Acer and VV, thanks for clearing up my lack of knowledge about the efficiency of @. Acer, your first group of three tests is to me definitive. The second group of three tests is insignificant regarding the efficiency of @.

See ?CurveFitting,ArrayInterpolation.

@vv I'd be very interested in discussing the speed of @. I chose what I did because it's easy to map without creating a user-defined function. Let LL be a very long list of short lists of digits. Which of the following is fastest?

map(parse@cat@op, LL);

map(`@`(parse,cat,op), LL);

map(L-> parse(cat(L[])), LL);

I'm prejudiced about the speed of the third because it uses a user-defined function. But perhaps my prejudice is unjustified.

Do you have some method to do it "by hand"? Perhaps by analyzing that we can figure out a way to do it with Maple. Of course, any method that starts with the final form is invalid. Maple has no trouble showing that the final form is equivalent to the starting form.

@mskalsi Yes, I did read Tom's solution. It's a fine solution. I simply propose an alternative.

@JessyOw My point is that whatever you want to add to each term, you can do it with +~.

I've told you before that Psi isn't a constant. You're taking code that I wrote regarding gamma and misappropriating it to Psi.

@Markiyan Hirnyk In your code for the first plot in this Answer, you plotted only 53 of the 182 points returned by DirectSearch. Why? Was it that the residuals for the other points were too high?

@Christian Wolinski I'd like to know how you segregated the branches by color in your first plot is this subthread (this Answer). Did you divide the solution points into equivalence classes based on distance? If so, did you measure the distance across all eight dimensions or only the three visible dimensions?

You say that you have a system of "equations". I see that f8, f9, and f10 are inequalities. That's fine. What about f1, ..., f7? I see no equals signs. Are they meant to be set equal to 0?

@AmirHosein Sadeghimanesh 

The "catch string" is the part after the procedure name in the error message. So, you just need to change your catch to

catch "no feasible solution found":

@Samuel Hollis 

Some (all?) expressions have a "zeroeth" operand, which is either the operator or a type specification of the expression (sometimes it's both). This zeroeth operand needs to be extracted separately, as you can see in my code for OpList. In the example, the `+`, `*`, `^`, and sin are all zeroeth operands.

@Bendesarts 

Psi isn't a constant. All that you need to redefine it is

local Psi;

@MUKUNDS 

For a basic (which is what you have) implicitplot, plottools:-getdata returns a sequence of lists, each of which is a piece of the curve. The string "curve" is the first item in each list, and a two-column matrix is the last. All of the data points of your implicitplot can be put into a single two-column matrix like this:

M:= <seq(`if`(a[1]="curve", a[-1], [][]), a= plottools:-getdata(E))>;

For me, this produces an 1197 x 2 matrix. I suppose that there may be a slight variation in the number of points in different versions of Maple.

@Vrbatim Well, if you're printing at 600 dpi or more, then your plot can accomodate millions of squares. But a relevant question is Can Maple print a plot at a higher resolution than is used on screen? I'm sure that someone here will know the answer to that.