Initial program 58.1
\[\frac{e^{x} - e^{-x}}{2}\]
Taylor expanded around 0 0.7
\[\leadsto \frac{\color{blue}{\frac{1}{3} \cdot {x}^{3} + \left(\frac{1}{60} \cdot {x}^{5} + 2 \cdot x\right)}}{2}\]
Applied simplify0.8
\[\leadsto \color{blue}{\frac{(x \cdot \left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) + \left(\frac{1}{60} \cdot {x}^{5}\right))_*}{2}}\]
- Using strategy
rm Applied fma-udef0.8
\[\leadsto \frac{\color{blue}{x \cdot (\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_* + \frac{1}{60} \cdot {x}^{5}}}{2}\]
- Using strategy
rm Applied fma-udef0.8
\[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{3} \cdot \left(x \cdot x\right) + 2\right)} + \frac{1}{60} \cdot {x}^{5}}{2}\]
Applied distribute-lft-in0.7
\[\leadsto \frac{\color{blue}{\left(x \cdot \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) + x \cdot 2\right)} + \frac{1}{60} \cdot {x}^{5}}{2}\]
Applied associate-+l+0.7
\[\leadsto \frac{\color{blue}{x \cdot \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) + \left(x \cdot 2 + \frac{1}{60} \cdot {x}^{5}\right)}}{2}\]
Applied simplify0.7
\[\leadsto \frac{x \cdot \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) + \color{blue}{(\frac{1}{60} \cdot \left({x}^{5}\right) + \left(2 \cdot x\right))_*}}{2}\]
