Initial program 17.9
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Taylor expanded around 0 0.4
\[\leadsto \left(J \cdot \color{blue}{\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Simplified0.4
\[\leadsto \left(J \cdot \color{blue}{(\left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60}\right))_*}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Taylor expanded around -inf 0.4
\[\leadsto \color{blue}{\left(\frac{1}{3} \cdot \left(J \cdot {\ell}^{3}\right) + \left(2 \cdot \left(J \cdot \ell\right) + \frac{1}{60} \cdot \left(J \cdot {\ell}^{5}\right)\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U\]
Simplified0.4
\[\leadsto \color{blue}{(\left(\ell \cdot J\right) \cdot \left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) + \left(\left(\frac{1}{60} \cdot J\right) \cdot {\ell}^{5}\right))_*} \cdot \cos \left(\frac{K}{2}\right) + U\]
- Using strategy
rm Applied pow10.4
\[\leadsto (\left(\ell \cdot J\right) \cdot \left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) + \left(\left(\frac{1}{60} \cdot J\right) \cdot {\ell}^{5}\right))_* \cdot \color{blue}{{\left(\cos \left(\frac{K}{2}\right)\right)}^{1}} + U\]
Applied pow10.4
\[\leadsto \color{blue}{{\left((\left(\ell \cdot J\right) \cdot \left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) + \left(\left(\frac{1}{60} \cdot J\right) \cdot {\ell}^{5}\right))_*\right)}^{1}} \cdot {\left(\cos \left(\frac{K}{2}\right)\right)}^{1} + U\]
Applied pow-prod-down0.4
\[\leadsto \color{blue}{{\left((\left(\ell \cdot J\right) \cdot \left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) + \left(\left(\frac{1}{60} \cdot J\right) \cdot {\ell}^{5}\right))_* \cdot \cos \left(\frac{K}{2}\right)\right)}^{1}} + U\]
Simplified0.4
\[\leadsto {\color{blue}{\left(\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot (\left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) \cdot \ell + \left(\frac{1}{60} \cdot {\ell}^{5}\right))_*\right)}}^{1} + U\]
Final simplification0.4
\[\leadsto (\left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60}\right))_* \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right) + U\]
