Initial program 17.4
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
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 fma-udef0.4
\[\leadsto \left(J \cdot \color{blue}{\left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_* \cdot \ell + {\ell}^{5} \cdot \frac{1}{60}\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Applied distribute-rgt-in0.4
\[\leadsto \color{blue}{\left(\left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_* \cdot \ell\right) \cdot J + \left({\ell}^{5} \cdot \frac{1}{60}\right) \cdot J\right)} \cdot \cos \left(\frac{K}{2}\right) + U\]
- Using strategy
rm Applied distribute-rgt-out0.4
\[\leadsto \color{blue}{\left(J \cdot \left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_* \cdot \ell + {\ell}^{5} \cdot \frac{1}{60}\right)\right)} \cdot \cos \left(\frac{K}{2}\right) + U\]
Applied associate-*l*0.4
\[\leadsto \color{blue}{J \cdot \left(\left((\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_* \cdot \ell + {\ell}^{5} \cdot \frac{1}{60}\right) \cdot \cos \left(\frac{K}{2}\right)\right)} + U\]
Final simplification0.4
\[\leadsto U + \left(\cos \left(\frac{K}{2}\right) \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot (\frac{1}{3} \cdot \left(\ell \cdot \ell\right) + 2)_*\right)\right) \cdot J\]
