Error

Derivation

1. Initial program 17.5

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

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. Simplified0.4

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

4. Taylor expanded around -inf 0.4

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

5. Simplified0.4

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

6. Final simplification0.4

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

Runtime

Time bar (total: 44.8s)Debug logProfile

herbie shell --seed 2018257 +o rules:numerics
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))