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  • $\begingroup$ 1. You changed the data by Rest. 2. Your fit $ 2.76855 \cosh \left(1.65609 x^{2.93246} \sin \left(4.74049 x^{0.705923}\right)\right)$ is far away from optimal ones (see dropbox.com/s/o08c8x0cm0dutcl/deep%20fit.pdf?dl=0 ). $\endgroup$ Commented Jan 28, 2019 at 20:10
  • $\begingroup$ Yes I omitted the first data point(as @JimB recommended). My plot seems to fit the data quite well , not more. $\endgroup$ Commented Jan 28, 2019 at 20:16
  • $\begingroup$ One of the aims of my question is to pay attention of Mathematica developers to the fact that NonlinearModelFit faces problems with some model functions. $\endgroup$ Commented Jan 28, 2019 at 20:21