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

↓

\[\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\ell \cdot \left(\frac{1}{3} \cdot \ell\right) + 2\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Error

The X axis uses an exponential scale — Bits error versus `J`

Derivation

Initial program 17.1
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
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
\[\leadsto \left(J \cdot \color{blue}{\left({\ell}^{5} \cdot \frac{1}{60} + \ell \cdot \left(\ell \cdot \left(\frac{1}{3} \cdot \ell\right) + 2\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Final simplification0.4
\[\leadsto \left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\ell \cdot \left(\frac{1}{3} \cdot \ell\right) + 2\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Reproduce

herbie shell --seed 2019068 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))