\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

↓

\[U + \cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot \left(J \cdot \ell\right)\right)\]

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Initial program 17.6
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Initial simplification17.7
\[\leadsto U + \left(J \cdot e^{\ell} - \frac{J}{e^{\ell}}\right) \cdot \cos \left(\frac{K}{2}\right)\]
Taylor expanded around 0 0.5
\[\leadsto U + \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right)\]
Final simplification0.5
\[\leadsto U + \cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot \left(J \cdot \ell\right)\right)\]

herbie shell --seed 2018216 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))