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

↓

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

Error

Derivation

Initial program 17.5
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Simplified17.5
\[\leadsto \color{blue}{U + \cos \left(\frac{K}{2}\right) \cdot \left(J \cdot e^{\ell} - \frac{J}{e^{\ell}}\right)}\]
Taylor expanded around 0 0.6
\[\leadsto U + \cos \left(\frac{K}{2}\right) \cdot \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)}\]
Final simplification0.6
\[\leadsto U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot \ell\right) \cdot 2\right)\]

herbie shell --seed 2019100 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))