How to build private function with built-in function's option

New analysis (in v10.1)

For your newly stated goal:

If I don't want to build a new function.I just wanna change the GeneralUtilities`BenchmarkPlot's default option into {"IncludeFits" -> True, "Models" -> Automatic, TimeConstraint -> .8}. ... Can it be implemented?

The standard options model in Mathematica means that this should work:

Options[BenchmarkPlot] =
  {TimeConstraint -> 8, MaxIterations -> 1024, 
   "IncludeFits" -> True, "Models" -> Automatic};

It does not however. That means that BenchmarkPlot or one of its subordinate functions is not written correctly. Let's have a look. Using PrintDefinitions from the same package we find that our code will call

GeneralUtilities`Benchmarking`PackagePrivate`plot

Which has the definition (contexts omitted):

plot[data_Association, opts___Rule] := 
  ListLogLogPlot[
   Sequence @@ 
    addfits[data,
     Lookup[{opts}, "Models", Automatic], 
     MemberQ[{opts}, "IncludeFits" -> True]],
   FilterOptions[opts], 
   PlotLegends -> fstyle[Keys[data]], GridLines -> Automatic, 
   PlotMarkers -> {$pmarker}, GridLinesStyle -> Opacity[0.05`], 
   AxesLabel -> {"n", "time (s)"}, ImageSize -> Medium, PlotRangeClipping -> True, 
   Mesh -> False, 
   PlotRange -> {Full, 
     With[{v = Values[data][[All, All, 2]]}, {LogFloor[Min[v]]*1.1`^(-1), 
       LogCeiling[Max[v]]*1.1`}]}];

Please draw your attention to the line MemberQ[{opts}, "IncludeFits" -> True] and note that here opts is the pattern that will match explicit options given to this function and nothing else. BenchmarkPlot does not pass all options to this function either. This means that only explicit appearences of "IncludeFits" will have effect. (Likewise for "Models" from the line above.)

To correct this we either need to expressly pass all of Options[BenchmarkPlot] to this inner plot function, or we need to modify plot so that it considers Options[BenchmarkPlot]. I'll do the latter.

<< "GeneralUtilities`"

With[{plot = GeneralUtilities`Benchmarking`PackagePrivate`plot},
  PrependTo[DownValues[plot],
    HoldPattern[plot[arg___]] :> 
      Block[{$fixGUBPopts = True}, 
        plot[arg, Sequence @@ Options[BenchmarkPlot]]
      ] /; ! TrueQ[$fixGUBPopts]
  ]
];

Options[BenchmarkPlot] =
  {TimeConstraint -> 8, MaxIterations -> 1024,
   "IncludeFits" -> True, "Models" -> Automatic};

BenchmarkPlot[{SortBy[#, Identity] &, Sort}, Range]

---

Old answer

I wrote a fairly lengthy answer hoping to guide just this sort of thing; please take a look:

• Functions with Options

From your comment

But Options[myBen4] get {}. I hope it can get all options. Can it be implement?

I think you want something like this.

Options[myBen] = {"IncludeFits" -> True, "Models" -> Automatic, 
   TimeConstraint -> .8};

myBen[args__, opts : OptionsPattern[]] := 
 BenchmarkPlot[args, opts, Sequence @@ Options[myBen]]

myBen[{SortBy[#, Identity] &, Sort}, Range]

_{(source: clouddn.com)}

And it meet the extra need:

Options[myBen]

{"IncludeFits"->True,Models->Automatic,TimeConstraint->0.8}

Including the options in the definition of your auxiliary function seems to work fine:

myBen3[x__, opt : OptionsPattern[]] := 
  GeneralUtilities`BenchmarkPlot[x, opt, "IncludeFits" -> True]

Above I left off the TimeConstraint option from the definition on purpose, because I wanted to showcase the fact that the helper function still correctly passes on extra options to BenchmarkPlot. Compare for instance:

myBen3[{SortBy[#, Identity] &, Sort}, Range, TimeConstraint -> 0.3]
myBen3[{SortBy[#, Identity] &, Sort}, Range]

---

So a more complete definition would be:

myBen4[x__, opt : OptionsPattern[]] :=
 GeneralUtilities`BenchmarkPlot[x, opt, "IncludeFits" -> True, TimeConstraint -> 8]