diff --git a/roofit/hs3/inc/RooFitHS3/RooJSONFactoryWSTool.h b/roofit/hs3/inc/RooFitHS3/RooJSONFactoryWSTool.h
index d4e10d3ba1dc8..c58ce70154cfc 100644
--- a/roofit/hs3/inc/RooFitHS3/RooJSONFactoryWSTool.h
+++ b/roofit/hs3/inc/RooFitHS3/RooJSONFactoryWSTool.h
@@ -23,6 +23,7 @@
 #include <map>
 #include <stdexcept>
 #include <set>
+#include <unordered_map>
 
 namespace RooFit {
 namespace JSONIO {
@@ -253,5 +254,12 @@ class RooJSONFactoryWSTool {
    std::unique_ptr<RooFit::JSONIO::Detail::Domains> _domains;
    std::vector<RooAbsArg const *> _serversToExport;
    std::vector<RooAbsArg const *> _serversToDelete;
+
+   // Name-keyed indices over the top-level "functions" and "distributions"
+   // sequences of the input JSON. Built once at the start of importAllNodes()
+   // so that requestImpl() lookups become O(1) instead of an O(N) scan over
+   // every sibling node.
+   std::unordered_map<std::string, RooFit::Detail::JSONNode const *> _functionsByName;
+   std::unordered_map<std::string, RooFit::Detail::JSONNode const *> _distributionsByName;
 };
 #endif
diff --git a/roofit/hs3/src/JSONFactories_RooFitCore.cxx b/roofit/hs3/src/JSONFactories_RooFitCore.cxx
index c3b771a9ee033..90ffd950c7fe6 100644
--- a/roofit/hs3/src/JSONFactories_RooFitCore.cxx
+++ b/roofit/hs3/src/JSONFactories_RooFitCore.cxx
@@ -35,6 +35,9 @@
 #include <RooLognormal.h>
 #include <RooMultiVarGaussian.h>
 #include <RooStats/HistFactory/ParamHistFunc.h>
+#include <RooAddition.h>
+#include <RooProduct.h>
+#include <RooProdPdf.h>
 #include <RooPoisson.h>
 #include <RooPolynomial.h>
 #include <RooPolyVar.h>
@@ -135,6 +138,43 @@ class RooFormulaArgFactory : public RooFit::JSONIO::Importer {
    }
 };
 
+// Fast-path importers for RooProduct, RooAddition, and RooProdPdf that
+// bypass the generic factory-expression mechanism. The default path
+// generates a string expression and passes it to gROOT->ProcessLineFast(),
+// which invokes the Cling JIT for every single call. For workspaces with
+// thousands of product/sum nodes (a common shape for HistFactory models)
+// that JIT cost dominates JSON import time. Constructing the RooFit object
+// directly here keeps the work O(N) of cheap C++ calls.
+class RooProductFactory : public RooFit::JSONIO::Importer {
+public:
+   bool importArg(RooJSONFactoryWSTool *tool, const JSONNode &p) const override
+   {
+      std::string name(RooJSONFactoryWSTool::name(p));
+      tool->wsEmplace<RooProduct>(name, tool->requestArgList<RooAbsReal>(p, "factors"));
+      return true;
+   }
+};
+
+class RooProdPdfFactory : public RooFit::JSONIO::Importer {
+public:
+   bool importArg(RooJSONFactoryWSTool *tool, const JSONNode &p) const override
+   {
+      std::string name(RooJSONFactoryWSTool::name(p));
+      tool->wsEmplace<RooProdPdf>(name, tool->requestArgList<RooAbsPdf>(p, "factors"));
+      return true;
+   }
+};
+
+class RooAdditionFactory : public RooFit::JSONIO::Importer {
+public:
+   bool importArg(RooJSONFactoryWSTool *tool, const JSONNode &p) const override
+   {
+      std::string name(RooJSONFactoryWSTool::name(p));
+      tool->wsEmplace<RooAddition>(name, tool->requestArgList<RooAbsReal>(p, "summands"));
+      return true;
+   }
+};
+
 class RooAddPdfFactory : public RooFit::JSONIO::Importer {
 public:
    bool importArg(RooJSONFactoryWSTool *tool, const JSONNode &p) const override
@@ -1195,6 +1235,9 @@ DEFINE_EXPORTER_KEY(RooSplineStreamer, "spline");
 STATIC_EXECUTE([]() {
    using namespace RooFit::JSONIO;
 
+   registerImporter<RooProductFactory>("product", false);
+   registerImporter<RooProdPdfFactory>("product_dist", false);
+   registerImporter<RooAdditionFactory>("sum", false);
    registerImporter<RooAddPdfFactory>("mixture_dist", false);
    registerImporter<RooAddModelFactory>("mixture_model", false);
    registerImporter<RooBinSamplingPdfFactory>("binsampling_dist", false);
diff --git a/roofit/hs3/src/RooJSONFactoryWSTool.cxx b/roofit/hs3/src/RooJSONFactoryWSTool.cxx
index 20d87473e408a..88ca1fd4d7f25 100644
--- a/roofit/hs3/src/RooJSONFactoryWSTool.cxx
+++ b/roofit/hs3/src/RooJSONFactoryWSTool.cxx
@@ -924,12 +924,11 @@ RooAbsPdf *RooJSONFactoryWSTool::requestImpl<RooAbsPdf>(const std::string &objna
 {
    if (RooAbsPdf *retval = _workspace.pdf(objname))
       return retval;
-   if (const auto &distributionsNode = _rootnodeInput->find("distributions")) {
-      if (const auto &child = findNamedChild(*distributionsNode, objname)) {
-         this->importFunction(*child, true);
-         if (RooAbsPdf *retval = _workspace.pdf(objname))
-            return retval;
-      }
+   auto it = _distributionsByName.find(objname);
+   if (it != _distributionsByName.end()) {
+      this->importFunction(*it->second, true);
+      if (RooAbsPdf *retval = _workspace.pdf(objname))
+         return retval;
    }
    return nullptr;
 }
@@ -945,12 +944,11 @@ RooAbsReal *RooJSONFactoryWSTool::requestImpl<RooAbsReal>(const std::string &obj
       return pdf;
    if (RooRealVar *var = requestImpl<RooRealVar>(objname))
       return var;
-   if (const auto &functionNode = _rootnodeInput->find("functions")) {
-      if (const auto &child = findNamedChild(*functionNode, objname)) {
-         this->importFunction(*child, true);
-         if (RooAbsReal *retval = _workspace.function(objname))
-            return retval;
-      }
+   auto it = _functionsByName.find(objname);
+   if (it != _functionsByName.end()) {
+      this->importFunction(*it->second, true);
+      if (RooAbsReal *retval = _workspace.function(objname))
+         return retval;
    }
    return nullptr;
 }
@@ -2175,6 +2173,31 @@ void RooJSONFactoryWSTool::importAllNodes(const JSONNode &n)
 
    _attributesNode = findRooFitInternal(*_rootnodeInput, "attributes");
 
+   // Build name-keyed indices over the "functions" and "distributions"
+   // sequences. Without these, every cross-reference resolved during import
+   // (e.g. dependencies of a PiecewiseInterpolation, or factory-expression
+   // arguments) triggers a linear scan over all sibling nodes via
+   // findNamedChild(), which becomes O(N^2) on workspaces with thousands of
+   // entries. Populating the maps up-front turns each lookup into O(1).
+   _functionsByName.clear();
+   _distributionsByName.clear();
+   if (auto seq = n.find("functions")) {
+      if (seq->is_seq()) {
+         _functionsByName.reserve(seq->num_children());
+         for (const auto &p : seq->children()) {
+            _functionsByName.emplace(RooJSONFactoryWSTool::name(p), &p);
+         }
+      }
+   }
+   if (auto seq = n.find("distributions")) {
+      if (seq->is_seq()) {
+         _distributionsByName.reserve(seq->num_children());
+         for (const auto &p : seq->children()) {
+            _distributionsByName.emplace(RooJSONFactoryWSTool::name(p), &p);
+         }
+      }
+   }
+
    this->importDependants(n);
 
    if (auto paramPointsNode = n.find("parameter_points")) {
@@ -2239,6 +2262,8 @@ void RooJSONFactoryWSTool::importAllNodes(const JSONNode &n)
 
    _rootnodeInput = nullptr;
    _domains.reset();
+   _functionsByName.clear();
+   _distributionsByName.clear();
 }
 
 /**
diff --git a/roofit/roofitcore/src/RooFactoryWSTool.cxx b/roofit/roofitcore/src/RooFactoryWSTool.cxx
index bbf8178d422b0..adcd24acf0889 100644
--- a/roofit/roofitcore/src/RooFactoryWSTool.cxx
+++ b/roofit/roofitcore/src/RooFactoryWSTool.cxx
@@ -211,7 +211,7 @@ namespace {
     return false;
   }
 
-  pair<list<string>,unsigned int> ctorArgs(const char* classname, std::size_t nPassedArgs) {
+  pair<list<string>,unsigned int> ctorArgsImpl(const char* classname, std::size_t nPassedArgs) {
     // Utility function for RooFactoryWSTool. Return arguments of 'first' non-default, non-copy constructor of any RooAbsArg
     // derived class. Only constructors that start with two `const char*` arguments (for name and title) are considered
     // The returned object contains
@@ -269,6 +269,22 @@ namespace {
     gInterpreter->ClassInfo_Delete(cls);
     return pair<list<string>,unsigned int>(ret,nreq);
   }
+
+  pair<list<string>,unsigned int> const & ctorArgs(const char* classname, std::size_t nPassedArgs) {
+    // Cache the result of ctorArgsImpl(). For a given (classname, nPassedArgs)
+    // the answer is determined by the static class definition and never changes
+    // at runtime, but ctorArgsImpl() drives the Cling interpreter to enumerate
+    // every constructor of the class. When the factory is invoked thousands of
+    // times (e.g. during HS3 JSON import of a large workspace), repeating that
+    // lookup dominates the import time.
+    static std::map<pair<string, std::size_t>, pair<list<string>, unsigned int>> cache;
+    auto key = std::make_pair(string(classname), nPassedArgs);
+    auto it = cache.find(key);
+    if (it == cache.end()) {
+      it = cache.emplace(std::move(key), ctorArgsImpl(classname, nPassedArgs)).first;
+    }
+    return it->second;
+  }
 }
 
 ////////////////////////////////////////////////////////////////////////////////
@@ -321,7 +337,7 @@ RooAbsArg* RooFactoryWSTool::createArg(const char* className, const char* objNam
   _args.push_back(tmp.substr(start_tok, end_tok));
 
   // Try Cling interface
-  pair<list<string>,unsigned int> ca = ctorArgs(className,_args.size()+2) ;
+  pair<list<string>,unsigned int> const & ca = ctorArgs(className,_args.size()+2) ;
   if (ca.first.empty()) {
     coutE(ObjectHandling) << "RooFactoryWSTool::createArg() ERROR no suitable constructor found for class " << className << std::endl ;
     logError() ;
@@ -352,7 +368,7 @@ RooAbsArg* RooFactoryWSTool::createArg(const char* className, const char* objNam
 
   try {
     Int_t i(0) ;
-    list<string>::iterator ti = ca.first.begin() ; ++ti ; ++ti ;
+    list<string>::const_iterator ti = ca.first.begin() ; ++ti ; ++ti ;
     for (vector<string>::iterator ai = _args.begin() ; ai != _args.end() ; ++ai,++ti,++i) {
       if ((*ti)=="RooAbsReal&" || (*ti)=="const RooAbsReal&" || (*ti)=="RooAbsReal::Ref") {
    RooFactoryWSTool::as_FUNC(i) ;