relevant_cst_profile_entry(cprofile(RT,WT,PropWT,Calls,PP,Kind,Ann,Phase,IDInfo,InstItself,ValInfo,InstList)) :-
        (try_get_unique_constants_state(CstState) -> true ; CstState=[]),
        (Category = constant_computation(Phase,IDInfo0),
         relevant_total_runtime(PP,Category,RT,WT,Calls,_MaxWT,_MaxWitnessID,_Min),
         Phase \= propagate_value,
         (abstract_constant(PP,_) -> Kind=abstract ; concrete_constant(PP,_) -> Kind=concrete ; Kind=unknown)
         ;
          (constants_profiling_on -> Phase = no_equation_detected
           ; Phase = '-'), % constants profiling on needed to keep track of all equations (except arith. at the moment)
          RT=0, WT=0, PropWT=0, Calls=0, IDInfo0 = [],
          (abstract_constant(PP,_), Kind=abstract ; concrete_constant(PP,_), Kind=concrete),
          \+ total_runtime(PP,constant_computation(_,_),_,_,_,_,_,_) % we have no profiling info at all for PP
        ),
        (get_det_solution_for_constant_value_kind(PP,DetValInfo)
          -> DetSolFound = true,
             exclude(is_value_info,IDInfo0,IDInfo)
           ; DetValInfo = '-',
             DetSolFound = false, IDInfo0=IDInfo
         ),
        ( (DetSolFound=false ; DetValInfo='LARGE-VALUE'),
          member(bind(PP,CstVal),CstState), translate_bvalue_kind(CstVal,ValInfo)
          -> SolFound=true
          ; ValInfo=DetValInfo, SolFound=DetSolFound
        ),
        % now check whether there are infos about propagation phase:
        (total_runtime(PP,constant_computation(propagate_value,PropInfo),_,PropWT,_,_,_,_)
          -> (member(instantiates(IList),PropInfo) ->
                (select(PP,IList,InstList)
                 -> InstItself=yes, % Equation determined directly the value
                    % check if we have a long closure expansion entry
                    % this has already been counted in the regular entry for the constant computation
                    (member(long_closure_expansion,IDInfo), Phase=phase0 -> fail ; true)
                  ; (DetSolFound=true -> InstItself = 'delayed'
                      ; SolFound=true -> InstItself = 'non-det'
                      ; InstItself='NO'),
                     InstList=IList)
               ; % no instantiation list stored; performance monitoring not on
                (SolFound=true -> InstItself='-' ; InstItself='NO'),
                InstList = '-'
             )
          ;  PropWT = 0,
             (DetSolFound=true -> InstItself='-' ; InstItself='NO'),
             InstList='-'
        ),
        (constant_variable_marked_as_expand(PP) -> Ann=expand
         ; constant_variable_marked_as_memo(PP) -> Ann=memo
         ; Ann = ''
     ).