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 |
|:----|:---------------|----------:|--------:|----------:|---------:|---------:|---------:|----------:|----------:|
| 1   | ADAIR          |   2855572 |       0 |    315402 |   200825 |        0 |   469275 |   3841074 |   3841074 |
| 2   | ADAMS          |   2187745 |  124591 |         0 |   371590 |        0 |      445 |   2684371 |   2684371 |
| 3   | ALLAMAKEE      |   8751580 |       0 |   1254100 |  2375900 |  2185600 |   646200 |  15213380 |  15213380 |
| 4   | APPANOOSE      |  10208000 |       0 |      2440 |   983820 |   509730 |   549260 |  12253250 |  12253250 |
| 5   | AUDUBON        |   3940800 |       0 |         0 |   500430 |   166210 |    45950 |   4653390 |   4653390 |
| 6   | BENTON         |   3450000 |       0 |    409000 |   745200 |        0 |        0 |   4604200 |   4604200 |
| 8   | BOONE          |   1020779 |       0 |      9700 |   416282 |   556437 |    75157 |   2078355 |   2078355 |
| 9   | BREMER         |  22913070 |  282010 |   9644980 |  3370290 |        0 |  1287090 |  37497440 |  37497440 |
| 10  | BUCHANAN       |   7358944 |       0 |   3147160 |  2499126 |        0 |        0 |  13005230 |  13005230 |
| 11  | BUENA VISTA    |  19138010 |   90970 |   1441980 |  2902980 |        0 |   518700 |  24092640 |  24092640 |
| 12  | BUTLER         |   8447619 |       0 |         0 |  3178692 |     9771 |        0 |  11636082 |  11636082 |
| 13  | CALHOUN        |  12214530 |       0 |    787980 |  1713580 |  1266510 |   224790 |  16207390 |  16207390 |
| 14  | CARROLL        |  13990600 |   33920 |   4510690 |  2230160 |        0 |   304480 |  21069850 |  21069850 |
| 15  | CASS           |   9324550 |  706320 |   2229660 |   537930 |        0 |   954460 |  13752920 |  13752920 |
| 16  | CEDAR          |   7817200 |       0 |   1277490 |   917200 |   727030 |   472060 |  11210980 |  11210980 |
| 17a | MASON CITY     |  25938871 |       0 |   3118109 |  2157450 |        0 |   650247 |  31864677 |  31864677 |
| 18  | CHEROKEE       |  19091223 |       0 |         0 |  1003989 |        0 |    50547 |  20145759 |  20145759 |
| 19  | CHICKASAW      |   5691400 |  225500 |   1588000 |  1267900 |        0 |        0 |   8772800 |   8772800 |
| 20  | CLARKE         |   3764050 |       0 |         0 |   377820 |        0 |        0 |   4141870 |   4141870 |
| 21  | CLAY           |  32852600 | 5643820 |   1383550 |  1336070 |        0 |   408300 |  41624340 |  41624340 |
| 22  | CLAYTON        |   5631418 |       0 |    425152 |  3135089 |   789975 |    79986 |  10061620 |  10061620 |
| 23  | CLINTON COUNTY |  11828585 |       0 |   1057223 |  2035282 |   388615 |   455359 |  15765064 |  15765064 |
| 23a | CLINTON CITY   |  23837277 |       0 |   1329724 |  1537008 |        0 |        0 |  26704009 |  26704009 |
| 24  | CRAWFORD       |  15359290 |       0 |   2981550 |  1520030 |        0 |  1696310 |  21557180 |  21557180 |
| 27  | DECATUR        |   2316087 |   50088 |         0 |   527363 |        0 |        0 |   2893538 |   2893538 |
| 28  | DELAWARE       |   6370900 |  519800 |   1652700 |  1517800 |        0 |   876700 |  10937900 |  10937900 |
| 29  | DES MOINES     |  65166600 |       0 |   3404300 |  3253335 |        0 |  2477503 |  74301738 |  74301738 |
| 30  | DICKINSON      |  34479900 |       0 |         0 |  1594900 | 76152800 |   175500 | 112403100 | 112403100 |
| 31  | DUBUQUE COUNTY |  16233330 |  208970 |  15627120 |  2344450 |        0 |  5094393 |  39508263 |  39508263 |
| 31A | DUBUQUE CITY   |  30761920 |  244110 |  21311820 | 55928820 |        0 |  6012850 | 114259520 | 114259520 |
| 32  | EMMET          |  11659200 |       0 |         0 |   786800 |   248400 |  1851900 |  14546300 |  14546300 |
| 33  | FAYETTE        |  20593610 |  726890 |    827690 |  2446850 |        0 |    73600 |  24668640 |  24668640 |
| 35  | FRANKLIN       |  13096700 |       0 |         0 |   587100 |        0 |   239000 |  13922800 |  13922800 |
| 36  | FREMONT        |   3132990 |       0 |         0 |   584370 |        0 |    41340 |   3758700 |   3758700 |
| 38  | GRUNDY         |  12711061 |       0 |    664684 |  2035708 |        0 |   288494 |  15699947 |  15699947 |
| 39  | GUTHRIE        |   7568908 |       0 |         0 |   667837 |   335021 |        0 |   8571766 |   8571766 |
| 41  | HANCOCK        |  13294360 |       0 |    234150 |  1847270 |        0 |   108350 |  15484130 |  15484130 |
| 43  | HARRISON       |   5720578 |       0 |    150813 |  1141344 |   269926 |   698424 |   7981085 |   7981085 |
| 44  | HENRY          |   5057225 |       0 |    847050 |  1100810 |        0 |   148884 |   7153969 |   7153969 |
| 45  | HOWARD         |   9652320 |  408080 |   3036010 |  1375040 |        0 |   284200 |  14755650 |  14755650 |
| 46  | HUMBOLDT       |   3056676 |       0 |         0 |   486929 |        0 |        0 |   3543605 |   3543605 |
| 47  | IDA            |   3187300 |       0 |         0 |   898660 |        0 |    89854 |   4175814 |   4175814 |
| 49  | JACKSON        |   7010360 |       0 |         0 |  1210400 |        0 |   404900 |   8625660 |   8625660 |
| 50  | JASPER         |  27916600 |       0 |    828350 |  2261880 |        0 |   715840 |  31722670 |  31722670 |
| 51  | JEFFERSON      |  28158800 |  325300 |         0 |  1997400 |        0 |   337500 |  30819000 |  30819000 |
| 52a | IOWA CITY      |  67821040 | 1603770 |  14720050 |  2874940 |        0 |  2262700 |  89282500 |  89282500 |
| 53  | JONES          |  30321710 |       0 |   3196740 |  2456710 |   610220 |        0 |  36585380 |  36585380 |
| 54  | KEOKUK         |   6972690 |       0 |  13956780 |  1155380 |        0 |        0 |  22084850 |  22084850 |
| 55  | KOSSUTH        |  15079305 |       0 |   4481512 |  1169118 |        0 |  2428733 |  23158668 |  23158668 |
| 56  | LEE            |  23428920 | 1437040 |   3207640 |  1492170 |        0 |   583880 |  30149650 |  30149650 |
| 57a | CEDAR RAPIDS   | 153952500 |       0 |  33493500 |  4038800 |        0 | 22108900 | 213593700 | 213593700 |
| 58  | LOUISA         |   2053987 |       0 |         0 |   526283 |        0 |        0 |   2580270 |   2580270 |
| 59  | LUCAS          |   3272508 |       0 |         0 |   575741 |   351145 |    71210 |   4270604 |   4270604 |
| 60  | LYON           |  29713156 |   98970 |   1342162 |  4422211 |        0 |   248608 |  35825107 |  35825107 |
| 62  | MAHASKA        |  31733250 | 2843320 |   1617750 |  2902370 |        0 |   534400 |  39631090 |  39631090 |
| 64  | MARSHALL       |  18314665 |       0 |   1092980 |  2105585 |        0 |   102300 |  21615530 |  21615530 |
| 65  | MILLS          |   8224708 |  150144 |         0 |   989680 |        0 |   195618 |   9560150 |   9560150 |
| 67  | MONONA         |   9814323 |       0 |    182586 |  1064866 |    94991 |        0 |  11156766 |  11156766 |
| 68  | MONROE         |   5926407 |  710606 |     57187 |   752156 |        0 |     7379 |   7453735 |   7453735 |
| 69  | MONTGOMERY     |   5109780 |       0 |      3000 |   809520 |        0 |   166430 |   6088730 |   6088730 |
| 70  | MUSCATINE      |  52847104 |       0 |   3650980 |  2876780 |  2432810 |   336110 |  62143784 |  62143784 |
| 71  | O'BRIEN        |  20874490 |       0 |   1457270 |  3018550 |        0 |        0 |  25350310 |  25350310 |
| 72  | OSCEOLA        |   6849162 |   19800 |    279500 |  1200994 |        0 |    38970 |   8388426 |   8388426 |
| 73  | PAGE           |  15322079 |   57145 |     16860 |  1125310 |        0 |   208320 |  16729714 |  16729714 |
| 74  | PALO ALTO      |  26301100 | 1018570 |   3435320 |  3198830 |        0 |   216540 |  34170360 |  34170360 |
| 75  | PLYMOUTH       |  12435570 |       0 |   3965500 |  2902520 |        0 |   536420 |  19840010 |  19840010 |
| 76  | POCAHONTAS     |   7200088 |       0 |    659634 |   537680 |        0 |    57639 |   8455041 |   8455041 |
| 78  | POTTAWATTAMIE  |  66734700 |  190702 |   5645779 |  7922844 |        0 |  7148933 |  87642958 |  87642958 |
| 80  | RINGGOLD       |   1955136 |       0 |         0 |   250767 |        0 |        0 |   2205903 |   2205903 |
| 81  | SAC            |  13836020 |       0 |      9250 |  1051470 |        0 |    67200 |  14963940 |  14963940 |
| 82  | SCOTT          |  34175350 |       0 |   3502460 |  4216930 |     4020 |        0 |  41898760 |  41898760 |
| 82a | DAVENPORT      | 130506390 |       0 | 117145540 |  6213060 |   115700 |  2531710 | 256512400 | 256512400 |
| 83  | SHELBY         |   4216964 |  600757 |    878418 |  1036299 |        0 |    38967 |   6771405 |   6771405 |
| 85  | STORY          |  24322800 |  102500 |    253300 |  1865400 |        0 |  3803900 |  30347900 |  30347900 |
| 85a | AMES           |  56730480 |       0 |   1956000 |  2445000 |        0 |  7654400 |  68785880 |  68785880 |
| 86  | TAMA           |  11094090 |       0 |    259470 |  1016530 |   978770 |   485200 |  13834060 |  13834060 |
| 87  | TAYLOR         |   2948132 |       0 |      5750 |   731820 |        0 |   300650 |   3986352 |   3986352 |
| 88  | UNION          |    586160 |       0 |    275000 |   285470 |        0 |        0 |   1146630 |   1146630 |
| 89  | VAN BUREN      |   3368760 |       0 |    283270 |   536020 |   546200 |        0 |   4734250 |   4734250 |
| 90  | WAPELLO        |  20102042 |       0 |   1210197 |  2443758 |  2007722 |    43851 |  25807570 |  25807570 |
| 91  | WARREN         |  49047000 |       0 |    396300 |  2797100 |  1420300 |        0 |  53660700 |  53660700 |
| 92  | WASHINGTON     |  14569200 |       0 |    132800 |  1062100 |  4509500 |  1523186 |  21796786 |  21796786 |
| 93  | WAYNE          |   3384932 |       0 |         0 |   691558 |        0 |        0 |   4076490 |   4076490 |
| 95  | WINNEBAGO      |   6307450 |       0 |         0 |   978650 |        0 |   568795 |   7854895 |   7854895 |
| 96  | WINNESHIEK     |   7689540 |       0 |    132020 |   408110 |        0 |        0 |   8229670 |   8229670 |
| 97  | WOODBURY       |  12798100 |       0 |    574670 |  2774080 |        0 |  1134830 |  17281680 |  17281680 |
| 98  | WORTH          |   6927154 |       0 |         0 |  1066517 |        0 |        0 |   7993671 |   7993671 |
| 99  | WRIGHT         |  11270700 |       0 |         0 |  1748100 |        0 |        0 |  13018800 |  13018800 |



labeled_formulas: J=(D*G)+I
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_450745___xlsx_daa4317c9627f49e50b0d26b2cd97bde17ca05f3.xlsx___line_958