Initial program 17.0
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
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
\[\leadsto \left(J \cdot \color{blue}{(\left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right) \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60}\right))_*}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
- Using strategy
rm Applied add-sqr-sqrt0.7
\[\leadsto \left(J \cdot (\color{blue}{\left(\sqrt{(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*} \cdot \sqrt{(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*}\right)} \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60}\right))_*\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
- Using strategy
rm Applied expm1-log1p-u0.4
\[\leadsto \left(J \cdot (\color{blue}{\left((e^{\log_* (1 + \sqrt{(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*} \cdot \sqrt{(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*})} - 1)^*\right)} \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60}\right))_*\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Final simplification0.4
\[\leadsto U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot (\left((e^{\log_* (1 + \sqrt{(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*} \cdot \sqrt{(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*})} - 1)^*\right) \cdot \ell + \left({\ell}^{5} \cdot \frac{1}{60}\right))_*\right)\]
