Excessive compilation time

General Usage
1

I have a problem with excessive compilation time. The problem is with code automatically translated from another system (gap3) so I cannot easily change it. As an example, the function below takes 2 minutes to compile; as you can see, the code is long but very simple. When you load the code, executing @time f(4) the first time takes 128sec (and some microseconds after that). The following should be noted:

  • If I move the definition of d outside the function the compilation takes a fraction of a second. I can move d out here but not on some other examples where the data defines polynomials that the function evaluates at its argument.

  • If I define the function by function f(x) instead of f=function(x) the time by my stopwatch is the same but @time does not show most of it.

f=function(x)
  d=Dict{Int,Vector{Vector{Int}}}(
  4=>[[1,0],[1,4],[1,8],[1,5,1,7],[1,3,1,5],[1,1,1,3],[1,2,1,4,1,6]],
  5=>[[1,0],[1,4],[1,8],[1,4],[1,8],[1,12],[1,8],[1,12],[1,16],[1,9,1,15],
      [1,7,1,13],[1,5,1,11],[1,7,1,13],[1,5,1,11],[1,3,1,9],[1,5,1,11],
      [1,3,1,9],[1,1,1,7],[1,4,2,10],[1,2,1,8,1,14],[2,6,1,12]],
  6=>[[1,0],[1,4],[1,8],[1,6],[1,10],[1,14],[1,5,1,13],[1,3,1,11],[1,3,1,7],
      [1,7,1,11],[1,1,1,9],[1,5,1,9],[1,2,1,6,1,10],[1,4,1,8,1,12]],
  7=>[[1,0],[1,4],[1,8],[1,4],[1,8],[1,12],[1,8],[1,12],[1,16],[1,6],[1,10],
      [1,14],[1,10],[1,14],[1,18],[1,14],[1,18],[1,22],[1,9,1,21],[1,7,1,19],
      [2,11],[1,7,1,19],[2,11],[2,9],[2,11],[2,9],[2,7],[2,15],[2,13],
      [1,5,1,17],[2,13],[1,5,1,17],[1,3,1,15],[1,5,1,17],[1,3,1,15],[1,1,1,13],
      [3,10],[1,4,2,16],[1,2,2,14],[2,8,1,20],[2,6,1,18],[3,12]],
  8=>[[1,0],[1,6],[1,12],[1,18],[1,1,1,5],[1,4,1,8],[1,7,1,11],[1,7,1,11],
      [1,10,1,14],[1,13,1,17],[1,8,1,12,1,16],[1,6,1,10,1,14],[1,4,1,8,1,12],
      [1,2,1,6,1,10],[1,5,2,9,1,13],[1,3,1,7,1,11,1,15]],
  9=>[[1,0],[1,6],[1,12],[1,18],[1,12],[1,18],[1,24],[1,30],[1,5,1,13],
      [1,4,1,20],[1,7,1,23],[1,7,1,23],[1,10,1,26],[1,13,1,29],[1,1,1,17],
      [1,14,1,22],[1,17,1,25],[1,11,1,19],[1,11,1,19],[1,8,1,16],
      [1,8,1,16,1,24],[1,6,1,14,1,22],[1,4,1,12,1,20],[1,2,1,10,1,18],
      [1,12,1,20,1,28],[1,10,1,18,1,26],[1,8,1,16,1,24],[1,6,1,14,1,22],
      [2,9,1,17,1,25],[1,7,2,15,1,23],[1,3,1,11,1,19,1,27],[1,5,1,13,2,21]],
 10=>[[1,0],[1,6],[1,12],[1,18],[1,8],[1,14],[1,20],[1,26],[1,16],[1,22],
      [1,28],[1,34],[1,9,1,21],[1,12,1,24],[1,15,1,27],[1,15,1,27],
      [1,18,1,30],[1,21,1,33],[1,5,1,17],[1,8,1,20],[1,11,1,23],[1,11,1,23],
      [1,14,1,26],[1,17,1,29],[1,1,1,13],[1,4,1,16],[1,7,1,19],[1,7,1,19],
      [1,10,1,22],[1,13,1,25],[1,8,1,20,1,32],[2,14,1,26],[1,8,2,20],
      [1,2,1,14,1,26],[2,16,1,28],[1,10,2,22],[1,4,1,16,1,28],[2,10,1,22],
      [1,12,2,24],[1,6,1,18,1,30],[2,12,1,24],[1,6,2,18],[2,9,2,21],
      [2,11,2,23],[1,7,2,19,1,31],[1,3,2,15,1,27],[1,5,2,17,1,29],[2,13,2,25]],
 11=>[[1,0],[1,6],[1,12],[1,18],[1,8],[1,14],[1,20],[1,26],[1,16],[1,22],
      [1,28],[1,34],[1,12],[1,18],[1,24],[1,30],[1,20],[1,26],[1,32],[1,38],
      [1,28],[1,34],[1,40],[1,46],[1,9,1,33],[1,12,1,36],[2,27],[2,27],
      [1,18,1,42],[2,33],[1,5,1,29],[2,20],[1,11,1,35],[1,11,1,35],[1,14,1,38],
      [2,29],[1,1,1,25],[1,4,1,28],[1,7,1,31],[1,7,1,31],[2,22],[2,25],[2,21],
      [2,24],[1,15,1,39],[1,15,1,39],[2,30],[1,21,1,45],[2,17],[1,8,1,32],
      [2,23],[2,23],[2,26],[1,17,1,41],[2,13],[2,16],[2,19],[2,19],
      [1,10,1,34],[1,13,1,37],[1,8,2,32],[2,14,1,38],[3,20],[1,2,2,26],
      [2,20,1,44],[3,26],[1,8,2,32],[2,14,1,38],[2,16,1,40],[3,22],[1,4,2,28],
      [2,10,1,34],[3,28],[1,10,2,34],[2,16,1,40],[3,22],[3,24],[1,6,2,30],
      [2,12,1,36],[3,18],[1,12,2,36],[2,18,1,42],[3,24],[1,6,2,30],[4,21],
      [4,23],[3,19,1,43],[1,3,3,27],[1,5,3,29],[4,25],[2,9,2,33],[2,11,2,35],
      [1,7,3,31],[3,15,1,39],[3,17,1,41],[2,13,2,37]],
 12=>[[1,0],[1,12],[1,1,1,11],[1,4,1,8],[1,5,1,7],[1,2,1,4,1,6],[1,6,1,8,1,10],
      [1,3,1,5,1,7,1,9]],
 13=>[[1,0],[1,6],[1,12],[1,18],[1,7,1,11],[1,4,1,8],[1,1,1,17],[1,5,1,13],
      [1,10,1,14],[1,7,1,11],[1,4,1,8,1,12],[1,2,1,6,1,10],[1,8,1,12,1,16],
      [1,6,1,10,1,14],[1,3,1,7,1,11,1,15],[1,5,2,9,1,13]],
 14=>[[1,0],[1,8],[1,16],[1,12],[1,20],[1,28],[1,15,1,21],[1,12,1,24],
      [1,9,1,27],[1,11,1,17],[1,8,1,20],[1,5,1,23],[1,7,1,13],[1,4,1,16],
      [1,1,1,19],[1,2,1,14,1,20],[1,8,1,14,1,26],[1,4,1,10,1,22],
      [1,10,1,16,1,22],[1,6,1,12,1,18],[1,6,1,18,1,24],[1,3,1,9,1,15,1,21],
      [1,5,1,11,1,17,1,23],[1,7,1,13,1,19,1,25]],
 15=>[[1,0],[1,6],[1,8],[1,14],[1,16],[1,22],[1,12],[1,18],[1,20],[1,26],
      [1,28],[1,34],[1,9,1,33],[1,12,1,24],[1,15,1,27],[1,15,1,27],[1,18,1,30],
      [2,21],[1,5,1,29],[1,8,1,20],[1,11,1,23],[1,11,1,23],[1,14,1,26],[2,17],
      [1,1,1,25],[1,4,1,16],[1,7,1,19],[1,7,1,19],[1,10,1,22],[2,13],[1,8,2,20],
      [1,2,1,14,1,26],[1,8,1,20,1,32],[2,14,1,26],[1,4,1,16,1,28],[2,10,1,22],
      [2,16,1,28],[1,10,2,22],[2,12,1,24],[1,6,2,18],[1,12,2,24],
      [1,6,1,18,1,30],[2,9,2,21],[2,11,2,23],[1,7,2,19,1,31],[1,3,2,15,1,27],
      [1,5,2,17,1,29],[2,13,2,25]],
 16=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,1,1,11],[1,7,1,17],[1,13,1,23],
      [1,19,1,29],[1,13,1,23],[1,19,1,29],[1,25,1,35],[1,25,1,35],[1,31,1,41],
      [1,37,1,47],[1,2,1,12,1,22],[1,6,1,16,1,26],[1,10,1,20,1,30],
      [1,10,1,20,1,30],[1,14,1,24,1,34],[1,18,1,28,1,38],[1,14,1,24,1,34],
      [1,18,1,28,1,38],[1,22,1,32,1,42],[1,26,1,36,1,46],[1,15,1,25,1,35,1,45],
      [1,17,2,27,1,37],[1,9,1,19,1,29,1,39],[1,11,2,21,1,31],
      [1,3,1,13,1,23,1,33],[1,20,2,30,1,40],[1,12,1,22,1,32,1,42],
      [1,14,2,24,1,34],[1,6,1,16,1,26,1,36],[1,8,2,18,1,28],[1,12,2,22,2,32],
      [1,4,1,14,1,24,1,34,1,44],[2,16,2,26,1,36],[1,8,1,18,2,28,1,38],
      [1,10,2,20,1,30,1,40],[1,5,2,15,2,25,1,35],[1,7,2,17,2,27,1,37],
      [1,9,2,19,2,29,1,39],[1,11,2,21,2,31,1,41],[1,13,2,23,2,33,1,43]],
 17=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,30],[1,42],[1,54],[1,66],[1,78],
      [1,11,1,31],[1,17,1,37],[1,13,1,53],[1,19,1,59],[1,13,1,53],[1,19,1,59],
      [1,25,1,65],[1,25,1,65],[1,31,1,71],[1,37,1,77],[1,1,1,41],[1,7,1,47],
      [1,35,1,55],[1,35,1,55],[1,41,1,61],[1,47,1,67],[1,23,1,43],[1,29,1,49],
      [1,23,1,43],[1,29,1,49],[1,2,1,22,1,42],[1,6,1,26,1,46],[1,10,1,30,1,50],
      [1,10,1,30,1,50],[1,14,1,34,1,54],[1,18,1,38,1,58],[1,14,1,34,1,54],
      [1,18,1,38,1,58],[1,22,1,42,1,62],[1,26,1,46,1,66],[1,12,1,32,1,52],
      [1,16,1,36,1,56],[1,20,1,40,1,60],[1,20,1,40,1,60],[1,24,1,44,1,64],
      [1,28,1,48,1,68],[1,24,1,44,1,64],[1,28,1,48,1,68],[1,32,1,52,1,72],
      [1,36,1,56,1,76],[1,15,1,35,1,55,1,75],[2,27,1,47,1,67],
      [1,19,2,39,1,59],[1,11,1,31,2,51],[1,3,1,23,1,43,1,63],
      [2,30,1,50,1,70],[1,22,2,42,1,62],[1,14,1,34,2,54],
      [1,6,1,26,1,46,1,66],[2,18,1,38,1,58],[1,25,2,45,1,65],[1,17,1,37,2,57],
      [1,9,1,29,1,49,1,69],[2,21,1,41,1,61],[1,13,2,33,1,53],[1,20,1,40,2,60],
      [1,12,1,32,1,52,1,72],[2,24,1,44,1,64],[1,16,2,36,1,56],[1,8,1,28,2,48],
      [1,12,2,32,2,52],[2,22,1,42,2,62],[1,4,1,24,2,44,1,64],
      [1,14,2,34,1,54,1,74],[2,16,1,36,2,56],[2,26,2,46,1,66],
      [1,8,2,28,1,48,1,68],[1,18,2,38,2,58],[2,20,2,40,1,60],
      [1,10,1,30,2,50,1,70],[2,15,2,35,2,55],[2,17,2,37,2,57],[2,19,2,39,2,59],
      [1,11,2,31,2,51,1,71],[1,13,2,33,2,53,1,73],[1,5,2,25,2,45,1,65],
      [1,7,2,27,2,47,1,67],[1,9,2,29,2,49,1,69],[2,21,2,41,2,61],
      [2,23,2,43,2,63]],
 18=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,20],[1,32],[1,44],[1,56],[1,68],
      [1,40],[1,52],[1,64],[1,76],[1,88],[1,21,1,51],[1,27,1,57],[1,33,1,63],
      [1,39,1,69],[1,33,1,63],[1,39,1,69],[1,45,1,75],[1,45,1,75],[1,51,1,81],
      [1,57,1,87],[1,11,1,41],[1,17,1,47],[1,23,1,53],[1,29,1,59],[1,23,1,53],
      [1,29,1,59],[1,35,1,65],[1,35,1,65],[1,41,1,71],[1,47,1,77],[1,1,1,31],
      [1,7,1,37],[1,13,1,43],[1,19,1,49],[1,13,1,43],[1,19,1,49],[1,25,1,55],
      [1,25,1,55],[1,31,1,61],[1,37,1,67],[1,2,1,32,1,62],[2,26,1,56],
      [1,20,2,50],[1,20,2,50],[1,14,1,44,1,74],[2,38,1,68],[1,14,1,44,1,74],
      [2,38,1,68],[1,32,2,62],[1,26,1,56,1,86],[2,22,1,52],[1,16,2,46],
      [1,10,1,40,1,70],[1,10,1,40,1,70],[2,34,1,64],[1,28,2,58],[2,34,1,64],
      [1,28,2,58],[1,22,1,52,1,82],[2,46,1,76],[1,12,2,42],[1,6,1,36,1,66],
      [2,30,1,60],[2,30,1,60],[1,24,2,54],[1,18,1,48,1,78],[1,24,2,54],
      [1,18,1,48,1,78],[2,42,1,72],[1,36,2,66],[1,15,2,45,1,75],[2,27,2,57],
      [1,9,2,39,1,69],[2,21,2,51],[1,3,2,33,1,63],[2,35,2,65],[1,17,2,47,1,77],
      [2,29,2,59],[1,11,2,41,1,71],[2,23,2,53],[1,25,2,55,1,85],[2,37,2,67],
      [1,19,2,49,1,79],[2,31,2,61],[1,13,2,43,1,73],[2,30,2,60],
      [1,12,2,42,1,72],[2,24,2,54],[1,6,2,36,1,66],[2,18,2,48],[1,20,2,50,1,80],
      [2,32,2,62],[1,14,2,44,1,74],[2,26,2,56],[1,8,2,38,1,68],[2,40,2,70],
      [1,22,2,52,1,82],[2,34,2,64],[1,16,2,46,1,76],[2,28,2,58],
      [1,12,2,42,2,72],[3,32,2,62],[2,22,3,52],[2,24,2,54,1,84],
      [1,14,3,44,1,74],[1,4,2,34,2,64],[3,36,2,66],[2,26,3,56],
      [2,16,2,46,1,76],[1,18,3,48,1,78],[1,8,2,38,2,68],[3,28,2,58],
      [2,30,3,60],[2,20,2,50,1,80],[1,10,3,40,1,70],[3,25,3,55],
      [1,7,3,37,2,67],[2,19,3,49,1,79],[3,31,3,61],[1,13,3,43,2,73],
      [1,5,3,35,2,65],[2,17,3,47,1,77],[3,29,3,59],[1,11,3,41,2,71],
      [2,23,3,53,1,83],[2,15,3,45,1,75],[3,27,3,57],[1,9,3,39,2,69],
      [2,21,3,51,1,81],[3,33,3,63]],
 19=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,20],[1,32],[1,44],[1,56],[1,68],
      [1,40],[1,52],[1,64],[1,76],[1,88],[1,30],[1,42],[1,54],[1,66],[1,78],
      [1,50],[1,62],[1,74],[1,86],[1,98],[1,70],[1,82],[1,94],[1,106],[1,118],
      [2,51],[2,57],[1,33,1,93],[1,39,1,99],[1,33,1,93],[1,39,1,99],
      [1,45,1,105],[1,45,1,105],[1,51,1,111],[1,57,1,117],[2,41],[2,47],[2,53],
      [2,59],[2,53],[2,59],[1,35,1,95],[1,35,1,95],[1,41,1,101],[1,47,1,107],
      [2,31],[2,37],[2,43],[2,49],[2,43],[2,49],[2,55],[2,55],[1,31,1,91],
      [1,37,1,97],[1,21,1,81],[1,27,1,87],[2,63],[2,69],[2,63],[2,69],[2,75],
      [2,75],[2,81],[2,87],[1,11,1,71],[1,17,1,77],[1,23,1,83],[1,29,1,89],
      [1,23,1,83],[1,29,1,89],[2,65],[2,65],[2,71],[2,77],[1,1,1,61],[1,7,1,67],
      [1,13,1,73],[1,19,1,79],[1,13,1,73],[1,19,1,79],[1,25,1,85],[1,25,1,85],
      [2,61],[2,67],[1,2,2,62],[2,26,1,86],[3,50],[3,50],[1,14,2,74],
      [2,38,1,98],[1,14,2,74],[2,38,1,98],[3,62],[1,26,2,86],[2,32,1,92],[3,56],      [1,20,2,80],[1,20,2,80],[2,44,1,104],[3,68],[2,44,1,104],[3,68],
      [1,32,2,92],[2,56,1,116],[2,22,1,82],[3,46],[1,10,2,70],[1,10,2,70],
      [2,34,1,94],[3,58],[2,34,1,94],[3,58],[1,22,2,82],[2,46,1,106],[3,52],
      [1,16,2,76],[2,40,1,100],[2,40,1,100],[3,64],[1,28,2,88],[3,64],
      [1,28,2,88],[2,52,1,112],[3,76],[3,42],[1,6,2,66],[2,30,1,90],[2,30,1,90],
      [3,54],[1,18,2,78],[3,54],[1,18,2,78],[2,42,1,102],[3,66],[1,12,2,72],
      [2,36,1,96],[3,60],[3,60],[1,24,2,84],[2,48,1,108],[1,24,2,84],
      [2,48,1,108],[3,72],[1,36,2,96],[1,15,3,75],[2,27,2,87],[3,39,1,99],
      [4,51],[1,3,3,63],[2,35,2,95],[3,47,1,107],[4,59],[1,11,3,71],[2,23,2,83],
      [3,55,1,115],[4,67],[1,19,3,79],[2,31,2,91],[3,43,1,103],[2,30,2,90],
      [3,42,1,102],[4,54],[1,6,3,66],[2,18,2,78],[3,50,1,110],[4,62],
      [1,14,3,74],[2,26,2,86],[3,38,1,98],[4,70],[1,22,3,82],[2,34,2,94],
      [3,46,1,106],[4,58],[3,45,1,105],[4,57],[1,9,3,69],[2,21,2,81],
      [3,33,1,93],[4,65],[1,17,3,77],[2,29,2,89],[3,41,1,101],[4,53],
      [1,25,3,85],[2,37,2,97],[3,49,1,109],[4,61],[1,13,3,73],[4,60],
      [1,12,3,72],[2,24,2,84],[3,36,1,96],[4,48],[1,20,3,80],[2,32,2,92],
      [3,44,1,104],[4,56],[1,8,3,68],[2,40,2,100],[3,52,1,112],[4,64],
      [1,16,3,76],[2,28,2,88],[1,12,4,72],[3,32,2,92],[5,52],[3,42,2,102],
      [5,62],[2,22,3,82],[2,24,3,84],[4,44,1,104],[1,4,4,64],[4,54,1,114],
      [1,14,4,74],[3,34,2,94],[3,36,2,96],[5,56],[2,16,3,76],[5,66],[2,26,3,86],
      [4,46,1,106],[4,48,1,108],[1,8,4,68],[3,28,2,88],[1,18,4,78],[3,38,2,98],
      [5,58],[5,60],[2,20,3,80],[4,40,1,100],[2,30,3,90],[4,50,1,110],
      [1,10,4,70],[3,25,3,85],[1,7,5,67],[5,49,1,109],[6,61],[4,43,2,103],
      [4,35,2,95],[2,17,4,77],[6,59],[1,11,5,71],[5,53,1,113],[5,45,1,105],
      [3,27,3,87],[1,9,5,69],[2,21,4,81],[6,63],[6,55],[4,37,2,97],[2,19,4,79],
      [3,31,3,91],[1,13,5,73],[1,5,5,65],[5,47,1,107],[3,29,3,89],[4,41,2,101],
      [2,23,4,83],[2,15,4,75],[6,57],[4,39,2,99],[5,51,1,111],[3,33,3,93]],
 20=>[[1,0],[1,20],[1,40],[1,21,1,39],[1,27,1,33],[1,11,1,29],[1,17,1,23],
      [1,1,1,19],[1,7,1,13],[1,2,1,20,1,38],[1,14,1,20,1,26],[1,10,1,22,1,28],
      [1,10,1,16,1,34],[1,12,1,18,1,30],[1,6,1,24,1,30],[1,3,1,9,1,21,1,27],
      [1,11,1,17,1,23,1,29],[1,13,1,19,1,31,1,37],[1,6,1,12,1,18,1,24],
      [1,8,1,14,1,26,1,32],[1,16,1,22,1,28,1,34],[1,12,1,18,1,24,1,30,1,36],
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 34=>[[1,0],[1,4],[1,8],[1,5,1,7],[1,3,1,5],[1,1,1,3],[1,2,1,4,1,6]],
 35=>[[1,0],[1,4],[1,8],[1,4],[1,8],[1,12],[1,8],[1,12],[1,16],[1,9,1,15],
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 36=>[[1,0],[1,4],[1,8],[1,6],[1,10],[1,14],[1,5,1,13],[1,3,1,11],[1,3,1,7],
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 37=>[[1,0],[1,4],[1,8],[1,4],[1,8],[1,12],[1,8],[1,12],[1,16],[1,6],[1,10],
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 38=>[[1,0],[1,6],[1,12],[1,18],[1,1,1,5],[1,4,1,8],[1,7,1,11],[1,7,1,11],
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310=>[[1,0],[1,6],[1,12],[1,18],[1,8],[1,14],[1,20],[1,26],[1,16],[1,22],[1,28],
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311=>[[1,0],[1,6],[1,12],[1,18],[1,8],[1,14],[1,20],[1,26],[1,16],[1,22],[1,28],
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312=>[[1,0],[1,12],[1,1,1,11],[1,4,1,8],[1,5,1,7],[1,2,1,4,1,6],[1,6,1,8,1,10],
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313=>[[1,0],[1,6],[1,12],[1,18],[1,7,1,11],[1,4,1,8],[1,1,1,17],[1,5,1,13],
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314=>[[1,0],[1,8],[1,16],[1,12],[1,20],[1,28],[1,15,1,21],[1,12,1,24],
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315=>[[1,0],[1,6],[1,8],[1,14],[1,16],[1,22],[1,12],[1,18],[1,20],[1,26],[1,28],
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316=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,1,1,11],[1,7,1,17],[1,13,1,23],
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317=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,30],[1,42],[1,54],[1,66],[1,78],
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318=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,20],[1,32],[1,44],[1,56],[1,68],
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319=>[[1,0],[1,12],[1,24],[1,36],[1,48],[1,20],[1,32],[1,44],[1,56],[1,68],
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      [3,55,1,115],[4,67],[1,19,3,79],[2,31,2,91],[3,43,1,103],[2,30,2,90],
      [3,42,1,102],[4,54],[1,6,3,66],[2,18,2,78],[3,50,1,110],[4,62],
      [1,14,3,74],[2,26,2,86],[3,38,1,98],[4,70],[1,22,3,82],[2,34,2,94],
      [3,46,1,106],[4,58],[3,45,1,105],[4,57],[1,9,3,69],[2,21,2,81],
      [3,33,1,93],[4,65],[1,17,3,77],[2,29,2,89],[3,41,1,101],[4,53],
      [1,25,3,85],[2,37,2,97],[3,49,1,109],[4,61],[1,13,3,73],[4,60],
      [1,12,3,72],[2,24,2,84],[3,36,1,96],[4,48],[1,20,3,80],[2,32,2,92],
      [3,44,1,104],[4,56],[1,8,3,68],[2,40,2,100],[3,52,1,112],[4,64],
      [1,16,3,76],[2,28,2,88],[1,12,4,72],[3,32,2,92],[5,52],[3,42,2,102],
      [5,62],[2,22,3,82],[2,24,3,84],[4,44,1,104],[1,4,4,64],[4,54,1,114],
      [1,14,4,74],[3,34,2,94],[3,36,2,96],[5,56],[2,16,3,76],[5,66],[2,26,3,86],
      [4,46,1,106],[4,48,1,108],[1,8,4,68],[3,28,2,88],[1,18,4,78],[3,38,2,98],
      [5,58],[5,60],[2,20,3,80],[4,40,1,100],[2,30,3,90],[4,50,1,110],
      [1,10,4,70],[3,25,3,85],[1,7,5,67],[5,49,1,109],[6,61],[4,43,2,103],
      [4,35,2,95],[2,17,4,77],[6,59],[1,11,5,71],[5,53,1,113],[5,45,1,105],
      [3,27,3,87],[1,9,5,69],[2,21,4,81],[6,63],[6,55],[4,37,2,97],[2,19,4,79],
      [3,31,3,91],[1,13,5,73],[1,5,5,65],[5,47,1,107],[3,29,3,89],[4,41,2,101],
      [2,23,4,83],[2,15,4,75],[6,57],[4,39,2,99],[5,51,1,111],[3,33,3,93]],
320=>[[1,0],[1,20],[1,40],[1,21,1,39],[1,27,1,33],[1,11,1,29],[1,17,1,23],
      [1,1,1,19],[1,7,1,13],[1,2,1,20,1,38],[1,14,1,20,1,26],[1,10,1,22,1,28],
      [1,10,1,16,1,34],[1,12,1,18,1,30],[1,6,1,24,1,30],[1,3,1,9,1,21,1,27],
      [1,11,1,17,1,23,1,29],[1,13,1,19,1,31,1,37],[1,6,1,12,1,18,1,24],
      [1,8,1,14,1,26,1,32],[1,16,1,22,1,28,1,34],[1,12,1,18,1,24,1,30,1,36],
      [1,8,1,14,1,20,1,26,1,32],[1,4,1,10,1,16,1,22,1,28],
      [1,7,1,13,1,19,2,25,1,31],[1,9,2,15,1,21,1,27,1,33],
      [1,5,1,11,1,17,1,23,1,29,1,35]],
321=>[[1,0],[1,20],[1,40],[1,30],[1,50],[1,70],[1,39,1,51],[1,33,1,57],
      [1,21,1,69],[1,27,1,63],[1,29,1,41],[1,23,1,47],[1,17,1,53],[1,11,1,59],
      [1,19,1,31],[1,13,1,37],[1,7,1,43],[1,1,1,49],[1,2,1,38,1,50],
      [1,14,1,26,1,50],[1,20,1,32,1,68],[1,20,1,44,1,56],[1,10,1,22,1,58],
      [1,10,1,34,1,46],[1,28,1,40,1,52],[1,16,1,40,1,64],[1,18,1,30,1,42],
      [1,6,1,30,1,54],[1,12,1,48,1,60],[1,24,1,36,1,60],[1,3,1,27,1,39,1,51],
      [1,11,1,23,1,47,1,59],[1,19,1,31,1,43,1,67],[1,6,1,18,1,42,1,54],
      [1,14,1,26,1,38,1,62],[1,22,1,34,1,46,1,58],[1,9,1,21,1,33,1,57],
      [1,17,1,29,1,41,1,53],[1,13,1,37,1,49,1,61],[1,12,1,24,1,36,1,48],
      [1,8,1,32,1,44,1,56],[1,16,1,28,1,52,1,64],[1,12,1,24,1,36,1,48,1,60],
      [1,8,1,20,1,32,1,44,1,56],[1,4,1,16,1,28,1,40,1,52],
      [1,18,1,30,1,42,1,54,1,66],[1,14,1,26,1,38,1,50,1,62],
      [1,10,1,22,1,34,1,46,1,58],[1,13,2,25,1,37,1,49,1,61],
      [1,7,1,19,1,31,1,43,2,55],[1,11,1,23,2,35,1,47,1,59],
      [1,5,1,17,1,29,1,41,1,53,1,65],[1,9,1,21,1,33,2,45,1,57],
      [2,15,1,27,1,39,1,51,1,63]],
322=>[[1,0],[1,30],[1,11,1,19],[1,13,1,17],[1,1,1,29],[1,7,1,23],
      [1,2,1,10,1,18],[1,6,1,10,1,14],[1,12,1,20,1,28],[1,16,1,20,1,24],
      [1,3,1,11,1,19,1,27],[1,6,1,14,1,18,1,22],[1,9,1,13,1,17,1,21],
      [1,8,1,12,1,16,1,24],[1,4,1,8,1,12,1,16,1,20],
      [1,10,1,14,1,18,1,22,1,26],[1,7,1,11,2,15,1,19,1,23],
      [1,5,1,9,1,13,1,17,1,21,1,25]])
  d[x]
end
2

This isn’t the source of your problem, as you’ve noticed already, but I believe that global anonymous function definitions result in type unstable functions because they aren’t constant to the compiler. For globally scoped functions, you should use function f(x) end syntax instead.

3

As already noted above, that’s not exactly usual Julia style. d should instead be a global constant, and f(x) = d[x] (I’d question the need to define such a function in the first place, but…). That said, the style doesn’t affect compilation latency. However, interestingly enough Julia 1.0 takes only 2 seconds for me to compile this function:

julia> @time f(4) # first call, including compilation
  2.515081 seconds (7.51 M allocations: 350.298 MiB, 5.63% gc time)
7-element Array{Array{Int64,1},1}:
 [1, 0]            
 [1, 4]            
 [1, 8]            
 [1, 5, 1, 7]      
 [1, 3, 1, 5]      
 [1, 1, 1, 3]      
 [1, 2, 1, 4, 1, 6]

julia> @time f(4) # second call, without compilation
  0.000131 seconds (2.11 k allocations: 245.953 KiB)
7-element Array{Array{Int64,1},1}:
 [1, 0]            
 [1, 4]            
 [1, 8]            
 [1, 5, 1, 7]      
 [1, 3, 1, 5]      
 [1, 1, 1, 3]      
 [1, 2, 1, 4, 1, 6]

julia> versioninfo()
Julia Version 1.0.5
Commit 3af96bcefc (2019-09-09 19:06 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i7-4870HQ CPU @ 2.50GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-6.0.0 (ORCJIT, haswell)
4

Could you post this example so we can see if we can improve compilation time in these cases?

5

It is difficult to give the example with polynomials since it also uses a big part of my huge package
Gapjm.jl. Imagine that a list [1,2,3,4] in the example is replaced by something like [1+x+2y^2+4x^3] where x,y,z are arguments to the function. But is not the example I gave already an example of something going wrong?

  • The time is exponential in the length of the data (if you double the length of the Dict definition the time is multiplied by 5 or 10).
  • From Giordano’s report it compiled quickly on Julia 1.0.5 so it is like a regression.
  • Why does the dictionary definition compile so slow inside a function?

By the way as already discussed I do prefer writing functions as function f(x) rather than f=function(x) but:

  • In recent julia (at least 1.7.2 which I use) it seems to make no performance difference (it was different with older julia)
  • The @time is only reported correctly with f=function(x). I also wonder why?
6

You may want to open an issue in GitHub. Since this seems to be a bug deep into Julia’s internals, I’m not sure you’ll get much help here.

Edit: issue opened at Excessive compilation time (regression) · Issue #45395 · JuliaLang/julia · GitHub.

7

This is answered by @time docstring:

help?> @time
  @time

  A macro to execute an expression, printing the time it took to execute, the number of allocations, and the total number of bytes its execution caused to be allocated, before returning the value of the
  expression. Any time spent garbage collecting (gc) or compiling is shown as a percentage.

  In some cases the system will look inside the @time expression and compile some of the called code before execution of the top-level expression begins. When that happens, some compilation time will not be
  counted. To include this time you can run @time @eval ....

You have to use @time @eval to always include compilation time when using @time.

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