Initial program 17.5
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Taylor expanded around 0 0.3
\[\leadsto \left(J \cdot \color{blue}{\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Simplified0.3
\[\leadsto \left(J \cdot \color{blue}{(\frac{1}{60} \cdot \left({\ell}^{5}\right) + \left(\ell \cdot (\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right))_*}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
- Using strategy
rm Applied fma-udef0.3
\[\leadsto \left(J \cdot (\frac{1}{60} \cdot \left({\ell}^{5}\right) + \left(\ell \cdot \color{blue}{\left(\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2\right)}\right))_*\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Applied distribute-lft-in0.3
\[\leadsto \left(J \cdot (\frac{1}{60} \cdot \left({\ell}^{5}\right) + \color{blue}{\left(\ell \cdot \left(\frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right) + \ell \cdot 2\right)})_*\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Final simplification0.3
\[\leadsto \left((\frac{1}{60} \cdot \left({\ell}^{5}\right) + \left(\ell \cdot 2 + \left(\frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right) \cdot \ell\right))_* \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
