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
\[\leadsto \frac{\color{blue}{(\left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) \cdot x + \left({x}^{5} \cdot \frac{1}{60}\right))_*}}{2}\]
- Using strategy
rm Applied add-cbrt-cube39.8
\[\leadsto \frac{\color{blue}{\sqrt[3]{\left((\left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) \cdot x + \left({x}^{5} \cdot \frac{1}{60}\right))_* \cdot (\left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) \cdot x + \left({x}^{5} \cdot \frac{1}{60}\right))_*\right) \cdot (\left((\frac{1}{3} \cdot \left(x \cdot x\right) + 2)_*\right) \cdot x + \left({x}^{5} \cdot \frac{1}{60}\right))_*}}}{2}\]
Taylor expanded around 0 35.6
\[\leadsto \frac{\color{blue}{e^{\frac{1}{3} \cdot \left(\log 8 + 3 \cdot \log x\right)} + \left(\frac{1}{120} \cdot \left(e^{\frac{1}{3} \cdot \left(\log 8 + 3 \cdot \log x\right)} \cdot {x}^{4}\right) + \frac{1}{6} \cdot \left(e^{\frac{1}{3} \cdot \left(\log 8 + 3 \cdot \log x\right)} \cdot {x}^{2}\right)\right)}}{2}\]
Simplified0.7
\[\leadsto \frac{\color{blue}{(\left((\left(x \cdot x\right) \cdot \frac{1}{6} + \left({x}^{4} \cdot \frac{1}{120}\right))_*\right) \cdot \left(\sqrt[3]{8} \cdot x\right) + \left(\sqrt[3]{8} \cdot x\right))_*}}{2}\]
Final simplification0.7
\[\leadsto \frac{(\left((\left(x \cdot x\right) \cdot \frac{1}{6} + \left({x}^{4} \cdot \frac{1}{120}\right))_*\right) \cdot \left(\sqrt[3]{8} \cdot x\right) + \left(\sqrt[3]{8} \cdot x\right))_*}{2}\]
