Part of complex plot disappears [mathematica]

[illuminates]

I have a very large expression:

    j - Sqrt[q^2 + qp^2 -
       2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 +
         1/2 (16 m5^2 + ma^2 + mp^2 -
            Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
             4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0

where

    \[Theta] = Pi/6; ma = 980; mp = 139;
     j = \[Sqrt](q^2 +
        1/2 (16 m5^2 + ma^2 + mp^2 +
           Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
            4 (ma^2 mp^2 - 16 m5^2 q^2)]))

And qp, m5, q is real and positive.There is two method to solve it, but they give some different result.
Namely, let's look at both methods

First solution

    eqn = j -
        Sqrt[q^2 + qp^2 -
          2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 +
           1/2 (16 m5^2 + ma^2 + mp^2 -
              Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
                4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0;
    With[{gensol = Solve[eqn , qp]},
      Block[{\[Theta] = Pi/6, ma = 980, mp = 139,
        j},(*subs vals when gensol is evaluated*)
       j = \[Sqrt](q^2 +
           1/2 (16 m5^2 + ma^2 + mp^2 +
              Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
                4 (ma^2 mp^2 - 16 m5^2 q^2)]));
       sols = gensol]];
    qpC13 = Compile[{{q, _Complex}, {m5, _Complex}},
       Evaluate[qp /. sols[[3]]],
       RuntimeOptions -> "EvaluateSymbolically" -> False] ;
       Plot3D[Re@qpC13[q, m5], {q, 0, 10000}, {m5, 0, 2000},
     AxesLabel -> Automatic]

Second solution

    eqn = j -
        Sqrt[q^2 + qp^2 -
          q qp Cos[\[Theta]]] - \[Sqrt](qp^2 +
           1/2 (16 m5^2 + ma^2 + mp^2 -
              Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
                4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0;
 
    With[{gensol = Solve[eqn, qp]},
      Block[{\[Theta] = Pi/6, ma = 980, mp = 139, j},
       j = \[Sqrt](q^2 +
           1/2 (16 m5^2 + ma^2 + mp^2 +
              Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
                4 (ma^2 mp^2 - 16 m5^2 q^2)]));
       sols = gensol]];
    opt = Experimental`OptimizeExpression[qp /. sols[[3]]];
    Block[{\[Theta] = Pi/6, f},
     f[q0_, m50_] :=
      Block[{q = SetPrecision[q0, 40], m5 = SetPrecision[m50, 40], qp},
       qp = First@opt;
       Re@qp /; Im@qp == 0];
     Plot3D[f[q, m5], {q, 0, 10000}, {m5, 0, 1000}, MaxRecursion -> 3,
      AxesLabel -> Automatic]]

The part of plot disappears in second solution! Why is this happening?

 

[NateD]

The reason is that the second solution uses the Experimental`OptimizeExpression function, which attempts to optimize the expression by performing numerical approximations. As a result, some of the values in the expression may be rounded off, or even set to zero in some cases. This can lead to a plot that does not display correctly, as part of the data is missing or incorrect.