Initial program 58.0
\[\frac{e^{x} - e^{-x}}{2}\]
Taylor expanded around 0 0.6
\[\leadsto \frac{\color{blue}{\frac{1}{3} \cdot {x}^{3} + \left(\frac{1}{60} \cdot {x}^{5} + 2 \cdot x\right)}}{2}\]
Applied simplify0.6
\[\leadsto \color{blue}{\frac{(x \cdot \left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) + \left(\frac{1}{60} \cdot {x}^{5}\right))_*}{2}}\]
- Using strategy
rm Applied add-cbrt-cube39.9
\[\leadsto \frac{\color{blue}{\sqrt[3]{\left((x \cdot \left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) + \left(\frac{1}{60} \cdot {x}^{5}\right))_* \cdot (x \cdot \left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) + \left(\frac{1}{60} \cdot {x}^{5}\right))_*\right) \cdot (x \cdot \left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) + \left(\frac{1}{60} \cdot {x}^{5}\right))_*}}}{2}\]
Applied simplify39.9
\[\leadsto \frac{\sqrt[3]{\color{blue}{{\left((x \cdot \left((\left(\frac{1}{3} \cdot x\right) \cdot x + 2)_*\right) + \left(\frac{1}{60} \cdot {x}^{5}\right))_*\right)}^{3}}}}{2}\]
Taylor expanded around 0 34.7
\[\leadsto \frac{\color{blue}{\frac{1}{6} \cdot \left(e^{\log x + \log 2} \cdot {x}^{2}\right) + \left(e^{\log x + \log 2} + \frac{1}{120} \cdot \left(e^{\log x + \log 2} \cdot {x}^{4}\right)\right)}}{2}\]
Applied simplify0.6
\[\leadsto \color{blue}{\frac{(x \cdot \left((\left({x}^{4}\right) \cdot \left(\frac{1}{120} \cdot 2\right) + 2)_*\right) + \left(\left(2 \cdot \frac{1}{6}\right) \cdot {x}^{3}\right))_*}{2}}\]
