Error

Try it out

Derivation

1. Initial program 17.4

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

2. Taylor expanded around 0 0.4

   \[\leadsto \left(J \cdot \color{blue}{\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
3. Using strategy rm

4. Applied distribute-rgt-in0.4

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

5. Final simplification0.4

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

Reproduce

herbie shell --seed 2018365 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))

Details

Time bar (total: 19.0s)Debug log