Normally there is some experimental or measurement error in the
data. It is rather rare to have all points lie exactly on the fitted
curve, unless whatever problem you are working on has given you
perfect data. When the number of coefficients equals the number of
data points, it usually gives a perfect fit. There are an infinite
number of equations that will fit your data perfectly, so always try
to find an equation that makes sense and actually models the problem
you are working on. Because the relationships in the problem being
worked on are often unknown, people use the function finders to try
and find the simplest and most reasonable equation that fits their
data.
The "polyfunctionals", which gave you a random equation that
could fit your data well, are linear combinations of functions like
x squared, square root of x, sine of x, etc. - and in the case of
tanh(x) the hyperbolic tangent of x. In the function finder's
"Equation Family Inclusion," uncheck the polyfunctionals and
possibly the polynomials - that will give you named equations only.
