\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]

↓

\[e^{\left(\left|m - n\right| - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right) - \ell}\]

Error

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

Derivation

Initial program 15.0
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
Simplified15.0
\[\leadsto \color{blue}{e^{\left(\left|m - n\right| - \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right) - \ell} \cdot \cos \left(\frac{K}{\frac{2}{m + n}} - M\right)}\]
Taylor expanded around 0 1.4
\[\leadsto e^{\left(\left|m - n\right| - \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right) - \ell} \cdot \color{blue}{1}\]
Final simplification1.4
\[\leadsto e^{\left(\left|m - n\right| - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right) - \ell}\]

Reproduce

herbie shell --seed 2019068 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))