Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
| A                                          |      B |      C |       D |       E |      F |        G |     H |     I |       J |       K |      L |      M |
|:-------------------------------------------|-------:|-------:|--------:|--------:|-------:|---------:|------:|------:|--------:|--------:|-------:|-------:|
| Adair County Public Library                |  25607 |   2392 |   91708 |       0 |  37589 |   208588 |  1235 |   262 |   91970 |    7742 |    837 |   8849 |
| Adrian Community Library                   |   1677 |   1664 |    5096 |       0 |   1508 |     5001 |     0 |     0 |    5096 |    1377 |   2132 |   2668 |
| Advance Community Library                  |   1347 |   1040 |    1676 |       0 |     25 |     1505 |     0 |     0 |    1676 |     824 |      0 |   1513 |
| Albany Carnegie Public Library             |   1730 |   2184 |    8213 |       0 |    416 |    15256 |  2098 |  1293 |    9506 |    1375 |    215 |   2395 |
| Appleton City Library                      |   1127 |   1092 |    1267 |       0 |    115 |     4397 |     0 |   400 |    1667 |     272 |      0 |    412 |
| Atchison County Library                    |   5685 |   5200 |   22456 |       0 |    774 |    38902 |   894 |   218 |   22674 |    1078 |      0 |   3555 |
| Barry-Lawrence Regional Library            |  74231 |  20007 |  222677 |       0 | 113880 |   404635 |  1234 |   963 |  223640 |   37690 |  11242 |  53640 |
| Barton County Library                      |  12402 |   5174 |   40248 |   17688 |   3432 |    52006 |   195 |   396 |   40644 |    7809 |   9594 |   9869 |
| Bernie Public Library                      |   1958 |   2080 |    4416 |       0 |     97 |     2148 |     0 |     0 |    4416 |    1351 |      0 |    766 |
| Bethany Public Library                     |   3292 |   1612 |   11763 |       0 |     20 |    18057 |     0 |     0 |   11763 |    1237 |   3640 |   4210 |
| Bloomfield Public Library                  |   1933 |   2080 |    6092 |       0 |    552 |    15806 |     0 |   223 |    6315 |    3589 |      0 |   1574 |
| Bollinger County Library                   |  12363 |   1716 |   11280 |       0 |   5200 |    33131 |  1039 |  1240 |   12520 |    6400 |   3550 |   5497 |
| Bonne Terre Memorial Library               |   6864 |   2340 |   14560 |       0 |    996 |    16125 |    43 |   186 |   14746 |    2740 |    465 |   5033 |
| Boonslick Regional Library                 |  58748 |  10868 |  457032 |       0 |  41854 |   370656 |  3187 |   828 |  457860 |   31878 |  12632 |  29959 |
| Bowling Green Public Library               |   5334 |   2236 |   18290 |       0 |   4991 |    40794 |   130 |   130 |   18420 |    7775 |    513 |   2173 |
| Brentwood Public Library                   |   8055 |   3380 |   73536 |   63280 |   1026 |   123727 | 16416 | 12579 |   86115 |   11915 |      0 |   6127 |
| Brookfield Public Library                  |   4542 |   2392 |   23400 |    2314 |   2195 |    30782 |   215 |   236 |   23636 |    3255 |   1419 |   2941 |
| Caldwell County Library                    |   7232 |   2184 |    4052 |       0 |     31 |    10747 |     0 |   117 |    4169 |    3756 |   1435 |    653 |
| Camden County Library                      |  44002 |  12584 |  177412 |   61170 |  97551 |   228842 |  3431 |  5239 |  182651 |   32771 | 303036 |  29228 |
| Cameron Public Library                     |   9933 |   2436 |   37723 |    1652 |    482 |    49141 |  2586 |  1721 |   39444 |    6786 |   1047 |   5392 |
| Canton Public Library                      |   2377 |   2080 |    9938 |       0 |    520 |     8609 |   748 |   575 |   10513 |    3152 |    882 |   1906 |
| Cape Girardeau Public Library              |  35549 |   3536 |  135804 |   69375 |  22236 |   231887 |   494 |  2109 |  137913 |   25557 |   5375 |   8558 |
| Carnegie (Shelbina) Public Library         |   1704 |   2028 |   10745 |       0 |    724 |    15086 |   260 |    12 |   10757 |    5613 |    682 |   3251 |
| Carrollton Public Library                  |   3784 |   2756 |   41472 |   38616 |  10723 |    67647 |  1691 |  3949 |   45421 |    9817 |   7784 |   4627 |
| Carter County Library                      |   6265 |   3744 |   29052 |      18 |    156 |    46735 |     0 |  1890 |   30942 |    7710 |   3530 |   3842 |
| Carthage Public Library                    |  14378 |   2912 |  101000 |       0 |   1982 |   101431 |  3408 |  2651 |  103651 |   18000 |   5911 |  16165 |
| Caruthersville Public Library              |   6168 |   2496 |   36729 |    6723 |   8315 |    34109 |  4684 |   778 |   37507 |    9572 |   1598 |   4154 |
| Cass County Public Library                 |  99478 |  16276 |  185314 |  212116 |  18620 |   528112 |  1983 |  1454 |  186768 |   35766 |  12284 |  45819 |
| Cedar County Library District              |  13982 |   4576 |   36348 |    8339 |   6162 |    31525 |   229 |   816 |   37164 |    9162 |    860 |   7931 |
| Centralia Public Library                   |   3784 |   2964 |   42640 |   17436 |   4680 |    48578 |   659 |   710 |   43350 |   13804 |  13520 |   5654 |
| Chaffee Public Library                     |   2955 |   1976 |    6396 |       0 |   2392 |    10568 |   447 |   486 |    6882 |    3560 |   1563 |   2233 |
| Christian County Library                   |  77422 |   5356 |   99002 |   68759 |  10302 |   329945 |  5147 | 14275 |  113277 |   15648 |  18941 |  42586 |
| Clarence Public Library                    |    813 |   2080 |     405 |       0 |      0 |      888 |     0 |     0 |     405 |     296 |      0 |    242 |
| Conran Memorial Library                    |   2939 |   1530 |    5564 |       0 |    520 |     2525 |     0 |     0 |    5564 |    1928 |    915 |   1016 |
| Crystal City Public Library                |   4855 |   2392 |   11916 |    1100 |     75 |    14214 |   222 |   152 |   12068 |    2672 |    882 |   1931 |
| Dade County Library                        |   6960 |   2418 |   18972 |       0 |   2523 |    19955 |   373 |   330 |   19302 |    4628 |   1622 |   3239 |
| Dallas County Library                      |  16777 |   2678 |   29172 |       0 |    303 |    65805 |   577 |   478 |   29650 |    7527 |   1255 |   4220 |
| Daniel Boone Regional Library              | 203190 |  11141 |  711766 | 1279219 | 216351 |  2430891 |  7589 |  2824 |  714590 |  178154 | 152342 | 111850 |
| Daviess County Library                     |   8433 |   2834 |   14924 |       0 |   3500 |    40053 |   438 |   330 |   15254 |    2672 |    327 |   5342 |
| De Soto Public Library                     |   6400 |   2444 |   67913 |  214355 |   3501 |    37057 |  3271 |  1517 |   69430 |    7523 |   8320 |   4665 |
| Desloge Public Library                     |   5054 |   1812 |    5859 |       0 |    274 |     7106 |     0 |     0 |    5859 |    2018 |   1560 |   4585 |
| Doniphan-Ripley County Library District    |  14100 |   4680 |   33455 |   14990 |    395 |    55304 |  4625 |  1943 |   35398 |   11358 |   2061 |   8851 |
| Douglas County Public Library              |  13684 |   2236 |   18616 |       0 |    416 |    26376 |   505 |   950 |   19566 |    3796 |    728 |   5326 |
| Dulany Memorial Library                    |   1618 |   1560 |    5320 |    1796 |    613 |    13620 |   501 |   404 |    5724 |    1526 |    341 |   1580 |
| Dunklin County Library                     |  31953 |  10608 |   78652 |       0 |   8352 |   273200 |    30 |    99 |   78751 |   46783 |   8051 |  20985 |
| Farmington Public Library                  |  16240 |   2958 |  127489 |       0 |   2982 |   119149 |   295 |   733 |  128222 |   14244 |   4721 |  14871 |
| Ferguson Municipal Public Library          |  21203 |   3120 |  172595 |   23649 |  28000 |    61206 | 13147 |  6138 |  178733 |   30642 |  19000 |  21849 |
| Festus Public Library                      |  11602 |   2756 |   66831 |       0 |   5128 |    81310 |  3127 |  3938 |   70769 |    8687 |      0 |  11293 |
| Gentry County Library                      |   5008 |   2132 |   45589 |       0 |   5641 |    52190 |    98 |    74 |   45663 |   32563 |    790 |   3921 |
| Grundy County-Jewett Norris Library        |  10261 |   2496 |   22758 |       0 |   1850 |    34935 |  2097 |   542 |   23300 |    5200 |    600 |   4799 |
| Hamilton Public Library                    |   1809 |   1820 |    4732 |       0 |   1404 |     6216 |     3 |   146 |    4878 |     864 |      0 |   1344 |
| Hannibal Free Public Library               |  17916 |   3952 |   59260 |  662811 |   7245 |   153657 |  1005 |   294 |   59554 |   10048 |      0 |   8549 |
| Heartland Regional Library System          |  33924 |   5720 |   23000 |    9356 |     52 |   157799 |   406 |  1865 |   24865 |   10133 |   1764 |  15279 |
| Henry County Library                       |  22272 |   6188 |  163337 |   17700 |   1647 |   103413 |     0 |   676 |  164013 |   10972 |  11791 |  12308 |
| Hickory County Library                     |   9627 |   2652 |   12270 |    2200 |   5035 |    34214 |    78 |   913 |   13183 |    3329 |    525 |   9641 |
| Howard County Public Library               |   9077 |   1612 |   17517 |       0 |   1000 |    23586 |  1258 |   830 |   18347 |    3657 |   1156 |   3435 |
| James Memorial Library                     |   4216 |   2080 |   15491 |       0 |    653 |    41667 |    18 |   704 |   16195 |    3107 |   1812 |   2200 |
| Jefferson County Library                   | 131842 |  10140 |  332868 |  124288 |  94781 |   718716 | 15781 | 13655 |  346523 |   38747 |  20848 |  63326 |
| Jessie E. McCully Memorial Library         |   1549 |   1156 |    3985 |       0 |      0 |     5635 |     0 |     0 |    3985 |     737 |    200 |    368 |
| Joplin Public Library                      |  48109 |   3432 |  244719 |       0 |  36454 |   590203 |  1751 |  2138 |  246857 |   30092 |      0 |  27122 |
| Kansas City Public Library                 | 218765 |  29588 | 1765302 | 2268570 |  69800 |  1966161 |  7679 |  1636 | 1766938 |  656095 | 143931 | 160805 |
| Keller Public Library of Dexter            |   7864 |   2080 |   27153 |    6057 |    570 |    38519 |   375 |   305 |   27458 |    3762 |   1560 |  12857 |
| Kirkwood Public Library                    |  27518 |   3536 |  192064 |   38222 |  35010 |   579867 | 26431 | 41389 |  233453 |   24897 |  21641 |  28097 |
| LaPlata Public Library                     |   1366 |    832 |    2080 |    1124 |    416 |     3186 |     0 |   120 |    2200 |     416 |     36 |    325 |
| Lebanon-Laclede County Library             |  35571 |   3294 |  135213 |  120026 |   1654 |   198038 |  8569 |  6459 |  141672 |   28387 |      0 |  31220 |
| Lewis Library of Glasgow                   |   1103 |   1352 |    6503 |       1 |   1120 |     9786 |    15 |    24 |    6527 |    2351 |     68 |   1306 |
| Lilbourn Memorial Library                  |   1010 |    832 |     326 |       0 |      8 |     1781 |     0 |     0 |     326 |       0 |      0 |    426 |
| Little Dixie Regional Libraries            |  32334 |   8242 |  238450 |       0 |   2456 |   189764 | 10499 | 14659 |  253109 |   14946 |  13182 |  23429 |
| Livingston County Library                  |  15195 |   2780 |   71417 |   33305 |   4876 |   148681 |   701 |  2486 |   73903 |    8034 |  36115 |  21405 |
| Lockwood Public Library                    |    923 |   1612 |    3805 |       0 |    206 |     3822 |     0 |     0 |    3805 |    1296 |      0 |    195 |
| Louisiana Public Library                   |   3364 |   2080 |   14200 |       0 |    210 |     8610 |     0 |   174 |   14374 |    3250 |   1000 |   6100 |
| Macon Public Library                       |   5471 |   2704 |   33635 |       0 |   2383 |    44616 |     0 |     0 |   33635 |    6167 |    962 |   4338 |
| Maplewood Public Library                   |   8046 |   3432 |   39460 |   50832 |   1196 |    90949 | 12118 |  7941 |   47401 |   10193 |      0 |   6625 |
| Marceline Carnegie Library                 |   2233 |   2080 |   10605 |   10300 |   9880 |    13865 |    11 |   240 |   10845 |    1228 |    360 |   1900 |
| Marion County Library District             |   6732 |   1872 |   18823 |  133744 |   2000 |    49374 |  3137 |  1831 |   20654 |     958 |      0 |   3387 |
| Marshall Public Library                    |  13065 |   3068 |   39371 |       0 |    375 |    29367 |  2034 |  2245 |   41616 |    6346 |   1325 |  11357 |
| Maryville Public Library                   |  11972 |   2652 |   35272 |    9760 |    600 |    78136 |   305 |   141 |   35413 |    5111 |   1660 |   5529 |
| McDonald County Library                    |  23083 |   5928 |   39927 |       0 |   4624 |    48832 |   861 |   392 |   40319 |   15560 |   8138 |  14547 |
| Mercer County Library                      |   3785 |   2392 |   10764 |       0 |    240 |    10494 |   198 |   122 |   10886 |    1626 |      0 |   2440 |
| Mexico-Audrain County Library District     |  25529 |   8268 |   72650 |       0 |   6734 |   102918 |   836 |   253 |   72903 |   12251 |   2460 |  15694 |
| Mid-Continent Public Library               | 762446 | 104904 | 2978823 | 4321516 | 165754 | 12113008 | 20769 | 58889 | 3037712 |  509428 | 328880 | 490017 |
| Mississippi County Library District        |  14358 |   5148 |   56360 |       0 |   1450 |    19310 |   188 |   136 |   56496 |    6657 |    460 |   6722 |
| Missouri River Regional Library            |  89868 |   7228 |  255997 |  136180 |  35795 |   617811 |  8240 |  6330 |  262327 |   35587 |  11770 |  58795 |
| Moniteau County Library                    |  12345 |    623 |     793 |       0 |    210 |     2356 |     0 |    55 |     848 |      69 |     76 |   3981 |
| Monroe City Public Library                 |   2456 |   1805 |    2683 |       0 |     45 |     4645 |     0 |     0 |    2683 |     933 |    150 |   1193 |
| Montgomery City Public Library             |   2834 |   3016 |   19544 |       0 |   1560 |    33528 |   197 |   197 |   19741 |    6855 |   1837 |   2011 |
| Morgan County Library                      |  20565 |   2418 |   35000 |    5414 |   1500 |    87219 |     0 |    54 |   35054 |    3431 |   1208 |   7972 |
| Mound City Public Library                  |   1159 |   1560 |    9152 |       0 |    207 |    10817 |   105 |   195 |    9347 |    4095 |   1040 |    631 |
| Mountain View Public Library               |   2719 |   2652 |   67906 |       0 |     25 |    65695 |   120 |   300 |   68206 |   10232 |   3500 |   5063 |
| Neosho Newton County Library               |  53960 |   4212 |  137501 |       0 |   1793 |   237087 |   913 |  1032 |  138533 |   11285 |  11114 |  19525 |
| Nevada Public Library                      |   8386 |   2600 |   46720 |   11785 |   7923 |    60491 |     0 |   593 |   47313 |   14556 |  20075 |   7241 |
| New Madrid County Library                  |  17256 |   7592 |   34404 |    1470 |   3984 |    52576 |     0 |     0 |   34404 |    4248 |  51540 |   5950 |
| Norborne Public Library                    |    708 |   2080 |    1112 |       0 |     44 |     1946 |     0 |     0 |    1112 |      44 |     12 |     76 |
| North Kansas City Public Library           |   4208 |   3588 |  139797 |  117383 |   6759 |   175787 | 18151 |  9429 |  149226 |   23195 |  13570 |  13007 |
| Northeast Missouri Library Service         |  19104 |   8008 |   25192 |     150 |   1166 |    51393 |     0 |     0 |   25192 |    4707 |   1178 |   3848 |
| Oregon County Library District             |  10881 |   6336 |   24494 |       0 |    403 |    28749 |     8 |   313 |   24807 |   13144 |   3863 |   3123 |
| Oregon Public Library                      |    857 |   1300 |    2571 |       0 |   3226 |     2271 |     0 |   377 |    2948 |     365 |     75 |   1685 |
| Ozark Regional Library                     |  46078 |  10738 |   99704 |       0 |  45428 |    91298 |  8580 |  8445 |  108149 |   36130 |  13222 |  10677 |
| Park Hills Public Library                  |   8759 |   2040 |   21636 |       0 |   3640 |    31285 |     5 |     3 |   21639 |    2731 |    285 |  16274 |
| Piedmont Public Library                    |   1977 |   2080 |   10878 |       0 |    292 |    21700 |     0 |     0 |   10878 |    1621 |      0 |   3480 |
| Polk County Library                        |  31137 |   9412 |   94669 |   46355 |   8500 |   183756 |  4726 |  8251 |  102920 |   22666 |  17190 |  15936 |
| Poplar Bluff Public Library                |  17023 |   2956 |  105060 |   72852 |  28390 |   358677 |  6785 | 11349 |  116409 |   20902 |  23803 |  14898 |
| Price James Memorial Library               |   3262 |   1612 |    5408 |     350 |      2 |    19255 |     0 |  3337 |    8745 |    1054 |    264 |   2487 |
| Pulaski County Library                     |  50781 |   6812 |   74538 |   47839 |   4388 |    69763 |  2453 |  3096 |   77634 |   12321 |   4864 |  10651 |
| Putnam County Public Library               |   4979 |   2340 |   22602 |       0 |   3813 |    36051 |   261 |    46 |   22648 |    3887 |   1982 |   2806 |
| Puxico Public Library                      |    881 |   1248 |    4295 |       0 |     25 |     4443 |     0 |   190 |    4485 |     813 |    265 |   2003 |
| Ralls County Library                       |   9826 |   2244 |    5856 |       0 |    120 |     5349 |     0 |     0 |    5856 |     347 |     20 |   4450 |
| Ray County Public Library                  |  23494 |   2754 |   32108 |   21191 |  26623 |    42118 |     0 |   810 |   32918 |   18748 |   2503 |   6966 |
| Reynolds County Library District           |   6696 |   7098 |   11596 |     565 |    543 |    29891 |     0 |     4 |   11600 |    2502 |      0 |   2658 |
| Rich Hill Memorial Library                 |   1396 |   1040 |    3750 |       0 |     75 |     8287 |     0 |     0 |    3750 |     645 |    644 |   1106 |
| Richmond Heights Memorial Library          |   8603 |   3692 |  145449 |  209697 |   7436 |   151527 | 14860 | 13300 |  158749 |   17975 |   7596 |   9539 |
| Riverside Regional Library                 |  81379 |  11180 |  322870 | 1689337 |  36652 |   325028 |    63 |   398 |  323268 |   21592 |   5379 |  36324 |
| Robertson Memorial Library                 |   4494 |   1768 |   13429 |       0 |    520 |    15346 |     0 |  1010 |   14439 |    2600 |      0 |   3513 |
| Rock Hill Public Library                   |   4635 |   2340 |   20000 |   38911 |   5000 |    38874 |  5885 |  5036 |   25036 |    2681 |    500 |   3008 |
| Rolla Public Library                       |  19559 |   3382 |   66597 |       0 |   4133 |   389837 |   317 |   861 |   67458 |   18926 |   6572 |   7886 |
| Rolling Hills Consolidated                 |  41428 |   7660 |  178761 |   76155 |   4296 |   364740 |  1554 |  2120 |  180881 |   21183 |  15757 |  16934 |
| Saint Charles City-County Library District | 360485 |  37596 | 1841576 | 1358874 | 442938 |  6209652 |  9016 |  5412 | 1846988 |  184627 | 136783 | 118013 |
| Saint Clair County Library                 |   8678 |   5286 |   69303 |   15479 |  28597 |    67755 |    48 |   433 |   69736 |    6686 |   4812 |   7228 |
| Saint Joseph Public Library                |  65064 |  11856 |  197392 |   61293 |  30924 |   348212 |  1641 |  2616 |  200008 |   49318 |  13870 |  39571 |
| Saint Louis County Library                 | 859148 |  70932 | 5012762 | 6322089 | 561422 | 14518840 | 10786 | 13062 | 5025824 | 1033890 | 717580 | 651055 |
| Saint Louis Public Library                 | 319294 |  48204 | 1762808 | 1576964 | 219746 |  4114060 |  5603 |  2493 | 1765301 |  327802 | 770484 |  62799 |
| Sainte Genevieve County Library            |  18145 |   2912 |   13728 |   11863 |   1104 |    19133 |  1796 |  1167 |   14895 |    3345 |    879 |   3255 |
| Salem Public Library                       |   4950 |   2080 |   21892 |       0 |   9427 |    39654 |  3190 |  2528 |   24420 |    3103 |    236 |   4181 |
| Sarcoxie Public Library                    |   1330 |   2548 |   10188 |       0 |   1004 |     3581 |    79 |   117 |   10305 |    3510 |   1100 |   1561 |
| Scenic Regional Library                    | 141988 |  29588 |  326934 |  331100 |  18486 |  1058715 | 35039 | 41114 |  368048 |   28205 |  14421 |  64522 |
| Schuyler County Library                    |   4431 |   1924 |    6240 |    6240 |    195 |    12645 |   856 |   567 |    6807 |     980 |   1404 |    508 |
| Scotland County Memorial Library           |   4843 |   2574 |   15353 |    6430 |    443 |    39686 |   284 |   241 |   15594 |    1285 |    350 |   2864 |
| Sedalia Public Library                     |  20110 |   3016 |   80159 |       0 |  26755 |    75304 |   372 |  1582 |   81741 |    9049 |   2184 |  14455 |
| Seymour Community Library                  |    950 |   2028 |   10625 |       0 |    200 |     9277 |     0 |     0 |   10625 |    4637 |    347 |   5178 |
| Sikeston Public Library                    |  14643 |   2964 |   31508 |   76775 |    780 |    39442 |  2716 |  1835 |   33343 |    3901 |   1505 |  11071 |
| Slater Public Library                      |   1856 |    780 |    2000 |       0 |    400 |     6025 |     0 |     0 |    2000 |     367 |      0 |    598 |
| Springfield-Greene County Library District | 275174 |  36132 | 1934371 | 1407575 | 139589 |  4095715 | 45621 | 40354 | 1974725 |  265747 | 341644 | 172160 |
| Steele Public Library                      |   2172 |    832 |    2877 |       0 |    156 |     1634 |     0 |     0 |    2877 |     731 |    260 |   1260 |
| Stone County Library                       |  32202 |   8294 |   47725 |       0 |   7992 |    32841 |  4337 |  5129 |   52854 |   13221 |   1719 |   8043 |



label: J=D+I
labeled_formulas: J=D+I
output: {"Arithmetic-Relationship": ["J=D+I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_715951___xlsx_ef3e24a608d4c421c8a5d092b0ebf3aef5786569.xlsx___line_942