Is there any alternative for conditional plot that gives a more precise result in a shorter time?

Question

I have the given function $Func$ and want to have a plot of those domains where $-3\leq Func\leq 3$ in precise details. I am using Plot[ConditionalExpression[1, -3 <= Func <= 3] for and I obtain this plot

Questions.

1. As can be seen, by increasing PlotPoints, MaxRecursion, and WorkingPrecision, the accuracy of the plots changes; however, when I set the mentioned items a big number, it takes a lot of time. My question is: is there any alternative rather than a conditional plot that gives a more precise result in a shorter time?

p1 = Plot[ConditionalExpression[1, -3 <= Func <= 3], {x, 11, 16}, PlotPoints -> 30, MaxRecursion -> 2, PlotStyle -> Directive[Red, CapForm["Butt"], Opacity[1], Thickness[.005]], Axes -> {False, False}, WorkingPrecision -> 20] ;
p2 = Plot[ConditionalExpression[2, -3 <= Func <= 3], {x, 11, 16}, PlotPoints -> 50, MaxRecursion -> 4, PlotStyle -> Directive[Blue, CapForm["Butt"], Opacity[1], Thickness[.005]], Axes -> {False, False}, WorkingPrecision -> 100] ;
p3 = Plot[ConditionalExpression[3, -3 <= Func <= 3], {x, 11, 16}, PlotPoints -> 80, MaxRecursion -> 6, PlotStyle -> Directive[Green, CapForm["Butt"], Opacity[1], Thickness[.005]], Axes -> {False, False}, WorkingPrecision -> 200] ;

Pic = Show[{p1, p2, p3}, PlotRange -> {{11, 16}, {0, 4}} ,  AspectRatio -> 1/6]

the function

Func:=(1/(1024*(-1 + x)^11*(1 + x)^11))*Csc[x]^11*(-264*x*(-1 + x^2)^2*(777 + 11928*x^2 + 73148*x^4 + 275752*x^6 + 653046*x^8 + 275752*x^10 + 73148*x^12 + 11928*x^14 + 777*x^16)*Cos[Pi/22] - 88*x*(-1 + x^2)^4*(69 + 2258*x^2 - 7733*x^4 - 132548*x^6 - 7733*x^8 + 2258*x^10 + 69*x^12)*Cos[(3*Pi)/22] + 88*x*(-1 + x^2)^6*(183 + 2532*x^2 - 7990*x^4 + 2532*x^6 + 183*x^8)*Cos[(5*Pi)/22] - 2816*(-1 + x^2)^2*(1 + x^2)^9*Cos[(5/22)*(Pi - 88*x)] + 
   22*(13031 + 2359*x + 94165*x^2 + 27282*x^3 + 247529*x^4 + 152299*x^5 + 424547*x^6 + 605784*x^7 + 1019270*x^8 + 1805534*x^9 + 2133618*x^10 + 2677804*x^11 + 2133618*x^12 + 1805534*x^13 + 1019270*x^14 + 605784*x^15 + 424547*x^16 + 152299*x^17 + 247529*x^18 + 27282*x^19 + 94165*x^20 + 2359*x^21 + 13031*x^22)*Cos[(5/22)*(Pi - 44*x)] - 704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Cos[Pi/22 - 18*x] + 704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Cos[(3*Pi)/22 - 18*x] + 176*(-1 + x^2)^2*(1 + x^2)^5*(247 + 612*x^2 + 330*x^4 + 612*x^6 + 247*x^8)*Cos[Pi/22 - 16*x] + 
   176*(-1 + x^2)^2*(1 + x^2)^5*(247 + 612*x^2 + 330*x^4 + 612*x^6 + 247*x^8)*Cos[(5*Pi)/22 - 16*x] - 264*(-1 + x^2)^2*(1 + x^2)^3*(69 + 1298*x^2 + 3019*x^4 + 3516*x^6 + 3019*x^8 + 1298*x^10 + 69*x^12)*Cos[Pi/22 - 14*x] + 44*(-1 + x^2)^2*(1 + x^2)^3*(413 - 8*x + 7762*x^2 - 40*x^3 + 18099*x^4 + 48*x^5 + 21180*x^6 + 48*x^7 + 18099*x^8 - 40*x^9 + 7762*x^10 - 8*x^11 + 413*x^12)*Cos[(3*Pi)/22 - 14*x] - 1056*(-1 + x^2)^2*(1 + x^2)^4*(17 - 2*x + 301*x^2 - 8*x^3 + 450*x^4 + 20*x^5 + 450*x^6 - 8*x^7 + 301*x^8 - 2*x^9 + 17*x^10)*Cos[(5*Pi)/22 - 14*x] - 
   11*(-1 + x^2)^2*(24547 - 48*x + 135563*x^2 - 192*x^3 + 343804*x^4 + 576*x^5 + 563948*x^6 + 192*x^7 + 701610*x^8 - 1056*x^9 + 701610*x^10 + 192*x^11 + 563948*x^12 + 576*x^13 + 343804*x^14 - 192*x^15 + 135563*x^16 - 48*x^17 + 24547*x^18)*Cos[Pi/22 - 12*x] - 22*(-1 + x^2)^2*(12691 - 363*x + 108935*x^2 - 4480*x^3 + 375232*x^4 - 18340*x^5 + 763352*x^6 + 2752*x^7 + 1099086*x^8 + 40862*x^9 + 1099086*x^10 + 2752*x^11 + 763352*x^12 - 18340*x^13 + 375232*x^14 - 4480*x^15 + 108935*x^16 - 363*x^17 + 12691*x^18)*Cos[(3*Pi)/22 - 10*x] + 
   44*(-1 + x^2)^2*(16295 + 167*x + 72447*x^2 + 488*x^3 + 155964*x^4 + 2180*x^5 + 251340*x^6 + 12888*x^7 + 290386*x^8 - 31446*x^9 + 290386*x^10 + 12888*x^11 + 251340*x^12 + 2180*x^13 + 155964*x^14 + 488*x^15 + 72447*x^16 + 167*x^17 + 16295*x^18)*Cos[Pi/22 - 8*x] - 44*(-1 + x^2)^2*(16373 + 999*x + 76477*x^2 + 13080*x^3 + 189364*x^4 + 72932*x^5 + 386276*x^6 + 270888*x^7 + 707766*x^8 + 463850*x^9 + 707766*x^10 + 270888*x^11 + 386276*x^12 + 72932*x^13 + 189364*x^14 + 13080*x^15 + 76477*x^16 + 999*x^17 + 16373*x^18)*Cos[(3*Pi)/22 - 8*x] + 
   44*(-1 + x^2)^2*(16015 - 2003*x + 63751*x^2 - 28840*x^3 + 78204*x^4 - 179860*x^5 - 134196*x^6 - 651928*x^7 - 613598*x^8 - 1027250*x^9 - 613598*x^10 - 651928*x^11 - 134196*x^12 - 179860*x^13 + 78204*x^14 - 28840*x^15 + 63751*x^16 - 2003*x^17 + 16015*x^18)*Cos[(5*Pi)/22 - 8*x] - 22*(-1 + x^2)^2*(52199 - 345*x + 315499*x^2 - 10560*x^3 + 899168*x^4 - 54156*x^5 + 1682776*x^6 - 112896*x^7 + 2555382*x^8 + 355914*x^9 + 2555382*x^10 - 112896*x^11 + 1682776*x^12 - 54156*x^13 + 899168*x^14 - 10560*x^15 + 315499*x^16 - 345*x^17 + 52199*x^18)*Cos[Pi/22 - 6*x] + 
   22*(52771 + 4399*x + 234321*x^2 + 52642*x^3 + 475893*x^4 + 275331*x^5 + 786607*x^6 + 982808*x^7 + 1480446*x^8 + 3255374*x^9 + 4834282*x^10 + 6587532*x^11 + 4834282*x^12 + 3255374*x^13 + 1480446*x^14 + 982808*x^15 + 786607*x^16 + 275331*x^17 + 475893*x^18 + 52642*x^19 + 234321*x^20 + 4399*x^21 + 52771*x^22)*Cos[(3*Pi)/22 - 6*x] - 22*(-1 + x^2)^2*(51891 - 3691*x + 305759*x^2 - 47488*x^3 + 827048*x^4 - 208292*x^5 + 1552080*x^6 - 13632*x^7 + 2768246*x^8 + 546206*x^9 + 2768246*x^10 - 13632*x^11 + 1552080*x^12 - 208292*x^13 + 827048*x^14 - 47488*x^15 + 305759*x^16 - 3691*x^17 + 51891*x^18)*
    Cos[(5*Pi)/22 - 6*x] - 11*(-1 + x^2)^2*(72015 + 6240*x + 310551*x^2 + 102720*x^3 + 813036*x^4 + 590592*x^5 + 2145436*x^6 + 2003648*x^7 + 4916498*x^8 + 5603648*x^9 + 4916498*x^10 + 2003648*x^11 + 2145436*x^12 + 590592*x^13 + 813036*x^14 + 102720*x^15 + 310551*x^16 + 6240*x^17 + 72015*x^18)*Cos[Pi/22 - 4*x] + 11*(-1 + x^2)^2*(70013 - 9616*x + 231445*x^2 - 142464*x^3 + 145220*x^4 - 945600*x^5 - 1033516*x^6 - 3497856*x^7 - 4918186*x^8 - 7324000*x^9 - 4918186*x^10 - 3497856*x^11 - 1033516*x^12 - 945600*x^13 + 145220*x^14 - 142464*x^15 + 231445*x^16 - 9616*x^17 + 70013*x^18)*Cos[(3*Pi)/22 - 4*x] - 
   11*(-1 + x^2)^2*(71223 + 3024*x + 285567*x^2 + 16512*x^3 + 555340*x^4 - 123712*x^5 + 438524*x^6 - 275584*x^7 + 1401858*x^8 + 759520*x^9 + 1401858*x^10 - 275584*x^11 + 438524*x^12 - 123712*x^13 + 555340*x^14 + 16512*x^15 + 285567*x^16 + 3024*x^17 + 71223*x^18)*Cos[(5*Pi)/22 - 4*x] + 44*(49997 + 3621*x + 173407*x^2 + 48822*x^3 + 294011*x^4 + 230337*x^5 + 476033*x^6 + 635912*x^7 + 1205090*x^8 + 1392922*x^9 + 3306486*x^10 + 6386820*x^11 + 3306486*x^12 + 1392922*x^13 + 1205090*x^14 + 635912*x^15 + 476033*x^16 + 230337*x^17 + 294011*x^18 + 48822*x^19 + 173407*x^20 + 3621*x^21 + 49997*x^22)*
    Cos[Pi/22 - 2*x] - 44*(-1 + x^2)^2*(49568 - 1083*x + 257024*x^2 - 17792*x^3 + 651936*x^4 - 90468*x^5 + 1160160*x^6 - 177472*x^7 + 2010080*x^8 + 573630*x^9 + 2010080*x^10 - 177472*x^11 + 1160160*x^12 - 90468*x^13 + 651936*x^14 - 17792*x^15 + 257024*x^16 - 1083*x^17 + 49568*x^18)*Cos[(3*Pi)/22 - 2*x] + 44*(-1 + x^2)^2*(49667 - 129*x + 262895*x^2 - 4800*x^3 + 697256*x^4 - 21740*x^5 + 1364304*x^6 + 96384*x^7 + 1754646*x^8 - 139430*x^9 + 1754646*x^10 + 96384*x^11 + 1364304*x^12 - 21740*x^13 + 697256*x^14 - 4800*x^15 + 262895*x^16 - 129*x^17 + 49667*x^18)*Cos[(5*Pi)/22 - 2*x] - 
   44*(-1 + x)^2*(49997 + 96373*x + 316156*x^2 + 487117*x^3 + 952089*x^4 + 1186724*x^5 + 1897392*x^6 + 1972148*x^7 + 3251994*x^8 + 3138918*x^9 + 6332328*x^10 + 3138918*x^11 + 3251994*x^12 + 1972148*x^13 + 1897392*x^14 + 1186724*x^15 + 952089*x^16 + 487117*x^17 + 316156*x^18 + 96373*x^19 + 49997*x^20)*Cos[Pi/22 + 2*x] + 44*(-1 + x^2)^2*(49568 + 1083*x + 257024*x^2 + 17792*x^3 + 651936*x^4 + 90468*x^5 + 1160160*x^6 + 177472*x^7 + 2010080*x^8 - 573630*x^9 + 2010080*x^10 + 177472*x^11 + 1160160*x^12 + 90468*x^13 + 651936*x^14 + 17792*x^15 + 257024*x^16 + 1083*x^17 + 49568*x^18)*Cos[(3*Pi)/22 + 2*x] - 
   44*(-1 + x^2)^2*(49667 + 129*x + 262895*x^2 + 4800*x^3 + 697256*x^4 + 21740*x^5 + 1364304*x^6 - 96384*x^7 + 1754646*x^8 + 139430*x^9 + 1754646*x^10 - 96384*x^11 + 1364304*x^12 + 21740*x^13 + 697256*x^14 + 4800*x^15 + 262895*x^16 + 129*x^17 + 49667*x^18)*Cos[(5*Pi)/22 + 2*x] + 11*(-1 + x^2)^2*(72015 - 6240*x + 310551*x^2 - 102720*x^3 + 813036*x^4 - 590592*x^5 + 2145436*x^6 - 2003648*x^7 + 4916498*x^8 - 5603648*x^9 + 4916498*x^10 - 2003648*x^11 + 2145436*x^12 - 590592*x^13 + 813036*x^14 - 102720*x^15 + 310551*x^16 - 6240*x^17 + 72015*x^18)*Cos[Pi/22 + 4*x] - 
   11*(-1 + x^2)^2*(70013 + 9616*x + 231445*x^2 + 142464*x^3 + 145220*x^4 + 945600*x^5 - 1033516*x^6 + 3497856*x^7 - 4918186*x^8 + 7324000*x^9 - 4918186*x^10 + 3497856*x^11 - 1033516*x^12 + 945600*x^13 + 145220*x^14 + 142464*x^15 + 231445*x^16 + 9616*x^17 + 70013*x^18)*Cos[(3*Pi)/22 + 4*x] + 11*(-1 + x^2)^2*(71223 - 3024*x + 285567*x^2 - 16512*x^3 + 555340*x^4 + 123712*x^5 + 438524*x^6 + 275584*x^7 + 1401858*x^8 - 759520*x^9 + 1401858*x^10 + 275584*x^11 + 438524*x^12 + 123712*x^13 + 555340*x^14 - 16512*x^15 + 285567*x^16 - 3024*x^17 + 71223*x^18)*Cos[(5*Pi)/22 + 4*x] + 
   22*(-1 + x^2)^2*(52199 + 345*x + 315499*x^2 + 10560*x^3 + 899168*x^4 + 54156*x^5 + 1682776*x^6 + 112896*x^7 + 2555382*x^8 - 355914*x^9 + 2555382*x^10 + 112896*x^11 + 1682776*x^12 + 54156*x^13 + 899168*x^14 + 10560*x^15 + 315499*x^16 + 345*x^17 + 52199*x^18)*Cos[Pi/22 + 6*x] - 22*(-1 + x)^2*(52771 + 101143*x + 383836*x^2 + 613887*x^3 + 1319831*x^4 + 1750444*x^5 + 2967664*x^6 + 3202076*x^7 + 4916934*x^8 + 3376418*x^9 + 6670184*x^10 + 3376418*x^11 + 4916934*x^12 + 3202076*x^13 + 2967664*x^14 + 1750444*x^15 + 1319831*x^16 + 613887*x^17 + 383836*x^18 + 101143*x^19 + 52771*x^20)*Cos[(3*Pi)/22 + 6*x] + 
   22*(-1 + x^2)^2*(51891 + 3691*x + 305759*x^2 + 47488*x^3 + 827048*x^4 + 208292*x^5 + 1552080*x^6 + 13632*x^7 + 2768246*x^8 - 546206*x^9 + 2768246*x^10 + 13632*x^11 + 1552080*x^12 + 208292*x^13 + 827048*x^14 + 47488*x^15 + 305759*x^16 + 3691*x^17 + 51891*x^18)*Cos[(5*Pi)/22 + 6*x] - 44*(-1 + x^2)^2*(16295 - 167*x + 72447*x^2 - 488*x^3 + 155964*x^4 - 2180*x^5 + 251340*x^6 - 12888*x^7 + 290386*x^8 + 31446*x^9 + 290386*x^10 - 12888*x^11 + 251340*x^12 - 2180*x^13 + 155964*x^14 - 488*x^15 + 72447*x^16 - 167*x^17 + 16295*x^18)*Cos[Pi/22 + 8*x] + 
   44*(-1 + x^2)^2*(16373 - 999*x + 76477*x^2 - 13080*x^3 + 189364*x^4 - 72932*x^5 + 386276*x^6 - 270888*x^7 + 707766*x^8 - 463850*x^9 + 707766*x^10 - 270888*x^11 + 386276*x^12 - 72932*x^13 + 189364*x^14 - 13080*x^15 + 76477*x^16 - 999*x^17 + 16373*x^18)*Cos[(3*Pi)/22 + 8*x] - 44*(-1 + x^2)^2*(16015 + 2003*x + 63751*x^2 + 28840*x^3 + 78204*x^4 + 179860*x^5 - 134196*x^6 + 651928*x^7 - 613598*x^8 + 1027250*x^9 - 613598*x^10 + 651928*x^11 - 134196*x^12 + 179860*x^13 + 78204*x^14 + 28840*x^15 + 63751*x^16 + 2003*x^17 + 16015*x^18)*Cos[(5*Pi)/22 + 8*x] - 
   22*(-1 + x^2)^2*(12691 + 163*x + 109863*x^2 + 832*x^3 + 383904*x^4 + 1732*x^5 + 782968*x^6 - 2688*x^7 + 1069870*x^8 - 78*x^9 + 1069870*x^10 - 2688*x^11 + 782968*x^12 + 1732*x^13 + 383904*x^14 + 832*x^15 + 109863*x^16 + 163*x^17 + 12691*x^18)*Cos[Pi/22 + 10*x] + 22*(-1 + x^2)^2*(12691 + 363*x + 108935*x^2 + 4480*x^3 + 375232*x^4 + 18340*x^5 + 763352*x^6 - 2752*x^7 + 1099086*x^8 - 40862*x^9 + 1099086*x^10 - 2752*x^11 + 763352*x^12 + 18340*x^13 + 375232*x^14 + 4480*x^15 + 108935*x^16 + 363*x^17 + 12691*x^18)*Cos[(3*Pi)/22 + 10*x] + 
   11*(-1 + x^2)^2*(24547 + 48*x + 135563*x^2 + 192*x^3 + 343804*x^4 - 576*x^5 + 563948*x^6 - 192*x^7 + 701610*x^8 + 1056*x^9 + 701610*x^10 - 192*x^11 + 563948*x^12 - 576*x^13 + 343804*x^14 + 192*x^15 + 135563*x^16 + 48*x^17 + 24547*x^18)*Cos[Pi/22 + 12*x] + 11*(-1 + x^2)^2*(24747 - 1472*x + 141523*x^2 - 16640*x^3 + 386524*x^4 - 96000*x^5 + 742092*x^6 - 278272*x^7 + 1064410*x^8 - 394880*x^9 + 1064410*x^10 - 278272*x^11 + 742092*x^12 - 96000*x^13 + 386524*x^14 - 16640*x^15 + 141523*x^16 - 1472*x^17 + 24747*x^18)*Cos[(5*Pi)/22 + 12*x] + 
   264*(-1 + x^2)^2*(1 + x^2)^3*(69 + 1298*x^2 + 3019*x^4 + 3516*x^6 + 3019*x^8 + 1298*x^10 + 69*x^12)*Cos[Pi/22 + 14*x] - 44*(-1 + x^2)^2*(1 + x^2)^3*(413 + 8*x + 7762*x^2 + 40*x^3 + 18099*x^4 - 48*x^5 + 21180*x^6 - 48*x^7 + 18099*x^8 + 40*x^9 + 7762*x^10 + 8*x^11 + 413*x^12)*Cos[(3*Pi)/22 + 14*x] + 1056*(-1 + x^2)^2*(1 + x^2)^4*(17 + 2*x + 301*x^2 + 8*x^3 + 450*x^4 - 20*x^5 + 450*x^6 + 8*x^7 + 301*x^8 + 2*x^9 + 17*x^10)*Cos[(5*Pi)/22 + 14*x] - 176*(-1 + x^2)^2*(1 + x^2)^5*(247 + 612*x^2 + 330*x^4 + 612*x^6 + 247*x^8)*Cos[Pi/22 + 16*x] + 
   176*(-1 + x^2)^2*(1 + x^2)^5*(247 + 612*x^2 + 330*x^4 + 612*x^6 + 247*x^8)*Cos[(3*Pi)/22 + 16*x] - 176*(-1 + x^2)^2*(1 + x^2)^5*(247 + 612*x^2 + 330*x^4 + 612*x^6 + 247*x^8)*Cos[(5*Pi)/22 + 16*x] + 704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Cos[Pi/22 + 18*x] - 704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Cos[(3*Pi)/22 + 18*x] + 704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Cos[(5*Pi)/22 + 18*x] + 2816*(-1 + x^2)^2*(1 + x^2)^9*Cos[Pi/22 + 20*x] - 2816*(-1 + x^2)^2*(1 + x^2)^9*Cos[(3*Pi)/22 + 20*x] - 
   22*(-1 + x)^2*(13031 + 23703*x + 128540*x^2 + 206095*x^3 + 531179*x^4 + 703964*x^5 + 1301296*x^6 + 1292844*x^7 + 2303662*x^8 + 1508946*x^9 + 2847848*x^10 + 1508946*x^11 + 2303662*x^12 + 1292844*x^13 + 1301296*x^14 + 703964*x^15 + 531179*x^16 + 206095*x^17 + 128540*x^18 + 23703*x^19 + 13031*x^20)*Cos[(5/22)*(Pi + 44*x)] - 44*(-1 + x)^2*(1 + x^2)^3*(473 + 498*x + 9059*x^2 + 13716*x^3 + 30401*x^4 + 26670*x^5 + 54275*x^6 + 24728*x^7 + 54275*x^8 + 26670*x^9 + 30401*x^10 + 13716*x^11 + 9059*x^12 + 498*x^13 + 473*x^14)*Cos[(7/22)*(Pi + 44*x)] + 
   5632*(-1 + x)^2*x*(1 + x^2)^7*(1 - 6*x - 6*x^2 - 6*x^3 + x^4)*Cos[(9/22)*(Pi + 44*x)] - 11*(-1 + x^2)^2*(24569 - 64*x + 135985*x^2 - 512*x^3 + 345204*x^4 - 2816*x^5 + 565188*x^6 + 512*x^7 + 698526*x^8 + 5760*x^9 + 698526*x^10 + 512*x^11 + 565188*x^12 - 2816*x^13 + 345204*x^14 - 512*x^15 + 135985*x^16 - 64*x^17 + 24569*x^18)*Cos[(3/22)*(Pi + 88*x)] + 2816*(-1 + x^2)^2*(1 + x^2)^9*Cos[(5/22)*(Pi + 88*x)] - 176*x*(-1 + x^2)^8*(31 - 14*x^2 + 31*x^4)*Sin[Pi/11] - 88*x*(-1 + x^2)^6*(399 - 604*x^2 + 1690*x^4 - 604*x^6 + 399*x^8)*Sin[(2*Pi)/11] - 
   704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Sin[(2/11)*(Pi - 99*x)] + 176*(-1 + x^2)^2*(1 + x^2)^5*(249 - 16*x + 668*x^2 - 112*x^3 + 470*x^4 - 112*x^5 + 668*x^6 - 16*x^7 + 249*x^8)*Sin[(2/11)*(Pi - 88*x)] - 11*(-1 + x^2)^2*(23859 + 5056*x + 114715*x^2 + 69376*x^3 + 157564*x^4 + 406272*x^5 - 170772*x^6 + 1110272*x^7 - 715190*x^8 + 1536640*x^9 - 715190*x^10 + 1110272*x^11 - 170772*x^12 + 406272*x^13 + 157564*x^14 + 69376*x^15 + 114715*x^16 + 5056*x^17 + 23859*x^18)*Sin[(2/11)*(Pi - 66*x)] + 
   22*(-1 + x^2)^2*(12221 + 3473*x + 96577*x^2 + 38720*x^3 + 312232*x^4 + 91180*x^5 + 724000*x^6 - 37632*x^7 + 1214266*x^8 - 191482*x^9 + 1214266*x^10 - 37632*x^11 + 724000*x^12 + 91180*x^13 + 312232*x^14 + 38720*x^15 + 96577*x^16 + 3473*x^17 + 12221*x^18)*Sin[(2/11)*(Pi - 55*x)] + 2816*(-1 + x^2)^2*(1 + x^2)^9*Sin[Pi/11 - 20*x] - 2816*(-1 + x^2)^2*(1 + x^2)^9*Sin[(2*Pi)/11 - 20*x] - 176*(-1 + x^2)^2*(1 + x^2)^5*(221 + 176*x + 76*x^2 + 976*x^3 - 850*x^4 + 976*x^5 + 76*x^6 + 176*x^7 + 221*x^8)*Sin[Pi/11 - 16*x] + 
   44*(-1 + x^2)^2*(1 + x^2)^3*(163 + 1336*x + 4846*x^2 + 3096*x^3 + 17933*x^4 - 4432*x^5 + 27844*x^6 - 4432*x^7 + 17933*x^8 + 3096*x^9 + 4846*x^10 + 1336*x^11 + 163*x^12)*Sin[Pi/11 - 14*x] + 11*(-1 + x^2)^2*(25489 - 2864*x + 137929*x^2 + 5184*x^3 + 324500*x^4 + 29760*x^5 + 540900*x^6 - 5184*x^7 + 740654*x^8 - 53792*x^9 + 740654*x^10 - 5184*x^11 + 540900*x^12 + 29760*x^13 + 324500*x^14 + 5184*x^15 + 137929*x^16 - 2864*x^17 + 25489*x^18)*Sin[Pi/11 - 12*x] - 
   22*(-1 + x^2)^2*(12671 + 1126*x + 106967*x^2 + 3840*x^3 + 386652*x^4 - 8440*x^5 + 792300*x^6 - 4480*x^7 + 1060706*x^8 + 15908*x^9 + 1060706*x^10 - 4480*x^11 + 792300*x^12 - 8440*x^13 + 386652*x^14 + 3840*x^15 + 106967*x^16 + 1126*x^17 + 12671*x^18)*Sin[Pi/11 - 10*x] - 44*(-1 + x^2)^2*(16381 - 278*x + 72181*x^2 + 1872*x^3 + 153700*x^4 - 2344*x^5 + 244532*x^6 - 3024*x^7 + 299638*x^8 + 7548*x^9 + 299638*x^10 - 3024*x^11 + 244532*x^12 - 2344*x^13 + 153700*x^14 + 1872*x^15 + 72181*x^16 - 278*x^17 + 16381*x^18)*Sin[Pi/11 - 8*x] + 
   44*(-1 + x^2)^2*(16423 - 949*x + 75359*x^2 - 2168*x^3 + 145884*x^4 + 28660*x^5 + 205484*x^6 + 6072*x^7 + 343282*x^8 - 63230*x^9 + 343282*x^10 + 6072*x^11 + 205484*x^12 + 28660*x^13 + 145884*x^14 - 2168*x^15 + 75359*x^16 - 949*x^17 + 16423*x^18)*Sin[(2*Pi)/11 - 8*x] + 22*(-1 + x^2)^2*(52055 + 1138*x + 320735*x^2 - 2304*x^3 + 946060*x^4 - 1256*x^5 + 1770172*x^6 + 7552*x^7 + 2416002*x^8 - 10260*x^9 + 2416002*x^10 + 7552*x^11 + 1770172*x^12 - 1256*x^13 + 946060*x^14 - 2304*x^15 + 320735*x^16 + 1138*x^17 + 52055*x^18)*Sin[Pi/11 - 6*x] - 
   22*(-1 + x^2)^2*(52293 + 643*x + 316745*x^2 + 15936*x^3 + 923528*x^4 - 17596*x^5 + 1837824*x^6 - 40320*x^7 + 2374634*x^8 + 82674*x^9 + 2374634*x^10 - 40320*x^11 + 1837824*x^12 - 17596*x^13 + 923528*x^14 + 15936*x^15 + 316745*x^16 + 643*x^17 + 52293*x^18)*Sin[(2*Pi)/11 - 6*x] + 11*(-1 + x^2)^2*(71797 - 304*x + 276109*x^2 + 1728*x^3 + 546660*x^4 - 6848*x^5 + 802292*x^6 + 16704*x^7 + 1055654*x^8 - 22560*x^9 + 1055654*x^10 + 16704*x^11 + 802292*x^12 - 6848*x^13 + 546660*x^14 + 1728*x^15 + 276109*x^16 - 304*x^17 + 71797*x^18)*Sin[Pi/11 - 4*x] - 
   11*(-1 + x^2)^2*(71135 - 2000*x + 284903*x^2 + 7552*x^3 + 501100*x^4 + 15168*x^5 + 892828*x^6 - 96640*x^7 + 1002546*x^8 + 151840*x^9 + 1002546*x^10 - 96640*x^11 + 892828*x^12 + 15168*x^13 + 501100*x^14 + 7552*x^15 + 284903*x^16 - 2000*x^17 + 71135*x^18)*Sin[(2*Pi)/11 - 4*x] - 88*(-1 + x^2)^2*(24861 + 95*x + 133003*x^2 - 544*x^3 + 356438*x^4 + 1364*x^5 + 658074*x^6 - 2080*x^7 + 892008*x^8 + 2330*x^9 + 892008*x^10 - 2080*x^11 + 658074*x^12 + 1364*x^13 + 356438*x^14 - 544*x^15 + 133003*x^16 + 95*x^17 + 24861*x^18)*Sin[Pi/11 - 2*x] + 
   44*(-1 + x^2)^2*(49678 + 313*x + 263726*x^2 + 2432*x^3 + 721096*x^4 - 13172*x^5 + 1305608*x^6 + 25792*x^7 + 1788660*x^8 - 30730*x^9 + 1788660*x^10 + 25792*x^11 + 1305608*x^12 - 13172*x^13 + 721096*x^14 + 2432*x^15 + 263726*x^16 + 313*x^17 + 49678*x^18)*Sin[(2*Pi)/11 - 2*x] - 88*(-1 + x^2)^2*(24933 + 132587*x^2 + 357438*x^4 + 656850*x^6 + 892576*x^8 + 892576*x^10 + 656850*x^12 + 357438*x^14 + 132587*x^16 + 24933*x^18)*Sin[2*x] + 11*(-1 + x^2)^2*(71095 + 279167*x^2 + 540620*x^4 + 809084*x^6 + 1052546*x^8 + 1052546*x^10 + 809084*x^12 + 540620*x^14 + 279167*x^16 + 71095*x^18)*Sin[4*x] + 
   22*(-1 + x^2)^2*(52469 + 321557*x^2 + 939580*x^4 + 1780540*x^6 + 2410878*x^8 + 2410878*x^10 + 1780540*x^12 + 939580*x^14 + 321557*x^16 + 52469*x^18)*Sin[6*x] - 44*(-1 + x^2)^2*(16415 + 72039*x^2 + 155692*x^4 + 239068*x^6 + 303218*x^8 + 303218*x^10 + 239068*x^12 + 155692*x^14 + 72039*x^16 + 16415*x^18)*Sin[8*x] - 22*(-1 + x^2)^2*(12349 + 111213*x^2 + 386380*x^4 + 778028*x^6 + 1071326*x^8 + 1071326*x^10 + 778028*x^12 + 386380*x^14 + 111213*x^16 + 12349*x^18)*Sin[10*x] + 
   11*(-1 + x^2)^2*(24619 + 134995*x^2 + 343772*x^4 + 566732*x^6 + 699354*x^8 + 699354*x^10 + 566732*x^12 + 343772*x^14 + 134995*x^16 + 24619*x^18)*Sin[12*x] + 44*(-1 + x^2)^2*(1 + x^2)^3*(309 + 7714*x^2 + 19099*x^4 + 19484*x^6 + 19099*x^8 + 7714*x^10 + 309*x^12)*Sin[14*x] - 176*(-1 + x^2)^2*(1 + x^2)^5*(277 + 428*x^2 + 638*x^4 + 428*x^6 + 277*x^8)*Sin[16*x] + 11264*(-1 + x^2)^2*(1 + x^2)^7*(1 - 4*x^2 + x^4)*Sin[18*x] - 2816*(-1 + x^2)^2*(1 + x^2)^9*Sin[20*x] + 1024*(1 + x^2)^11*Sin[22*x] + 
   88*(-1 + x^2)^2*(24861 - 95*x + 133003*x^2 + 544*x^3 + 356438*x^4 - 1364*x^5 + 658074*x^6 + 2080*x^7 + 892008*x^8 - 2330*x^9 + 892008*x^10 + 2080*x^11 + 658074*x^12 - 1364*x^13 + 356438*x^14 + 544*x^15 + 133003*x^16 - 95*x^17 + 24861*x^18)*Sin[Pi/11 + 2*x] - 44*(-1 + x^2)^2*(49678 - 313*x + 263726*x^2 - 2432*x^3 + 721096*x^4 + 13172*x^5 + 1305608*x^6 - 25792*x^7 + 1788660*x^8 + 30730*x^9 + 1788660*x^10 - 25792*x^11 + 1305608*x^12 + 13172*x^13 + 721096*x^14 - 2432*x^15 + 263726*x^16 - 313*x^17 + 49678*x^18)*Sin[(2*Pi)/11 + 2*x] - 
   11*(-1 + x^2)^2*(71797 + 304*x + 276109*x^2 - 1728*x^3 + 546660*x^4 + 6848*x^5 + 802292*x^6 - 16704*x^7 + 1055654*x^8 + 22560*x^9 + 1055654*x^10 - 16704*x^11 + 802292*x^12 + 6848*x^13 + 546660*x^14 - 1728*x^15 + 276109*x^16 + 304*x^17 + 71797*x^18)*Sin[Pi/11 + 4*x] + 11*(-1 + x^2)^2*(71135 + 2000*x + 284903*x^2 - 7552*x^3 + 501100*x^4 - 15168*x^5 + 892828*x^6 + 96640*x^7 + 1002546*x^8 - 151840*x^9 + 1002546*x^10 + 96640*x^11 + 892828*x^12 - 15168*x^13 + 501100*x^14 - 7552*x^15 + 284903*x^16 + 2000*x^17 + 71135*x^18)*Sin[(2*Pi)/11 + 4*x] - 
   22*(-1 + x^2)^2*(52055 - 1138*x + 320735*x^2 + 2304*x^3 + 946060*x^4 + 1256*x^5 + 1770172*x^6 - 7552*x^7 + 2416002*x^8 + 10260*x^9 + 2416002*x^10 - 7552*x^11 + 1770172*x^12 + 1256*x^13 + 946060*x^14 + 2304*x^15 + 320735*x^16 - 1138*x^17 + 52055*x^18)*Sin[Pi/11 + 6*x] + 22*(-1 + x^2)^2*(52293 - 643*x + 316745*x^2 - 15936*x^3 + 923528*x^4 + 17596*x^5 + 1837824*x^6 + 40320*x^7 + 2374634*x^8 - 82674*x^9 + 2374634*x^10 + 40320*x^11 + 1837824*x^12 + 17596*x^13 + 923528*x^14 - 15936*x^15 + 316745*x^16 - 643*x^17 + 52293*x^18)*Sin[(2*Pi)/11 + 6*x] + 
   44*(-1 + x^2)^2*(16381 + 278*x + 72181*x^2 - 1872*x^3 + 153700*x^4 + 2344*x^5 + 244532*x^6 + 3024*x^7 + 299638*x^8 - 7548*x^9 + 299638*x^10 + 3024*x^11 + 244532*x^12 + 2344*x^13 + 153700*x^14 - 1872*x^15 + 72181*x^16 + 278*x^17 + 16381*x^18)*Sin[Pi/11 + 8*x] - 44*(-1 + x^2)^2*(16423 + 949*x + 75359*x^2 + 2168*x^3 + 145884*x^4 - 28660*x^5 + 205484*x^6 - 6072*x^7 + 343282*x^8 + 63230*x^9 + 343282*x^10 - 6072*x^11 + 205484*x^12 - 28660*x^13 + 145884*x^14 + 2168*x^15 + 75359*x^16 + 949*x^17 + 16423*x^18)*Sin[(2*Pi)/11 + 8*x] + 
   22*(-1 + x^2)^2*(12671 - 1126*x + 106967*x^2 - 3840*x^3 + 386652*x^4 + 8440*x^5 + 792300*x^6 + 4480*x^7 + 1060706*x^8 - 15908*x^9 + 1060706*x^10 + 4480*x^11 + 792300*x^12 + 8440*x^13 + 386652*x^14 - 3840*x^15 + 106967*x^16 - 1126*x^17 + 12671*x^18)*Sin[Pi/11 + 10*x] - 11*(-1 + x^2)^2*(25489 + 2864*x + 137929*x^2 - 5184*x^3 + 324500*x^4 - 29760*x^5 + 540900*x^6 + 5184*x^7 + 740654*x^8 + 53792*x^9 + 740654*x^10 + 5184*x^11 + 540900*x^12 - 29760*x^13 + 324500*x^14 - 5184*x^15 + 137929*x^16 + 2864*x^17 + 25489*x^18)*Sin[Pi/11 + 12*x] - 
   44*(-1 + x^2)^2*(1 + x^2)^3*(163 - 1336*x + 4846*x^2 - 3096*x^3 + 17933*x^4 + 4432*x^5 + 27844*x^6 + 4432*x^7 + 17933*x^8 - 3096*x^9 + 4846*x^10 - 1336*x^11 + 163*x^12)*Sin[Pi/11 + 14*x] + 176*(-1 + x^2)^2*(1 + x^2)^5*(221 - 176*x + 76*x^2 - 976*x^3 - 850*x^4 - 976*x^5 + 76*x^6 - 176*x^7 + 221*x^8)*Sin[Pi/11 + 16*x] + 5632*x*(1 + x)^2*(1 + x^2)^7*(1 + 6*x - 6*x^2 + 6*x^3 + x^4)*Sin[Pi/11 + 18*x] - 2816*(-1 + x^2)^2*(1 + x^2)^9*Sin[Pi/11 + 20*x] + 2816*(-1 + x^2)^2*(1 + x^2)^9*Sin[(2*Pi)/11 + 20*x] + 
   22*(-1 + x^2)^2*(12691 - 163*x + 109863*x^2 - 832*x^3 + 383904*x^4 - 1732*x^5 + 782968*x^6 + 2688*x^7 + 1069870*x^8 + 78*x^9 + 1069870*x^10 + 2688*x^11 + 782968*x^12 - 1732*x^13 + 383904*x^14 - 832*x^15 + 109863*x^16 - 163*x^17 + 12691*x^18)*Sin[(5/11)*(Pi + 22*x)] + 11*(-1 + x^2)^2*(24569 + 64*x + 135985*x^2 + 512*x^3 + 345204*x^4 + 2816*x^5 + 565188*x^6 - 512*x^7 + 698526*x^8 - 5760*x^9 + 698526*x^10 - 512*x^11 + 565188*x^12 + 2816*x^13 + 345204*x^14 + 512*x^15 + 135985*x^16 + 64*x^17 + 24569*x^18)*Sin[(4/11)*(Pi + 33*x)] - 
   11*(-1 + x^2)^2*(24747 + 1472*x + 141523*x^2 + 16640*x^3 + 386524*x^4 + 96000*x^5 + 742092*x^6 + 278272*x^7 + 1064410*x^8 + 394880*x^9 + 1064410*x^10 + 278272*x^11 + 742092*x^12 + 96000*x^13 + 386524*x^14 + 16640*x^15 + 141523*x^16 + 1472*x^17 + 24747*x^18)*Sin[(3/11)*(Pi + 44*x)] - 176*(-1 + x^2)^2*(1 + x^2)^5*(247 + 612*x^2 + 330*x^4 + 612*x^6 + 247*x^8)*Sin[(4/11)*(Pi + 44*x)] - 2816*(-1 + x^2)^2*(1 + x^2)^9*Sin[(5/11)*(Pi + 44*x)] - 
   22*(-1 + x^2)^2*(12221 - 3473*x + 96577*x^2 - 38720*x^3 + 312232*x^4 - 91180*x^5 + 724000*x^6 + 37632*x^7 + 1214266*x^8 + 191482*x^9 + 1214266*x^10 + 37632*x^11 + 724000*x^12 - 91180*x^13 + 312232*x^14 - 38720*x^15 + 96577*x^16 - 3473*x^17 + 12221*x^18)*Sin[(2/11)*(Pi + 55*x)] + 2816*(-1 + x^2)^2*(1 + x^2)^9*Sin[(4/11)*(Pi + 55*x)] + 11*(-1 + x^2)^2*(23859 - 5056*x + 114715*x^2 - 69376*x^3 + 157564*x^4 - 406272*x^5 - 170772*x^6 - 1110272*x^7 - 715190*x^8 - 1536640*x^9 - 715190*x^10 - 1110272*x^11 - 170772*x^12 - 406272*x^13 + 157564*x^14 - 69376*x^15 + 114715*x^16 - 5056*x^17 + 23859*x^18)*
    Sin[(2/11)*(Pi + 66*x)] - 704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Sin[(3/11)*(Pi + 66*x)] + 44*(1 + x)^2*(1 + x^2)^3*(473 - 498*x + 9059*x^2 - 13716*x^3 + 30401*x^4 - 26670*x^5 + 54275*x^6 - 24728*x^7 + 54275*x^8 - 26670*x^9 + 30401*x^10 - 13716*x^11 + 9059*x^12 - 498*x^13 + 473*x^14)*Sin[(2/11)*(Pi + 77*x)] - 176*(-1 + x^2)^2*(1 + x^2)^5*(249 + 16*x + 668*x^2 + 112*x^3 + 470*x^4 + 112*x^5 + 668*x^6 + 16*x^7 + 249*x^8)*Sin[(2/11)*(Pi + 88*x)] + 704*(-1 + x^2)^2*(1 + x^2)^7*(1 - 34*x^2 + x^4)*Sin[(2/11)*(Pi + 99*x)])

using Plot[ConditionalExpression[1, -3 <= compiledfunc[x] <= 3], {x, 12, 13}, PlotPoints -> 100000, PlotStyle -> Directive[Red, CapForm["Butt"], Thickness[.007]], Axes ->{False, False}], I get

Answer 1

I will address 3 points:

• There is a pole that is easy to remove.

• The function is very long you might want to compile it.

• I do not understand why you want such high precision in a plot but there are other ways to obtain those lines

---

Removing the poles from the analysis

The function has poles from the Csc function. They can be removed by considering instead the function:

deflated = Func[x]/Csc[x]^11;

I placed an explantion of how I found that at the end of this section and before the next section.

Then, instead of considering the equation Func[x]==3 for example we can consider deflated==3*Sin[x]^11 or deflated-3*Sin[x]^11 which is a non singular equation in the interval you are considering (note there are still poles at x=1 and x=-1).

---

How I found that in that long expression:

I checked the different types of functions by using

Cases[Func[x], _[_], All] // DeleteDuplicates

I noticed the Csc. I looked for its positions in the expression using:

Position[Func[x], Csc[x]]

I obtained {{4, 1}}

Func[x][[4]]

evaluates to

Csc[x]^11

I checked the Head of Func and saw it is times, I check the number of terms with Length and used //Together //Denominator on the most complicated term to check that there are no other poles

---

---

Compilation

It turns out that your problem seems to require high accuracy which Compile does not support see however posts on stack exchange that use NumericalFunction to obtain high accuracy.

Also, in the next section NDSolve will be use and there was no benefit in using compilation. As I understand, NDSolve compiles automatically when it sees fit. For a discussion about that see here. The benefit of compilation here is if you really want to use plot.

(see update mentions in bold)

Compiling is tricky because not all functions can be compiled and in the default setting of Compile it will not display any error if it skips compilation and just evaluates the function as usual. To make compile complain if something is wrong :

SetSystemOptions[
  "CompileOptions" -> "CompileReportExternal" -> True];
On[Compile::noinfo]

I do not remember what each one does I just remember I saved them for whenever I want to compile a function. If you are interested see this reference on stack exchange here

I changed Func:= to Func[x_]:= because I do not see the point of Func:= in that expression. To compile the function one may use:

Note: …=\[Ellipsis]

update

deflated…compiled = 
  Compile[{{x, _Real}}, Evaluate@deflated];

Test the speed difference:

update

RepeatedTiming[
  deflated…compiled[
    RandomReal[{11, 16}]];] // ScientificForm 

RepeatedTiming[deflated /. x -> RandomReal[{11, 16}];] // 
  ScientificForm // TeXForm

$$\left\{2.31868\times 10^{-5},\text{Null}\right\}$$

$$\left\{1.46028\times 10^{-3},\text{Null}\right\}$$

So you might expect a 10 to 100 times speed up.

---

Alternative method using NDSolve (updated)

To obtain crossings of a function $f$ one can solve the differential equation:

$$y'(x)=f'(x), \qquad y(x_{\text{min}})=f(x_{\text{min}})$$

such that $y(x)=f(x)$ and use WhenEvent to detect special points such as crossings. We will compare the compile and non compiled case.

The crossing condition can be written as :

Abs[deflated]==Abs[3*Sin[x]^11]

where Abs was introduced to incorporate both Func[x]==3 and Func[x]==-3

Default precision

Solve the differential equation with WhenEvent:

xmin = 11;
xmax = 16; AbsoluteTiming[
 res = Reap[
    NDSolve[{s'[x] == ddeflated, s[xmin] == (deflated /. x -> xmin), 
      WhenEvent[Abs[s[x]] == Abs[3*Sin[x]^11], Sow[x]]}, 
     s, {x, xmin, xmax}]];]

Timing: 0.12 seconds

Check:

Plot[Abs[s[x]] - Abs[3*Sin[x]^11] /. res[[1, 1, 1]], {x, xmin, xmax}, 
 PlotRange -> {-0.1, 0.1}, 
 Epilog -> {PointSize[Large], Red, Point[{#, 0} & /@ res[[2, 1]]]}]

The red points bellow represent the crossings Func[x]==3 or Func[x]==-3 which are translated to zeroes of the functions considered in the plot.

Notice that there are no zeroes in the interval you showed in your update. This is in fact an artifact here of low precision and there are indeed 0's in that interval.

• High Precision

Solve the differential equation (I did not check if a lower precision is enough) :

xmin = 11;
xmax = 16; AbsoluteTiming[
 res = Reap[
    NDSolve[{s'[x] == ddeflated, s[xmin] == (deflated /. x -> xmin), 
      WhenEvent[Abs[s[x]] == Abs[3*Sin[x]^11], Sow[x]]}, 
     s, {x, xmin, xmax}, PrecisionGoal -> 15, AccuracyGoal -> 15, 
     WorkingPrecision -> 20]];]

Timing : 13.4 seconds

Plot[Abs[s[x]] - Abs[3*Sin[x]^11] /. res[[1, 1, 1]], {x, xmin, xmax}, 
 PlotRange -> {-0.1, 0.1}, 
 Epilog -> {PointSize[Large], Red, Point[{#, 0} & /@ res[[2, 1]]]}]

The points can be also viewed with NumberLinePlot :

res[[2, 1]] // NumberLinePlot

We can extract the points between 12 and 13 :

Select[res[[2, 1]], 12 < # < 13 &]

{12.461458413778561480, 12.461645303474289146, 12.473084286833757123, \ 12.474549028597047319, 12.477815775272624841, 12.481004423258161594, \ 12.482612164386612858, 12.487570045422328843, 12.660291420025539393, \ 12.668827725840002865}

From those points you could just draw the lines with Line and Graphics