[RF] Using a conditional RooProdPdf in a multi-channel fit spawns too many integrals with new CPU evaluation backend

[guitargeek]

Description

Using a conditional RooProdPdf in a RooSimultaneous spawns too many integrals with new CPU evaluation backend.

This is a deal breaker for fitting the open likelihood of the CMS Run 1 Higgs analysis with the new CPU evaluation backend, because evaluating these unnecessary integrals takes too much time (although the result is correct).

Since the RooFit AD backend uses the same "compileForNormSet" method to sanitize the computation graph, it's also a blocker for minimizing the CMS Higgs Run 1 likelihood with AD.

Reproducer

RooRealVar x{"x", "x", 0, 1};
RooRealVar y{"y", "y", 0, 1};

RooGenericPdf pdfx{"pdfx", "1.0 + x - x", {x}};
RooGenericPdf pdfxy{"pdfxy", "1.0 + x - x + y - y", {x, y}};

RooProdPdf pdf{"pdf", "pdf", pdfx, RooFit::Conditional(pdfxy, y)};

RooArgSet normSet{x, y};

RooCategory cat{"cat", "cat", {{"0", 0}}};
RooSimultaneous simPdf{"simPdf", "simPdf", {{"0", &pdf}}, cat};

{
   std::cout << "This looks good:" << std::endl;
   RooFit::Detail::CompileContext ctx{normSet};
   std::unique_ptr<RooAbsPdf> compiled{static_cast<RooAbsPdf*>(pdf.compileForNormSet(normSet, ctx).release())};
   compiled->getVal(normSet);
}
{
   std::cout << "Too many integrals:" << std::endl;
   RooFit::Detail::CompileContext ctx{normSet};
   std::unique_ptr<RooAbsPdf> compiled{static_cast<RooAbsPdf*>(simPdf.compileForNormSet(normSet, ctx).release())};
   compiled->getVal(normSet);
}

The output is:

This looks good:
[#1] INFO:NumericIntegration -- RooRealIntegral::init(pdfx_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(pdfxy_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)

Too many integrals:
[#1] INFO:NumericIntegration -- RooRealIntegral::init(_0_pdfx_Int[_0_x]) using numeric integrator RooIntegrator1D to calculate Int(_0_x)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(_0_pdfxy_Int[_0_y]) using numeric integrator RooIntegrator1D to calculate Int(_0_y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([_0_pdfx_over__0_pdfx_Int[_0_x]_X__0_pdfxy_over__0_pdfxy_Int[_0_y]]_Norm[_0_x,_0_y]_denominator_Int[_0_x,_0_y]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(_0_x,_0_y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(_0_pdfx_Int[_0_x]) using numeric integrator RooIntegrator1D to calculate Int(_0_x)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(_0_pdfxy_Int[_0_y]) using numeric integrator RooIntegrator1D to calculate Int(_0_y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(_0_pdfx_Int[_0_x]) using numeric integrator RooIntegrator1D to calculate Int(_0_x)