[Backend] fix differentiation of functions with function arguments

Belonging to [master]:
  - OpenModelica/OMCompiler#2184
  - OpenModelica/OpenModelica-testsuite#850

Compiler/BackEnd/Differentiate.mo

@@ -1365,13 +1365,21 @@ algorithm
         cr = ComponentReference.crefPrefixDer(cr);
         cr = createDifferentiatedCrefName(cr, inDiffwrtCref, matrixName);
         res = Expression.makeCrefExp(cr, tp);
+      then
+        (res,  inFunctionTree);
 
-        b = ComponentReference.crefEqual(DAE.CREF_IDENT("$",DAE.T_REAL_DEFAULT,{}), inDiffwrtCref);
-        (zero,_) = Expression.makeZeroExpression(Expression.arrayDimension(tp));
+    /* Differentiate with respect to DAE.CREF_IDENT(ident="$") demands zero expressions */
+    case (DAE.CALL(path=Absyn.IDENT(name = "der"),expLst = {e}), DAE.CREF_IDENT(ident="$"), _, _, _)
+      equation
+        (zero,_) = Expression.makeZeroExpression(Expression.arrayDimension(Expression.typeof(e)));
+      then
+        (zero,  inFunctionTree);
 
-        res = if b then zero else res;
+    case (e as DAE.CALL(attr=DAE.CALL_ATTR(ty=tp)), DAE.CREF_IDENT(ident="$"), _, _, _)
+      equation
+        (zero,_) = Expression.makeZeroExpression(Expression.arrayDimension(tp));
       then
-        (res,  inFunctionTree);
+        (zero, inFunctionTree);
 
     // differentiate builtin calls with 1 argument
     case (DAE.CALL(path=Absyn.IDENT(name),attr=DAE.CALL_ATTR(builtin=true),expLst={e}), _, _, _, _)
@@ -1383,7 +1391,6 @@ algorithm
         //print("\nresults to exp: " + s1);
       then (res,  funcs);
 
-
     // differentiate builtin calls with N arguments with match
     // der(arctan2(y,0)) = der(sign(y)*pi/2) = 0
     case (DAE.CALL(path=Absyn.IDENT("atan2"),attr=DAE.CALL_ATTR(builtin=true),expLst={_,e1 as  DAE.RCONST(real=0.0)}), _, _, _, _)
@@ -2301,20 +2308,26 @@ algorithm
         expBoolLst = List.threadTuple(expl, blst);
         expBoolLst = List.filterOnTrue(expBoolLst, Util.tuple22);
         expl1 = List.map(expBoolLst, Util.tuple21);
-        (dexpl, functions) = List.map3Fold(expl1, function differentiateExp(maxIter=maxIter), inDiffwrtCref, inInputData, inDiffType, functions);
-        (dexplZero, functions) = List.map3Fold(expl1, function differentiateExp(maxIter=maxIter), DAE.CREF_IDENT("$",DAE.T_REAL_DEFAULT,{}), BackendDAE.emptyInputData, BackendDAE.GENERIC_GRADIENT(), functions);
+        if Flags.isSet(Flags.DEBUG_DIFFERENTIATION_VERBOSE) then
+          print("### Selected Arguments: \n");
+          print(stringDelimitList(List.map(expl1, ExpressionDump.printExpStr), ", ") + "\n");
+        end if;
 
-        if Flags.isSet(Flags.DEBUG_DIFFERENTIATION) then
-          print("### differentiated argument list:\n");
+        (dexpl, functions) = List.map3Fold(expl1, function differentiateExp(maxIter=maxIter), inDiffwrtCref, inInputData, inDiffType, functions);
+        if Flags.isSet(Flags.DEBUG_DIFFERENTIATION_VERBOSE) then
           print("### Diffed ExpList: \n");
           print(stringDelimitList(List.map(dexpl, ExpressionDump.printExpStr), ", ") + "\n");
+        end if;
+
+        (dexplZero, functions) = List.map3Fold(expl1, function differentiateExp(maxIter=maxIter), DAE.CREF_IDENT("$",DAE.T_REAL_DEFAULT,{}), BackendDAE.emptyInputData, BackendDAE.GENERIC_GRADIENT(), functions);
+        if Flags.isSet(Flags.DEBUG_DIFFERENTIATION_VERBOSE) then
           print("### Diffed ExpList extended: \n");
           print(stringDelimitList(List.map(dexplZero, ExpressionDump.printExpStr), ", ") + "\n");
         end if;
 
         e = DAE.CALL(dpath,dexpl,DAE.CALL_ATTR(dtp,b,false,isImpure,false,DAE.NO_INLINE(),tc));
         exp = createPartialArguments(ty, dexpl, dexplZero, expl, e);
-        if Flags.isSet(Flags.DEBUG_DIFFERENTIATION) then
+        if Flags.isSet(Flags.DEBUG_DIFFERENTIATION_VERBOSE) then
           print("### differentiated Call :\n");
           print(ExpressionDump.printExpStr(e) + "\n");
           print("### -> result exp: \n");