \left(x \cdot \frac{1}{6} + \frac{1}{2}\right) \cdot \left(x \cdot x\right)\right)}}\]
Taylor expanded around 0 34.9
\[\leadsto e^{\color{blue}{\frac{1}{2} \cdot x + \left(\frac{1}{24} \cdot {x}^{2} + \log x\right)}}\]
- Using strategy
rm Applied add-log-exp34.9
\[\leadsto e^{\frac{1}{2} \cdot x + \left(\color{blue}{\log \left(e^{\frac{1}{24} \cdot {x}^{2}}\right)} + \log x\right)}\]
Applied sum-log34.9
\[\leadsto e^{\frac{1}{2} \cdot x + \color{blue}{\log \left(e^{\frac{1}{24} \cdot {x}^{2}} \cdot x\right)}}\]
Applied add-log-exp34.9
\[\leadsto e^{\color{blue}{\log \left(e^{\frac{1}{2} \cdot x}\right)} + \log \left(e^{\frac{1}{24} \cdot {x}^{2}} \cdot x\right)}\]
Applied sum-log34.9
\[\leadsto e^{\color{blue}{\log \left(e^{\frac{1}{2} \cdot x} \cdot \left(e^{\frac{1}{24} \cdot {x}^{2}} \cdot x\right)\right)}}\]
Applied rem-exp-log0.3
\[\leadsto \color{blue}{e^{\frac{1}{2} \cdot x} \cdot \left(e^{\frac{1}{24} \cdot {x}^{2}} \cdot x\right)}\]
Final simplification0.3
\[\leadsto e^{\frac{1}{2} \cdot x} \cdot \left(e^{{x}^{2} \cdot \frac{1}{24}} \cdot x\right)\]
