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Timing by profiling

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  • Stalkern 2
    I wonder whether let print_differentEls al1 al2 = List.iter2 (fun a b - if (a=b) then () else print_endline (string_of_int b)) (List.rev al1) (List.rev al2);;
    Message 1 of 1 , Feb 27, 2003
    • 0 Attachment
      I wonder whether

      let print_differentEls al1 al2 = List.iter2 (fun a b -> if (a=b) then () else
      print_endline (string_of_int b)) (List.rev al1) (List.rev al2);;

      is more efficient than

      let print_differentEls al1 al2 = List.iter (fun el -> match el with None -> ()
      | Some r -> print_endline (string_of_int r)) (List.rev_map2 (fun a b -> if
      (a=b) then None else Some b) al1 al2);;


      To test this, I've thought about timing the two of them. I've never timed
      anything in Ocaml, I thought that "profiling" would make it.

      So I've written two samples
      ---------------------------------------------
      checkout1.ml
      ---------------------------------------------
      let l1 = [10;9;8;7;6;5;4;3;2;1;0] in

      let l2 = [100;9;80;7;60;5;40;3;20;1;0] in

      let print_differentEls al1 al2 = List.iter2 (fun a b -> if (a=b) then () else
      print_endline (string_of_int b)) (List.rev al1) (List.rev al2)
      in

      for i=0 to 100000 do
      print_differentEls l1 l2
      done;;
      ---------------------------------------------

      and

      ---------------------------------------------
      checkout2.ml
      ---------------------------------------------
      let l1 = [10;9;8;7;6;5;4;3;2;1;0] in

      let l2 = [100;9;80;7;60;5;40;3;20;1;0] in

      let print_differentEls al1 al2 = List.iter (fun el -> match el with None -> ()
      | Some r -> print_endline (string_of_int r)) (List.rev_map2 (fun a b -> if
      (a=b) then None else Some b) al1 al2)
      in

      for i=0 to 100000 do
      print_differentEls l1 l2
      done;;
      ---------------------------------------------

      and then I've used commands

      $ ocamlopt -p checkout1.ml -o checkout1.opt
      $ gprof checkout1.opt > gprof_checkout1.txt

      $ ocamlopt -p checkout2.ml -o checkout2.opt
      $ gprof checkout2.opt > gprof_checkout2.txt

      Obtaining the two files that I join. What should I be attentive to, to
      understand what form works quicker?

      Thank you in advance
      Ernesto



      ----------

      Flat profile:

      Each sample counts as 0.00195312 seconds.
      no time accumulated

      % cumulative self self total
      time seconds seconds calls Ts/call Ts/call name
      0.00 0.00 0.00 29 0.00 0.00 caml_alloc
      0.00 0.00 0.00 11 0.00 0.00 Checkout1__fun_65
      0.00 0.00 0.00 11 0.00 0.00 caml_apply2
      0.00 0.00 0.00 10 0.00 0.00 modify
      0.00 0.00 0.00 6 0.00 0.00 classify_float
      0.00 0.00 0.00 6 0.00 0.00 ge_float
      0.00 0.00 0.00 6 0.00 0.00 nativeint_format
      0.00 0.00 0.00 5 0.00 0.00 Pervasives__bool_of_string_151
      0.00 0.00 0.00 5 0.00 0.00 Pervasives__open_out_bin_202
      0.00 0.00 0.00 5 0.00 0.00 Pervasives__print_string_285
      0.00 0.00 0.00 5 0.00 0.00 alloc_shr
      0.00 0.00 0.00 5 0.00 0.00 alloc_small
      0.00 0.00 0.00 5 0.00 0.00 alloc_string
      0.00 0.00 0.00 5 0.00 0.00 allocate_block
      0.00 0.00 0.00 5 0.00 0.00 caml_flush
      0.00 0.00 0.00 5 0.00 0.00 caml_output_partial
      0.00 0.00 0.00 5 0.00 0.00 ext_table_free
      0.00 0.00 0.00 5 0.00 0.00 final_register
      0.00 0.00 0.00 5 0.00 0.00 finalize_channel
      0.00 0.00 0.00 5 0.00 0.00 init_signals
      0.00 0.00 0.00 5 0.00 0.00 minor_collection
      0.00 0.00 0.00 5 0.00 0.00 parse_format
      0.00 0.00 0.00 5 0.00 0.00 parse_long
      0.00 0.00 0.00 5 0.00 0.00 putword
      0.00 0.00 0.00 5 0.00 0.00 shrink_heap
      0.00 0.00 0.00 4 0.00 0.00 gc_get
      0.00 0.00 0.00 3 0.00 0.00 alloc_channel
      0.00 0.00 0.00 3 0.00 0.00 alloc_custom
      0.00 0.00 0.00 3 0.00 0.00 is_printable
      0.00 0.00 0.00 2 0.00 0.00 List__nth_68
      0.00 0.00 0.00 2 0.00 0.00 alloc
      0.00 0.00 0.00 2 0.00 0.00 callback2_exn
      0.00 0.00 0.00 2 0.00 0.00 caml_flush_partial
      0.00 0.00 0.00 2 0.00 0.00 do_write
      0.00 0.00 0.00 2 0.00 0.00 flush_partial
      0.00 0.00 0.00 2 0.00 0.00 open_descriptor_in
      0.00 0.00 0.00 1 0.00 0.00 Checkout1__print_differentEls_58
      0.00 0.00 0.00 1 0.00 0.00 List__rev_map2_122
      0.00 0.00 0.00 1 0.00 0.00 List__stable_sort_271
      0.00 0.00 0.00 1 0.00 0.00 Pervasives__code_begin
      0.00 0.00 0.00 1 0.00 0.00 Pervasives__do_at_exit_329
      0.00 0.00 0.00 1 0.00 0.00 Pervasives__open_out_gen_196
      0.00 0.00 0.00 1 0.00 0.00 Std_exit__entry
      0.00 0.00 0.00 1 0.00 0.00 callback3
      0.00 0.00 0.00 1 0.00 0.00 callbackN
      0.00 0.00 0.00 1 0.00 0.00 caml_alloc2
      0.00 0.00 0.00 1 0.00 0.00 channel_size
      0.00 0.00 0.00 1 0.00 0.00 clip_heap_chunk_size
      0.00 0.00 0.00 1 0.00 0.00 compare_channel
      0.00 0.00 0.00 1 0.00 0.00 do_local_roots
      0.00 0.00 0.00 1 0.00 0.00 enter_blocking_section
      0.00 0.00 0.00 1 0.00 0.00 fatal_error_arg
      0.00 0.00 0.00 1 0.00 0.00 final_custom_operations
      0.00 0.00 0.00 1 0.00 0.00 finish_major_cycle
      0.00 0.00 0.00 1 0.00 0.00 fl_allocate
      0.00 0.00 0.00 1 0.00 0.00 fl_init_merge
      0.00 0.00 0.00 1 0.00 0.00 garbage_collection
      0.00 0.00 0.00 1 0.00 0.00 gc_major_slice
      0.00 0.00 0.00 1 0.00 0.00 init_custom_operations
      0.00 0.00 0.00 1 0.00 0.00 init_major_heap
      0.00 0.00 0.00 1 0.00 0.00 is_stack_overflow
      0.00 0.00 0.00 1 0.00 0.00 minmax_table
      0.00 0.00 0.00 1 0.00 0.00 norm_pfree
      0.00 0.00 0.00 1 0.00 0.00 parse_camlrunparam
      0.00 0.00 0.00 1 0.00 0.00 random_level
      0.00 0.00 0.00 1 0.00 0.00 realloc_ref_table
      0.00 0.00 0.00 1 0.00 0.00 scanmult
      0.00 0.00 0.00 1 0.00 0.00 startup__code_begin
      0.00 0.00 0.00 1 0.00 0.00 sys_error
      0.00 0.00 0.00 1 0.00 0.00 sys_get_argv

      % the percentage of the total running time of the
      time program used by this function.

      cumulative a running sum of the number of seconds accounted
      seconds for by this function and those listed above it.

      self the number of seconds accounted for by this
      seconds function alone. This is the major sort for this
      listing.

      calls the number of times this function was invoked, if
      this function is profiled, else blank.

      self the average number of milliseconds spent in this
      ms/call function per call, if this function is profiled,
      else blank.

      total the average number of milliseconds spent in this
      ms/call function and its descendents per call, if this
      function is profiled, else blank.

      name the name of the function. This is the minor sort
      for this listing. The index shows the location of
      the function in the gprof listing. If the index is
      in parenthesis it shows where it would appear in
      the gprof listing if it were to be printed.

      Call graph (explanation follows)


      granularity: each sample hit covers 4 byte(s) no time propagated

      index % time self children called name
      0.00 0.00 1/29 Pervasives__open_out_200 [170]
      0.00 0.00 1/29 caml_main [246]
      0.00 0.00 2/29 Pervasives__code_begin [40]
      0.00 0.00 5/29 Pervasives__bool_of_string_151 [8]
      0.00 0.00 5/29 Pervasives__flush_all_206 [135]
      0.00 0.00 5/29 Pervasives__print_int_287 [183]
      0.00 0.00 10/29 Pervasives__entry [132]
      [1] 0.0 0.00 0.00 29 caml_alloc [1]
      -----------------------------------------------
      0.00 0.00 11/11 List__rev_map2_122 [38]
      [2] 0.0 0.00 0.00 11 Checkout1__fun_65 [2]
      0.00 0.00 5/5 Pervasives__bool_of_string_151 [8]
      -----------------------------------------------
      0.00 0.00 11/11 List__rev_map2_122 [38]
      [3] 0.0 0.00 0.00 11 caml_apply2 [3]
      -----------------------------------------------
      0.00 0.00 1/10 register_global_root [523]
      0.00 0.00 1/10 init_major_heap [60]
      0.00 0.00 1/10 set_minor_heap_size [544]
      0.00 0.00 1/10 hash_value_name [366]
      0.00 0.00 3/10 is_printable [29]
      0.00 0.00 3/10 alloc_custom [28]
      [4] 0.0 0.00 0.00 10 modify [4]
      -----------------------------------------------
      0.00 0.00 1/6 parse_camlrunparam [64]
      0.00 0.00 5/6 parse_long [23]
      [5] 0.0 0.00 0.00 6 classify_float [5]
      -----------------------------------------------
      0.00 0.00 6/6 Pervasives__entry [132]
      [6] 0.0 0.00 0.00 6 ge_float [6]
      0.00 0.00 6/6 nativeint_format [7]
      -----------------------------------------------
      0.00 0.00 6/6 ge_float [6]
      [7] 0.0 0.00 0.00 6 nativeint_format [7]
      -----------------------------------------------
      0.00 0.00 5/5 Checkout1__fun_65 [2]
      [8] 0.0 0.00 0.00 5 Pervasives__bool_of_string_151 [8]
      0.00 0.00 5/5 parse_format [22]
      0.00 0.00 5/29 caml_alloc [1]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__print_int_287 [183]
      [9] 0.0 0.00 0.00 5 Pervasives__open_out_bin_202 [9]
      -----------------------------------------------
      0.00 0.00 5/5 List__rev_map2_122 [38]
      [10] 0.0 0.00 0.00 5 Pervasives__print_string_285 [10]
      -----------------------------------------------
      0.00 0.00 5/5 alloc_custom [28]
      [11] 0.0 0.00 0.00 5 alloc_shr [11]
      -----------------------------------------------
      0.00 0.00 5/5 alloc_final [207]
      [12] 0.0 0.00 0.00 5 alloc_small [12]
      -----------------------------------------------
      0.00 0.00 5/5 parse_format [22]
      [13] 0.0 0.00 0.00 5 alloc_string [13]
      -----------------------------------------------
      0.00 0.00 5/5 allocation_color [210]
      [14] 0.0 0.00 0.00 5 allocate_block [14]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__print_int_287 [183]
      [15] 0.0 0.00 0.00 5 caml_flush [15]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__flush_all_206 [135]
      [16] 0.0 0.00 0.00 5 caml_output_partial [16]
      -----------------------------------------------
      0.00 0.00 5/5 fl_allocate [55]
      [17] 0.0 0.00 0.00 5 ext_table_free [17]
      -----------------------------------------------
      0.00 0.00 5/5 finalize_channel [19]
      [18] 0.0 0.00 0.00 5 final_register [18]
      0.00 0.00 5/5 shrink_heap [25]
      -----------------------------------------------
      0.00 0.00 1/5 compare_channel [49]
      0.00 0.00 2/5 alloc_channel [27]
      0.00 0.00 2/5 caml_out_channels_list [250]
      [19] 0.0 0.00 0.00 5 finalize_channel [19]
      0.00 0.00 5/5 final_register [18]
      -----------------------------------------------
      0.00 0.00 5/5 init_gc [371]
      [20] 0.0 0.00 0.00 5 init_signals [20]
      -----------------------------------------------
      0.00 0.00 5/5 alloc_custom [28]
      [21] 0.0 0.00 0.00 5 minor_collection [21]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__bool_of_string_151 [8]
      [22] 0.0 0.00 0.00 5 parse_format [22]
      0.00 0.00 5/5 parse_long [23]
      0.00 0.00 5/5 alloc_string [13]
      -----------------------------------------------
      0.00 0.00 5/5 parse_format [22]
      [23] 0.0 0.00 0.00 5 parse_long [23]
      0.00 0.00 5/6 classify_float [5]
      -----------------------------------------------
      0.00 0.00 5/5 caml_output [251]
      [24] 0.0 0.00 0.00 5 putword [24]
      -----------------------------------------------
      0.00 0.00 5/5 final_register [18]
      [25] 0.0 0.00 0.00 5 shrink_heap [25]
      -----------------------------------------------
      0.00 0.00 1/4 gc_major_slice [58]
      0.00 0.00 1/4 gc_compaction [352]
      0.00 0.00 2/4 init_gc [371]
      [26] 0.0 0.00 0.00 4 gc_get [26]
      -----------------------------------------------
      0.00 0.00 1/3 Pervasives__open_out_200 [170]
      0.00 0.00 2/3 Pervasives__entry [132]
      [27] 0.0 0.00 0.00 3 alloc_channel [27]
      0.00 0.00 2/2 open_descriptor_in [36]
      0.00 0.00 2/5 finalize_channel [19]
      -----------------------------------------------
      0.00 0.00 3/3 final_custom_operations [53]
      [28] 0.0 0.00 0.00 3 alloc_custom [28]
      0.00 0.00 5/5 alloc_shr [11]
      0.00 0.00 5/5 minor_collection [21]
      0.00 0.00 3/10 modify [4]
      -----------------------------------------------
      0.00 0.00 1/3 compare_channel [49]
      0.00 0.00 2/3 open_descriptor_in [36]
      [29] 0.0 0.00 0.00 3 is_printable [29]
      0.00 0.00 3/10 modify [4]
      -----------------------------------------------
      0.00 0.00 2/2 Checkout1__print_differentEls_58 [37]
      [30] 0.0 0.00 0.00 2 List__nth_68 [30]
      -----------------------------------------------
      0.00 0.00 2/2 caml_out_channels_list [250]
      [31] 0.0 0.00 0.00 2 alloc [31]
      -----------------------------------------------
      0.00 0.00 1/2 minmax_table [62]
      0.00 0.00 1/2 init_atoms [368]
      [32] 0.0 0.00 0.00 2 callback2_exn [32]
      -----------------------------------------------
      0.00 0.00 2/2 Pervasives__code_begin [40]
      [33] 0.0 0.00 0.00 2 caml_flush_partial [33]
      0.00 0.00 2/2 flush_partial [35]
      -----------------------------------------------
      0.00 0.00 2/2 flush_partial [35]
      [34] 0.0 0.00 0.00 2 do_write [34]
      0.00 0.00 1/1 channel_size [47]
      -----------------------------------------------
      0.00 0.00 2/2 caml_flush_partial [33]
      [35] 0.0 0.00 0.00 2 flush_partial [35]
      0.00 0.00 2/2 do_write [34]
      -----------------------------------------------
      0.00 0.00 2/2 alloc_channel [27]
      [36] 0.0 0.00 0.00 2 open_descriptor_in [36]
      0.00 0.00 2/3 is_printable [29]
      -----------------------------------------------
      0.00 0.00 1/1 startup__code_begin [68]
      [37] 0.0 0.00 0.00 1 Checkout1__print_differentEls_58 [37]
      0.00 0.00 2/2 List__nth_68 [30]
      0.00 0.00 1/1 List__rev_map2_122 [38]
      -----------------------------------------------
      0.00 0.00 1/1 Checkout1__print_differentEls_58 [37]
      [38] 0.0 0.00 0.00 1 List__rev_map2_122 [38]
      0.00 0.00 11/11 Checkout1__fun_65 [2]
      0.00 0.00 11/11 caml_apply2 [3]
      0.00 0.00 5/5 Pervasives__print_string_285 [10]
      -----------------------------------------------
      0.00 0.00 1/1 startup__code_begin [68]
      [39] 0.0 0.00 0.00 1 List__stable_sort_271 [39]
      -----------------------------------------------
      0.00 0.00 1/1 Std_exit__entry [43]
      [40] 0.0 0.00 0.00 1 Pervasives__code_begin [40]
      0.00 0.00 2/2 caml_flush_partial [33]
      0.00 0.00 2/29 caml_alloc [1]
      -----------------------------------------------
      0.00 0.00 1/1 startup__code_begin [68]
      [41] 0.0 0.00 0.00 1 Pervasives__do_at_exit_329 [41]
      -----------------------------------------------
      0.00 0.00 1/1 Std_exit__entry [43]
      [42] 0.0 0.00 0.00 1 Pervasives__open_out_gen_196 [42]
      -----------------------------------------------
      0.00 0.00 1/1 startup__code_begin [68]
      [43] 0.0 0.00 0.00 1 Std_exit__entry [43]
      0.00 0.00 1/1 Pervasives__code_begin [40]
      0.00 0.00 1/1 Pervasives__open_out_gen_196 [42]
      -----------------------------------------------
      0.00 0.00 1/1 callbackN [45]
      [44] 0.0 0.00 0.00 1 callback3 [44]
      -----------------------------------------------
      0.00 0.00 1/1 Pervasives__entry [132]
      [45] 0.0 0.00 0.00 1 callbackN [45]
      0.00 0.00 1/1 callback3 [44]
      -----------------------------------------------
      0.00 0.00 1/1 Pervasives__entry [132]
      [46] 0.0 0.00 0.00 1 caml_alloc2 [46]
      -----------------------------------------------
      0.00 0.00 1/1 do_write [34]
      [47] 0.0 0.00 0.00 1 channel_size [47]
      0.00 0.00 1/1 garbage_collection [57]
      0.00 0.00 1/1 enter_blocking_section [51]
      -----------------------------------------------
      0.00 0.00 1/1 init_gc [371]
      [48] 0.0 0.00 0.00 1 clip_heap_chunk_size [48]
      0.00 0.00 1/1 finish_major_cycle [54]
      -----------------------------------------------
      0.00 0.00 1/1 Pervasives__entry [132]
      [49] 0.0 0.00 0.00 1 compare_channel [49]
      0.00 0.00 1/3 is_printable [29]
      0.00 0.00 1/5 finalize_channel [19]
      -----------------------------------------------
      0.00 0.00 1/1 register_global_root [523]
      [50] 0.0 0.00 0.00 1 do_local_roots [50]
      -----------------------------------------------
      0.00 0.00 1/1 channel_size [47]
      [51] 0.0 0.00 0.00 1 enter_blocking_section [51]
      -----------------------------------------------
      0.00 0.00 1/1 realloc_ref_table [66]
      [52] 0.0 0.00 0.00 1 fatal_error_arg [52]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [64]
      [53] 0.0 0.00 0.00 1 final_custom_operations [53]
      0.00 0.00 3/3 alloc_custom [28]
      -----------------------------------------------
      0.00 0.00 1/1 clip_heap_chunk_size [48]
      [54] 0.0 0.00 0.00 1 finish_major_cycle [54]
      -----------------------------------------------
      0.00 0.00 1/1 init_major_heap [60]
      [55] 0.0 0.00 0.00 1 fl_allocate [55]
      0.00 0.00 5/5 ext_table_free [17]
      -----------------------------------------------
      0.00 0.00 1/1 init_major_heap [60]
      [56] 0.0 0.00 0.00 1 fl_init_merge [56]
      -----------------------------------------------
      0.00 0.00 1/1 channel_size [47]
      [57] 0.0 0.00 0.00 1 garbage_collection [57]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [64]
      [58] 0.0 0.00 0.00 1 gc_major_slice [58]
      0.00 0.00 1/4 gc_get [26]
      -----------------------------------------------
      0.00 0.00 1/1 Pervasives__entry [132]
      [59] 0.0 0.00 0.00 1 init_custom_operations [59]
      -----------------------------------------------
      0.00 0.00 1/1 gc_compaction [352]
      [60] 0.0 0.00 0.00 1 init_major_heap [60]
      0.00 0.00 1/1 fl_allocate [55]
      0.00 0.00 1/1 fl_init_merge [56]
      0.00 0.00 1/10 modify [4]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [64]
      [61] 0.0 0.00 0.00 1 is_stack_overflow [61]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [64]
      [62] 0.0 0.00 0.00 1 minmax_table [62]
      0.00 0.00 1/2 callback2_exn [32]
      -----------------------------------------------
      0.00 0.00 1/1 gc_compaction [352]
      [63] 0.0 0.00 0.00 1 norm_pfree [63]
      -----------------------------------------------
      0.00 0.00 1/1 List__entry [81]
      [64] 0.0 0.00 0.00 1 parse_camlrunparam [64]
      0.00 0.00 1/6 classify_float [5]
      0.00 0.00 1/1 final_custom_operations [53]
      0.00 0.00 1/1 scanmult [67]
      0.00 0.00 1/1 gc_major_slice [58]
      0.00 0.00 1/1 minmax_table [62]
      0.00 0.00 1/1 is_stack_overflow [61]
      -----------------------------------------------
      0.00 0.00 1/1 register_named_value [524]
      [65] 0.0 0.00 0.00 1 random_level [65]
      -----------------------------------------------
      0.00 0.00 1/1 round_heap_chunk_size [529]
      [66] 0.0 0.00 0.00 1 realloc_ref_table [66]
      0.00 0.00 1/1 fatal_error_arg [52]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [64]
      [67] 0.0 0.00 0.00 1 scanmult [67]
      -----------------------------------------------
      0.00 0.00 1/1 caml_c_call [228]
      [68] 0.0 0.00 0.00 1 startup__code_begin [68]
      0.00 0.00 1/1 Pervasives__do_at_exit_329 [41]
      0.00 0.00 1/1 List__stable_sort_271 [39]
      0.00 0.00 1/1 Checkout1__print_differentEls_58 [37]
      0.00 0.00 1/1 Std_exit__entry [43]
      -----------------------------------------------
      0.00 0.00 1/1 List__entry [81]
      [69] 0.0 0.00 0.00 1 sys_error [69]
      -----------------------------------------------
      0.00 0.00 1/1 caml_main [246]
      [70] 0.0 0.00 0.00 1 sys_get_argv [70]
      -----------------------------------------------

      This table describes the call tree of the program, and was sorted by
      the total amount of time spent in each function and its children.

      Each entry in this table consists of several lines. The line with the
      index number at the left hand margin lists the current function.
      The lines above it list the functions that called this function,
      and the lines below it list the functions this one called.
      This line lists:
      index A unique number given to each element of the table.
      Index numbers are sorted numerically.
      The index number is printed next to every function name so
      it is easier to look up where the function in the table.

      % time This is the percentage of the `total' time that was spent
      in this function and its children. Note that due to
      different viewpoints, functions excluded by options, etc,
      these numbers will NOT add up to 100%.

      self This is the total amount of time spent in this function.

      children This is the total amount of time propagated into this
      function by its children.

      called This is the number of times the function was called.
      If the function called itself recursively, the number
      only includes non-recursive calls, and is followed by
      a `+' and the number of recursive calls.

      name The name of the current function. The index number is
      printed after it. If the function is a member of a
      cycle, the cycle number is printed between the
      function's name and the index number.


      For the function's parents, the fields have the following meanings:

      self This is the amount of time that was propagated directly
      from the function into this parent.

      children This is the amount of time that was propagated from
      the function's children into this parent.

      called This is the number of times this parent called the
      function `/' the total number of times the function
      was called. Recursive calls to the function are not
      included in the number after the `/'.

      name This is the name of the parent. The parent's index
      number is printed after it. If the parent is a
      member of a cycle, the cycle number is printed between
      the name and the index number.

      If the parents of the function cannot be determined, the word
      `<spontaneous>' is printed in the `name' field, and all the other
      fields are blank.

      For the function's children, the fields have the following meanings:

      self This is the amount of time that was propagated directly
      from the child into the function.

      children This is the amount of time that was propagated from the
      child's children to the function.

      called This is the number of times the function called
      this child `/' the total number of times the child
      was called. Recursive calls by the child are not
      listed in the number after the `/'.

      name This is the name of the child. The child's index
      number is printed after it. If the child is a
      member of a cycle, the cycle number is printed
      between the name and the index number.

      If there are any cycles (circles) in the call graph, there is an
      entry for the cycle-as-a-whole. This entry shows who called the
      cycle (as parents) and the members of the cycle (as children.)
      The `+' recursive calls entry shows the number of function calls that
      were internal to the cycle, and the calls entry for each member shows,
      for that member, how many times it was called from other members of
      the cycle.


      Index by function name

      [2] Checkout1__fun_65 [3] caml_apply2 [59] init_custom_operations
      [37] Checkout1__print_differentEls_58 [15] caml_flush [60] init_major_heap
      [30] List__nth_68 [33] caml_flush_partial [20] init_signals
      [38] List__rev_map2_122 [16] caml_output_partial [29] is_printable
      [39] List__stable_sort_271 [47] channel_size [61] is_stack_overflow
      [8] Pervasives__bool_of_string_151 [5] classify_float [62] minmax_table
      [40] Pervasives__code_begin [48] clip_heap_chunk_size [21] minor_collection
      [41] Pervasives__do_at_exit_329 [49] compare_channel [4] modify
      [9] Pervasives__open_out_bin_202 [50] do_local_roots [7] nativeint_format
      [42] Pervasives__open_out_gen_196 [34] do_write [63] norm_pfree
      [10] Pervasives__print_string_285 [51] enter_blocking_section [36] open_descriptor_in
      [43] Std_exit__entry [17] ext_table_free [64] parse_camlrunparam
      [31] alloc [52] fatal_error_arg [22] parse_format
      [27] alloc_channel [53] final_custom_operations [23] parse_long
      [28] alloc_custom [18] final_register [24] putword
      [11] alloc_shr [19] finalize_channel [65] random_level
      [12] alloc_small [54] finish_major_cycle [66] realloc_ref_table
      [13] alloc_string [55] fl_allocate [67] scanmult
      [14] allocate_block [56] fl_init_merge [25] shrink_heap
      [32] callback2_exn [35] flush_partial [68] startup__code_begin
      [44] callback3 [57] garbage_collection [69] sys_error
      [45] callbackN [26] gc_get [70] sys_get_argv
      [1] caml_alloc [58] gc_major_slice
      [46] caml_alloc2 [6] ge_float

      ----------

      Flat profile:

      Each sample counts as 0.00195312 seconds.
      no time accumulated

      % cumulative self self total
      time seconds seconds calls Ts/call Ts/call name
      0.00 0.00 0.00 28 0.00 0.00 caml_alloc3
      0.00 0.00 0.00 12 0.00 0.00 Checkout2__fun_69
      0.00 0.00 0.00 11 0.00 0.00 caml_apply2
      0.00 0.00 0.00 10 0.00 0.00 modify
      0.00 0.00 0.00 8 0.00 0.00 final_register
      0.00 0.00 0.00 6 0.00 0.00 lt_float
      0.00 0.00 0.00 6 0.00 0.00 nativeint_format
      0.00 0.00 0.00 5 0.00 0.00 Pervasives__open_out_gen_196
      0.00 0.00 0.00 5 0.00 0.00 Pervasives__print_char_283
      0.00 0.00 0.00 5 0.00 0.00 Pervasives__string_of_bool_149
      0.00 0.00 0.00 5 0.00 0.00 alloc_shr
      0.00 0.00 0.00 5 0.00 0.00 alloc_small
      0.00 0.00 0.00 5 0.00 0.00 alloc_string
      0.00 0.00 0.00 5 0.00 0.00 allocate_block
      0.00 0.00 0.00 5 0.00 0.00 caml_flush_partial
      0.00 0.00 0.00 5 0.00 0.00 caml_output_partial
      0.00 0.00 0.00 5 0.00 0.00 classify_float
      0.00 0.00 0.00 5 0.00 0.00 empty_minor_heap
      0.00 0.00 0.00 5 0.00 0.00 ext_table_add
      0.00 0.00 0.00 5 0.00 0.00 finalize_channel
      0.00 0.00 0.00 5 0.00 0.00 gc_get
      0.00 0.00 0.00 5 0.00 0.00 init_signals
      0.00 0.00 0.00 5 0.00 0.00 parse_format
      0.00 0.00 0.00 5 0.00 0.00 parse_long
      0.00 0.00 0.00 5 0.00 0.00 putword
      0.00 0.00 0.00 5 0.00 0.00 shrink_heap
      0.00 0.00 0.00 3 0.00 0.00 compare_channel
      0.00 0.00 0.00 3 0.00 0.00 is_printable
      0.00 0.00 0.00 2 0.00 0.00 List__tl_65
      0.00 0.00 0.00 2 0.00 0.00 alloc
      0.00 0.00 0.00 2 0.00 0.00 bitvect_test
      0.00 0.00 0.00 2 0.00 0.00 callback_exn
      0.00 0.00 0.00 2 0.00 0.00 caml_channel_size_64
      0.00 0.00 0.00 2 0.00 0.00 channel_binary_mode
      0.00 0.00 0.00 2 0.00 0.00 do_local_roots
      0.00 0.00 0.00 2 0.00 0.00 final_custom_operations
      0.00 0.00 0.00 2 0.00 0.00 fl_allocate
      0.00 0.00 0.00 2 0.00 0.00 flush_partial
      0.00 0.00 0.00 1 0.00 0.00 List__map2_113
      0.00 0.00 0.00 1 0.00 0.00 List__stable_sort_271
      0.00 0.00 0.00 1 0.00 0.00 Pervasives__$40_164
      0.00 0.00 0.00 1 0.00 0.00 Pervasives__at_exit_326
      0.00 0.00 0.00 1 0.00 0.00 Pervasives__code_begin
      0.00 0.00 0.00 1 0.00 0.00 Std_exit__entry
      0.00 0.00 0.00 1 0.00 0.00 callback2
      0.00 0.00 0.00 1 0.00 0.00 callback3_exn
      0.00 0.00 0.00 1 0.00 0.00 callbackN
      0.00 0.00 0.00 1 0.00 0.00 caml_alloc
      0.00 0.00 0.00 1 0.00 0.00 caml_alloc2
      0.00 0.00 0.00 1 0.00 0.00 channel_size
      0.00 0.00 0.00 1 0.00 0.00 execute_signal
      0.00 0.00 0.00 1 0.00 0.00 fatal_error
      0.00 0.00 0.00 1 0.00 0.00 finish_major_cycle
      0.00 0.00 0.00 1 0.00 0.00 float_of_bytes
      0.00 0.00 0.00 1 0.00 0.00 gc_full_major
      0.00 0.00 0.00 1 0.00 0.00 init_atoms
      0.00 0.00 0.00 1 0.00 0.00 init_major_heap
      0.00 0.00 0.00 1 0.00 0.00 is_stack_overflow
      0.00 0.00 0.00 1 0.00 0.00 parse_camlrunparam
      0.00 0.00 0.00 1 0.00 0.00 realloc_ref_table
      0.00 0.00 0.00 1 0.00 0.00 startup__code_begin
      0.00 0.00 0.00 1 0.00 0.00 sys_error
      0.00 0.00 0.00 1 0.00 0.00 sys_get_argv
      0.00 0.00 0.00 1 0.00 0.00 urge_major_slice

      % the percentage of the total running time of the
      time program used by this function.

      cumulative a running sum of the number of seconds accounted
      seconds for by this function and those listed above it.

      self the number of seconds accounted for by this
      seconds function alone. This is the major sort for this
      listing.

      calls the number of times this function was invoked, if
      this function is profiled, else blank.

      self the average number of milliseconds spent in this
      ms/call function per call, if this function is profiled,
      else blank.

      total the average number of milliseconds spent in this
      ms/call function and its descendents per call, if this
      function is profiled, else blank.

      name the name of the function. This is the minor sort
      for this listing. The index shows the location of
      the function in the gprof listing. If the index is
      in parenthesis it shows where it would appear in
      the gprof listing if it were to be printed.

      Call graph (explanation follows)


      granularity: each sample hit covers 4 byte(s) no time propagated

      index % time self children called name
      0.00 0.00 1/28 Pervasives__open_out_gen_196 [8]
      0.00 0.00 2/28 Pervasives__code_begin [43]
      0.00 0.00 5/28 Pervasives__string_of_bool_149 [10]
      0.00 0.00 5/28 Pervasives__open_out_bin_202 [167]
      0.00 0.00 5/28 Pervasives__print_string_285 [181]
      0.00 0.00 10/28 Pervasives__entry [128]
      [1] 0.0 0.00 0.00 28 caml_alloc3 [1]
      -----------------------------------------------
      0.00 0.00 1/12 startup__code_begin [61]
      0.00 0.00 11/12 List__rev_map2_122 [108]
      [2] 0.0 0.00 0.00 12 Checkout2__fun_69 [2]
      0.00 0.00 5/5 Pervasives__string_of_bool_149 [10]
      -----------------------------------------------
      0.00 0.00 11/11 List__rev_map2_122 [108]
      [3] 0.0 0.00 0.00 11 caml_apply2 [3]
      -----------------------------------------------
      0.00 0.00 1/10 register_global_root [524]
      0.00 0.00 1/10 init_major_heap [57]
      0.00 0.00 1/10 set_minor_heap_size [546]
      0.00 0.00 1/10 callbackN [47]
      0.00 0.00 3/10 is_printable [28]
      0.00 0.00 3/10 alloc_custom [201]
      [4] 0.0 0.00 0.00 10 modify [4]
      -----------------------------------------------
      0.00 0.00 3/8 final_custom_operations [36]
      0.00 0.00 5/8 finalize_channel [20]
      [5] 0.0 0.00 0.00 8 final_register [5]
      0.00 0.00 5/5 shrink_heap [26]
      0.00 0.00 5/5 alloc_shr [11]
      0.00 0.00 5/5 empty_minor_heap [18]
      -----------------------------------------------
      0.00 0.00 6/6 Pervasives__entry [128]
      [6] 0.0 0.00 0.00 6 lt_float [6]
      0.00 0.00 6/6 nativeint_format [7]
      -----------------------------------------------
      0.00 0.00 6/6 lt_float [6]
      [7] 0.0 0.00 0.00 6 nativeint_format [7]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__print_char_283 [9]
      [8] 0.0 0.00 0.00 5 Pervasives__open_out_gen_196 [8]
      0.00 0.00 1/3 compare_channel [27]
      0.00 0.00 1/28 caml_alloc3 [1]
      -----------------------------------------------
      0.00 0.00 5/5 List__rev_map2_122 [108]
      [9] 0.0 0.00 0.00 5 Pervasives__print_char_283 [9]
      0.00 0.00 5/5 Pervasives__open_out_gen_196 [8]
      -----------------------------------------------
      0.00 0.00 5/5 Checkout2__fun_69 [2]
      [10] 0.0 0.00 0.00 5 Pervasives__string_of_bool_149 [10]
      0.00 0.00 5/5 parse_format [23]
      0.00 0.00 5/28 caml_alloc3 [1]
      -----------------------------------------------
      0.00 0.00 5/5 final_register [5]
      [11] 0.0 0.00 0.00 5 alloc_shr [11]
      -----------------------------------------------
      0.00 0.00 5/5 alloc_string [13]
      [12] 0.0 0.00 0.00 5 alloc_small [12]
      -----------------------------------------------
      0.00 0.00 5/5 parse_format [23]
      [13] 0.0 0.00 0.00 5 alloc_string [13]
      0.00 0.00 5/5 alloc_small [12]
      -----------------------------------------------
      0.00 0.00 5/5 shrink_heap [26]
      [14] 0.0 0.00 0.00 5 allocate_block [14]
      0.00 0.00 5/5 ext_table_add [19]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__print_string_285 [181]
      [15] 0.0 0.00 0.00 5 caml_flush_partial [15]
      0.00 0.00 2/2 flush_partial [38]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__open_out_bin_202 [167]
      [16] 0.0 0.00 0.00 5 caml_output_partial [16]
      0.00 0.00 5/5 putword [25]
      -----------------------------------------------
      0.00 0.00 5/5 parse_long [24]
      [17] 0.0 0.00 0.00 5 classify_float [17]
      -----------------------------------------------
      0.00 0.00 5/5 final_register [5]
      [18] 0.0 0.00 0.00 5 empty_minor_heap [18]
      -----------------------------------------------
      0.00 0.00 5/5 allocate_block [14]
      [19] 0.0 0.00 0.00 5 ext_table_add [19]
      -----------------------------------------------
      1 finalize_channel [20]
      0.00 0.00 1/5 Pervasives__entry [128]
      0.00 0.00 2/5 compare_channel [27]
      0.00 0.00 2/5 caml_open_descriptor_out [244]
      [20] 0.0 0.00 0.00 5+1 finalize_channel [20]
      0.00 0.00 5/8 final_register [5]
      0.00 0.00 1/3 is_printable [28]
      1 finalize_channel [20]
      -----------------------------------------------
      0.00 0.00 1/5 gc_compaction [348]
      0.00 0.00 2/5 gc_full_major [55]
      0.00 0.00 2/5 gc_major_slice [351]
      [21] 0.0 0.00 0.00 5 gc_get [21]
      -----------------------------------------------
      0.00 0.00 5/5 init_gc [368]
      [22] 0.0 0.00 0.00 5 init_signals [22]
      -----------------------------------------------
      0.00 0.00 5/5 Pervasives__string_of_bool_149 [10]
      [23] 0.0 0.00 0.00 5 parse_format [23]
      0.00 0.00 5/5 parse_long [24]
      0.00 0.00 5/5 alloc_string [13]
      -----------------------------------------------
      0.00 0.00 5/5 parse_format [23]
      [24] 0.0 0.00 0.00 5 parse_long [24]
      0.00 0.00 5/5 classify_float [17]
      -----------------------------------------------
      0.00 0.00 5/5 caml_output_partial [16]
      [25] 0.0 0.00 0.00 5 putword [25]
      -----------------------------------------------
      0.00 0.00 5/5 final_register [5]
      [26] 0.0 0.00 0.00 5 shrink_heap [26]
      0.00 0.00 5/5 allocate_block [14]
      -----------------------------------------------
      0.00 0.00 1/3 Pervasives__open_out_gen_196 [8]
      0.00 0.00 2/3 Pervasives__entry [128]
      [27] 0.0 0.00 0.00 3 compare_channel [27]
      0.00 0.00 2/2 bitvect_test [31]
      0.00 0.00 2/5 finalize_channel [20]
      -----------------------------------------------
      0.00 0.00 1/3 finalize_channel [20]
      0.00 0.00 2/3 bitvect_test [31]
      [28] 0.0 0.00 0.00 3 is_printable [28]
      0.00 0.00 3/10 modify [4]
      -----------------------------------------------
      0.00 0.00 2/2 Checkout2__fun_67 [69]
      [29] 0.0 0.00 0.00 2 List__tl_65 [29]
      -----------------------------------------------
      0.00 0.00 2/2 caml_out_channels_list [245]
      [30] 0.0 0.00 0.00 2 alloc [30]
      -----------------------------------------------
      0.00 0.00 2/2 compare_channel [27]
      [31] 0.0 0.00 0.00 2 bitvect_test [31]
      0.00 0.00 2/3 is_printable [28]
      -----------------------------------------------
      0.00 0.00 2/2 minmax_table [452]
      [32] 0.0 0.00 0.00 2 callback_exn [32]
      -----------------------------------------------
      0.00 0.00 2/2 Pervasives__code_begin [43]
      [33] 0.0 0.00 0.00 2 caml_channel_size_64 [33]
      -----------------------------------------------
      0.00 0.00 2/2 flush_partial [38]
      [34] 0.0 0.00 0.00 2 channel_binary_mode [34]
      -----------------------------------------------
      0.00 0.00 1/2 random_level [518]
      0.00 0.00 1/2 hash_value_name [363]
      [35] 0.0 0.00 0.00 2 do_local_roots [35]
      -----------------------------------------------
      0.00 0.00 1/2 Pervasives__entry [128]
      0.00 0.00 1/2 parse_camlrunparam [59]
      [36] 0.0 0.00 0.00 2 final_custom_operations [36]
      0.00 0.00 3/8 final_register [5]
      -----------------------------------------------
      0.00 0.00 2/2 init_major_heap [57]
      [37] 0.0 0.00 0.00 2 fl_allocate [37]
      -----------------------------------------------
      0.00 0.00 2/2 caml_flush_partial [15]
      [38] 0.0 0.00 0.00 2 flush_partial [38]
      0.00 0.00 2/2 channel_binary_mode [34]
      -----------------------------------------------
      0.00 0.00 1/1 Checkout2__fun_67 [69]
      [39] 0.0 0.00 0.00 1 List__map2_113 [39]
      -----------------------------------------------
      0.00 0.00 1/1 startup__code_begin [61]
      [40] 0.0 0.00 0.00 1 List__stable_sort_271 [40]
      -----------------------------------------------
      0.00 0.00 1/1 Std_exit__entry [44]
      [41] 0.0 0.00 0.00 1 Pervasives__$40_164 [41]
      -----------------------------------------------
      0.00 0.00 1/1 startup__code_begin [61]
      [42] 0.0 0.00 0.00 1 Pervasives__at_exit_326 [42]
      -----------------------------------------------
      0.00 0.00 1/1 Std_exit__entry [44]
      [43] 0.0 0.00 0.00 1 Pervasives__code_begin [43]
      0.00 0.00 2/2 caml_channel_size_64 [33]
      0.00 0.00 2/28 caml_alloc3 [1]
      -----------------------------------------------
      0.00 0.00 1/1 startup__code_begin [61]
      [44] 0.0 0.00 0.00 1 Std_exit__entry [44]
      0.00 0.00 1/1 Pervasives__code_begin [43]
      0.00 0.00 1/1 Pervasives__$40_164 [41]
      -----------------------------------------------
      0.00 0.00 1/1 callbackN [47]
      [45] 0.0 0.00 0.00 1 callback2 [45]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [59]
      [46] 0.0 0.00 0.00 1 callback3_exn [46]
      -----------------------------------------------
      0.00 0.00 1/1 Pervasives__entry [128]
      [47] 0.0 0.00 0.00 1 callbackN [47]
      0.00 0.00 1/1 callback2 [45]
      0.00 0.00 1/10 modify [4]
      -----------------------------------------------
      0.00 0.00 1/1 caml_main [241]
      [48] 0.0 0.00 0.00 1 caml_alloc [48]
      0.00 0.00 1/1 startup__code_begin [61]
      -----------------------------------------------
      0.00 0.00 1/1 Pervasives__entry [128]
      [49] 0.0 0.00 0.00 1 caml_alloc2 [49]
      -----------------------------------------------
      0.00 0.00 1/1 do_write [307]
      [50] 0.0 0.00 0.00 1 channel_size [50]
      0.00 0.00 1/1 execute_signal [51]
      0.00 0.00 1/1 urge_major_slice [64]
      -----------------------------------------------
      0.00 0.00 1/1 channel_size [50]
      [51] 0.0 0.00 0.00 1 execute_signal [51]
      -----------------------------------------------
      0.00 0.00 1/1 realloc_ref_table [60]
      [52] 0.0 0.00 0.00 1 fatal_error [52]
      -----------------------------------------------
      1 finish_major_cycle [53]
      0.00 0.00 1/1 gc_compaction [348]
      [53] 0.0 0.00 0.00 1+1 finish_major_cycle [53]
      1 finish_major_cycle [53]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [59]
      [54] 0.0 0.00 0.00 1 float_of_bytes [54]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [59]
      [55] 0.0 0.00 0.00 1 gc_full_major [55]
      0.00 0.00 2/5 gc_get [21]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [59]
      [56] 0.0 0.00 0.00 1 init_atoms [56]
      -----------------------------------------------
      0.00 0.00 1/1 gc_major_slice [351]
      [57] 0.0 0.00 0.00 1 init_major_heap [57]
      0.00 0.00 2/2 fl_allocate [37]
      0.00 0.00 1/10 modify [4]
      -----------------------------------------------
      0.00 0.00 1/1 parse_camlrunparam [59]
      [58] 0.0 0.00 0.00 1 is_stack_overflow [58]
      -----------------------------------------------
      0.00 0.00 1/1 List__entry [77]
      [59] 0.0 0.00 0.00 1 parse_camlrunparam [59]
      0.00 0.00 1/1 float_of_bytes [54]
      0.00 0.00 1/2 final_custom_operations [36]
      0.00 0.00 1/1 init_atoms [56]
      0.00 0.00 1/1 gc_full_major [55]
      0.00 0.00 1/1 callback3_exn [46]
      0.00 0.00 1/1 is_stack_overflow [58]
      -----------------------------------------------
      0.00 0.00 1/1 clip_heap_chunk_size [263]
      [60] 0.0 0.00 0.00 1 realloc_ref_table [60]
      0.00 0.00 1/1 fatal_error [52]
      -----------------------------------------------
      0.00 0.00 1/1 caml_alloc [48]
      [61] 0.0 0.00 0.00 1 startup__code_begin [61]
      0.00 0.00 1/1 Pervasives__at_exit_326 [42]
      0.00 0.00 1/1 List__stable_sort_271 [40]
      0.00 0.00 1/12 Checkout2__fun_69 [2]
      0.00 0.00 1/1 Std_exit__entry [44]
      -----------------------------------------------
      0.00 0.00 1/1 List__entry [77]
      [62] 0.0 0.00 0.00 1 sys_error [62]
      -----------------------------------------------
      0.00 0.00 1/1 caml_main [241]
      [63] 0.0 0.00 0.00 1 sys_get_argv [63]
      -----------------------------------------------
      0.00 0.00 1/1 channel_size [50]
      [64] 0.0 0.00 0.00 1 urge_major_slice [64]
      -----------------------------------------------

      This table describes the call tree of the program, and was sorted by
      the total amount of time spent in each function and its children.

      Each entry in this table consists of several lines. The line with the
      index number at the left hand margin lists the current function.
      The lines above it list the functions that called this function,
      and the lines below it list the functions this one called.
      This line lists:
      index A unique number given to each element of the table.
      Index numbers are sorted numerically.
      The index number is printed next to every function name so
      it is easier to look up where the function in the table.

      % time This is the percentage of the `total' time that was spent
      in this function and its children. Note that due to
      different viewpoints, functions excluded by options, etc,
      these numbers will NOT add up to 100%.

      self This is the total amount of time spent in this function.

      children This is the total amount of time propagated into this
      function by its children.

      called This is the number of times the function was called.
      If the function called itself recursively, the number
      only includes non-recursive calls, and is followed by
      a `+' and the number of recursive calls.

      name The name of the current function. The index number is
      printed after it. If the function is a member of a
      cycle, the cycle number is printed between the
      function's name and the index number.


      For the function's parents, the fields have the following meanings:

      self This is the amount of time that was propagated directly
      from the function into this parent.

      children This is the amount of time that was propagated from
      the function's children into this parent.

      called This is the number of times this parent called the
      function `/' the total number of times the function
      was called. Recursive calls to the function are not
      included in the number after the `/'.

      name This is the name of the parent. The parent's index
      number is printed after it. If the parent is a
      member of a cycle, the cycle number is printed between
      the name and the index number.

      If the parents of the function cannot be determined, the word
      `<spontaneous>' is printed in the `name' field, and all the other
      fields are blank.

      For the function's children, the fields have the following meanings:

      self This is the amount of time that was propagated directly
      from the child into the function.

      children This is the amount of time that was propagated from the
      child's children to the function.

      called This is the number of times the function called
      this child `/' the total number of times the child
      was called. Recursive calls by the child are not
      listed in the number after the `/'.

      name This is the name of the child. The child's index
      number is printed after it. If the child is a
      member of a cycle, the cycle number is printed
      between the name and the index number.

      If there are any cycles (circles) in the call graph, there is an
      entry for the cycle-as-a-whole. This entry shows who called the
      cycle (as parents) and the members of the cycle (as children.)
      The `+' recursive calls entry shows the number of function calls that
      were internal to the cycle, and the calls entry for each member shows,
      for that member, how many times it was called from other members of
      the cycle.


      Index by function name

      [2] Checkout2__fun_69 [49] caml_alloc2 [55] gc_full_major
      [39] List__map2_113 [1] caml_alloc3 [21] gc_get
      [40] List__stable_sort_271 [3] caml_apply2 [56] init_atoms
      [29] List__tl_65 [33] caml_channel_size_64 [57] init_major_heap
      [41] Pervasives__$40_164 [15] caml_flush_partial [22] init_signals
      [42] Pervasives__at_exit_326 [16] caml_output_partial [28] is_printable
      [43] Pervasives__code_begin [34] channel_binary_mode [58] is_stack_overflow
      [8] Pervasives__open_out_gen_196 [50] channel_size [6] lt_float
      [9] Pervasives__print_char_283 [17] classify_float [4] modify
      [10] Pervasives__string_of_bool_149 [27] compare_channel [7] nativeint_format
      [44] Std_exit__entry [35] do_local_roots [59] parse_camlrunparam
      [30] alloc [18] empty_minor_heap [23] parse_format
      [11] alloc_shr [51] execute_signal [24] parse_long
      [12] alloc_small [19] ext_table_add [25] putword
      [13] alloc_string [52] fatal_error [60] realloc_ref_table
      [14] allocate_block [36] final_custom_operations [26] shrink_heap
      [31] bitvect_test [5] final_register [61] startup__code_begin
      [45] callback2 [20] finalize_channel [62] sys_error
      [46] callback3_exn [53] finish_major_cycle [63] sys_get_argv
      [47] callbackN [37] fl_allocate [64] urge_major_slice
      [32] callback_exn [54] float_of_bytes
      [48] caml_alloc [38] flush_partial


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