Initial program 58.0
\[\frac{e^{x} - e^{-x}}{2}\]
Taylor expanded around 0 0.7
\[\leadsto \frac{\color{blue}{2 \cdot x + \left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{60} \cdot {x}^{5}\right)}}{2}\]
Simplified0.7
\[\leadsto \frac{\color{blue}{x \cdot \left(x \cdot \left(\frac{1}{3} \cdot x\right) + 2\right) + {x}^{5} \cdot \frac{1}{60}}}{2}\]
- Using strategy
rm Applied +-commutative0.7
\[\leadsto \frac{x \cdot \color{blue}{\left(2 + x \cdot \left(\frac{1}{3} \cdot x\right)\right)} + {x}^{5} \cdot \frac{1}{60}}{2}\]
Applied distribute-lft-in0.7
\[\leadsto \frac{\color{blue}{\left(x \cdot 2 + x \cdot \left(x \cdot \left(\frac{1}{3} \cdot x\right)\right)\right)} + {x}^{5} \cdot \frac{1}{60}}{2}\]
Final simplification0.7
\[\leadsto \frac{{x}^{5} \cdot \frac{1}{60} + \left(x \cdot 2 + \left(\left(\frac{1}{3} \cdot x\right) \cdot x\right) \cdot x\right)}{2}\]
