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 |   N |       O |         P |       Q |        R |    S |        T |    U | V                     |
|--------:|-------:|----------:|----------:|---------:|---------:|-----:|-------:|-------:|--------:|-----:|-----:|-----:|----:|--------:|----------:|--------:|---------:|-----:|---------:|-----:|:----------------------|
|       0 |      0 |      0    |      0    |     0    |     0    |    0 |    0   |    0   |     0   |    0 |    0 |    0 |   0 |       0 |     0     |    0    |     0    |    0 |     0    |    0 | -                     |
|   20000 |   5000 |   2341.81 |   2484.9  |  2290.28 |   535.63 |    0 |  372   |  372   |   744   |   87 |   87 |  174 |   0 |   20000 |  -143.093 | 1546.28 |   361.63 |    0 |  1764.82 |   20 | 8.8240837500000016E-2 |
|   40000 |  10000 |   5222.27 |   5699.25 |  4580.56 |  1071.26 |    0 |  744   |  744   |  1488   |  174 |  174 |  348 |   0 |   40000 |  -476.978 | 3092.56 |   723.26 |    0 |  3338.84 |   40 | 8.3471062499999998E-2 |
|   60000 |  15000 |   9869.03 |  10584.5  |  6870.84 |  1606.89 |    0 | 1116   | 1116   |  2232   |  261 |  261 |  522 |   0 |   60000 |  -715.466 | 4638.84 |  1084.89 |    0 |  5008.26 |   60 | 8.3471062500000012E-2 |
|   80000 |  20000 |  14515.8  |  15469.8  |  9161.12 |  2142.52 |    0 | 1488   | 1488   |  2976   |  348 |  348 |  696 |   0 |   80000 |  -953.955 | 6185.12 |  1446.52 |    0 |  6677.69 |   80 | 8.3471062499999998E-2 |
|  100000 |  25000 |  19315.1  |  20650.7  | 11451.4  |  2678.15 |    0 | 1860   | 1860   |  3720   |  435 |  435 |  870 |   0 |  100000 | -1335.54  | 7731.4  |  1808.15 |    0 |  8204.01 |  100 | 8.2040129999999989E-2 |
|  120000 |  30000 |  24519.5  |  26122.1  | 13741.7  |  3213.78 |    0 | 2232   | 2232   |  4464   |  522 |  522 | 1044 |   0 |  120000 | -1602.64  | 9277.68 |  2169.78 |    0 |  9844.82 |  120 | 8.2040130000000003E-2 |
|  140000 |  35000 |  29994.5  |  31593.6  | 14098.8  |  3749.41 |    0 | 2604   | 2604   |  5208   |  609 |  609 | 1218 |   0 |  140000 | -1599.11  | 8890.8  |  2531.41 |    0 |  9823.1  |  140 | 7.0165004285714275E-2 |
|  160000 |  40000 |  35519.5  |  37065.1  | 14098.8  |  4285.04 |    0 | 2976   | 2976   |  5952   |  696 |  696 | 1392 |   0 |  160000 | -1545.58  | 8146.8  |  2893.04 |    0 |  9494.26 |  160 | 5.9339140000000019E-2 |
|  180000 |  45000 |  41044.5  |  42536.6  | 14098.8  |  4820.67 |    0 | 3348   | 3348   |  6696   |  783 |  783 | 1566 |   0 |  180000 | -1492.05  | 7402.8  |  3254.67 |    0 |  9165.42 |  180 | 5.0919023333333327E-2 |
|  200000 |  50000 |  46920.7  |  48616.1  | 14098.8  |  5356.3  |    0 | 3720   | 3720   |  7440   |  870 |  870 | 1740 |   0 |  200000 | -1695.39  | 6658.8  |  3616.3  |    0 |  8579.71 |  200 | 4.2898542500000005E-2 |
|  380000 |  95000 | 105525    | 106659    | 14098.8  | 10177    | 1620 | 7049.4 | 7049.4 | 14098.8 | 1653 | 1653 | 3306 |   0 |  380000 | -1133.71  |    0    |  6870.97 | 1620 |  7357.26 |  380 | 1.9361210394736823E-2 |
|  400000 | 100000 | 112037    | 113230    | 14098.8  | 10712.6  | 1800 | 7049.4 | 7049.4 | 14098.8 | 1740 | 1740 | 3480 |   0 |  400000 | -1193.38  |    0    |  7232.6  | 1800 |  7839.22 |  400 | 1.9598052500000036E-2 |
|  420000 | 105000 | 119065    | 120569    | 14098.8  | 11248.2  | 1980 | 7049.4 | 7049.4 | 14098.8 | 1827 | 1827 | 3654 |   0 |  420000 | -1503.66  |    0    |  7594.23 | 1980 |  8070.57 |  420 | 1.9215648714285716E-2 |
|  440000 | 110000 | 126879    | 128454    | 14098.8  | 11783.9  | 2160 | 7049.4 | 7049.4 | 14098.8 | 1914 | 1914 | 3828 |   0 |  440000 | -1575.26  |    0    |  7955.86 | 2160 |  8540.6  |  440 | 1.9410453909090939E-2 |
|  460000 | 115000 | 134693    | 136340    | 14098.8  | 12319.5  | 2340 | 7049.4 | 7049.4 | 14098.8 | 2001 | 2001 | 4002 |   0 |  460000 | -1646.86  |    0    |  8317.49 | 2340 |  9010.63 |  460 | 1.9588319521739152E-2 |
|  480000 | 120000 | 142507    | 144225    | 14098.8  | 12855.1  | 2520 | 7049.4 | 7049.4 | 14098.8 | 2088 | 2088 | 4176 |   0 |  480000 | -1718.47  |    0    |  8679.12 | 2520 |  9480.65 |  480 | 1.9751362999999959E-2 |
|  500000 | 125000 | 150321    | 152111    | 14098.8  | 13390.8  | 2700 | 7049.4 | 7049.4 | 14098.8 | 2175 | 2175 | 4350 |   0 |  500000 | -1790.07  |    0    |  9040.75 | 2700 |  9950.68 |  500 | 1.9901363000000012E-2 |
|  520000 | 130000 | 158135    | 159996    | 14098.8  | 13926.4  | 2880 | 7049.4 | 7049.4 | 14098.8 | 2262 | 2262 | 4524 |   0 |  520000 | -1861.67  |    0    |  9402.38 | 2880 | 10420.7  |  520 | 2.0039824538461547E-2 |
|  540000 | 135000 | 165949    | 167882    | 14098.8  | 14462    | 3060 | 7049.4 | 7049.4 | 14098.8 | 2349 | 2349 | 4698 |   0 |  540000 | -1933.27  |    0    |  9764.01 | 3060 | 10890.7  |  540 | 2.016802966666667E-2  |
|  560000 | 140000 | 173763    | 175768    | 14098.8  | 14997.6  | 3240 | 7049.4 | 7049.4 | 14098.8 | 2436 | 2436 | 4872 |   0 |  560000 | -2004.88  |    0    | 10125.6  | 3240 | 11360.8  |  560 | 2.0287077285714338E-2 |
|  580000 | 145000 | 181577    | 183653    | 14098.8  | 15533.3  | 3420 | 7049.4 | 7049.4 | 14098.8 | 2523 | 2523 | 5046 |   0 |  580000 | -2076.48  |    0    | 10487.3  | 3420 | 11830.8  |  580 | 2.0397914724137926E-2 |
|  600000 | 150000 | 189391    | 191539    | 14098.8  | 16068.9  | 3600 | 7049.4 | 7049.4 | 14098.8 | 2610 | 2610 | 5220 |   0 |  600000 | -2148.08  |    0    | 10848.9  | 3600 | 12300.8  |  600 | 2.0501362999999995E-2 |
|  620000 | 155000 | 197204    | 199424    | 14098.8  | 16604.5  | 3780 | 7049.4 | 7049.4 | 14098.8 | 2697 | 2697 | 5394 |   0 |  620000 | -2219.68  |    0    | 11210.5  | 3780 | 12770.8  |  620 | 2.0598137193548426E-2 |
|  640000 | 160000 | 205018    | 207310    | 14098.8  | 17140.2  | 3960 | 7049.4 | 7049.4 | 14098.8 | 2784 | 2784 | 5568 |   0 |  640000 | -2291.29  |    0    | 11572.2  | 3960 | 13240.9  |  640 | 2.0688863000000033E-2 |
|  660000 | 165000 | 212832    | 215195    | 14098.8  | 17675.8  | 4140 | 7049.4 | 7049.4 | 14098.8 | 2871 | 2871 | 5742 |   0 |  660000 | -2362.89  |    0    | 11933.8  | 4140 | 13710.9  |  660 | 2.0774090272727259E-2 |
|  680000 | 170000 | 220646    | 223081    | 14098.8  | 18211.4  | 4320 | 7049.4 | 7049.4 | 14098.8 | 2958 | 2958 | 5916 |  36 |  680000 | -2434.49  |    0    | 12295.4  | 4284 | 14144.9  |  680 | 2.0801363000000028E-2 |
|  700000 | 175000 | 228460    | 230966    | 14098.8  | 18747    | 4500 | 7049.4 | 7049.4 | 14098.8 | 3045 | 3045 | 6090 |  90 |  700000 | -2506.1   |    0    | 12657    | 4410 | 14561    |  700 | 2.0801362999999979E-2 |
|  720000 | 180000 | 236274    | 238852    | 14098.8  | 19282.7  | 4680 | 7049.4 | 7049.4 | 14098.8 | 3132 | 3132 | 6264 | 144 |  720000 | -2577.7   |    0    | 13018.7  | 4536 | 14977    |  720 | 2.0801362999999976E-2 |
|  740000 | 185000 | 244088    | 246737    | 14098.8  | 19818.3  | 4860 | 7049.4 | 7049.4 | 14098.8 | 3219 | 3219 | 6438 | 198 |  740000 | -2649.3   |    0    | 13380.3  | 4662 | 15393    |  740 | 2.0801362999999976E-2 |
|  760000 | 190000 | 251902    | 254623    | 14098.8  | 20353.9  | 5040 | 7049.4 | 7049.4 | 14098.8 | 3306 | 3306 | 6612 | 252 |  760000 | -2720.9   |    0    | 13741.9  | 4788 | 15809    |  760 | 2.0801363000000014E-2 |
|  780000 | 195000 | 259716    | 262509    | 14098.8  | 20889.6  | 5220 | 7049.4 | 7049.4 | 14098.8 | 3393 | 3393 | 6786 | 306 |  780000 | -2792.51  |    0    | 14103.6  | 4914 | 16225.1  |  780 | 2.0801362999999934E-2 |
|  800000 | 200000 | 267530    | 270394    | 14098.8  | 21425.2  | 5400 | 7049.4 | 7049.4 | 14098.8 | 3480 | 3480 | 6960 | 360 |  800000 | -2864.11  |    0    | 14465.2  | 5040 | 16641.1  |  800 | 2.0801363000000041E-2 |
|  820000 | 205000 | 275344    | 278280    | 14098.8  | 21960.8  | 5580 | 7049.4 | 7049.4 | 14098.8 | 3567 | 3567 | 7134 | 414 |  820000 | -2935.71  |    0    | 14826.8  | 5166 | 17057.1  |  820 | 2.0801363000000041E-2 |
|  840000 | 210000 | 283158    | 286165    | 14098.8  | 22496.5  | 5760 | 7049.4 | 7049.4 | 14098.8 | 3654 | 3654 | 7308 | 468 |  840000 | -3007.32  |    0    | 15188.5  | 5292 | 17473.1  |  840 | 2.0801363000000038E-2 |
|  860000 | 215000 | 290972    | 294051    | 14098.8  | 23032.1  | 5940 | 7049.4 | 7049.4 | 14098.8 | 3741 | 3741 | 7482 | 522 |  860000 | -3078.92  |    0    | 15550.1  | 5418 | 17889.2  |  860 | 2.0801363000000031E-2 |
|  880000 | 220000 | 298786    | 301936    | 14098.8  | 23567.7  | 6120 | 7049.4 | 7049.4 | 14098.8 | 3828 | 3828 | 7656 | 576 |  880000 | -3150.52  |    0    | 15911.7  | 5544 | 18305.2  |  880 | 2.0801362999999962E-2 |
|  900000 | 225000 | 306600    | 309822    | 14098.8  | 24103.3  | 6300 | 7049.4 | 7049.4 | 14098.8 | 3915 | 3915 | 7830 | 630 |  900000 | -3222.12  |    0    | 16273.4  | 5670 | 18721.2  |  900 | 2.0801363000000028E-2 |
|  920000 | 230000 | 314414    | 317707    | 14098.8  | 24639    | 6480 | 7049.4 | 7049.4 | 14098.8 | 4002 | 4002 | 8004 | 684 |  920000 | -3293.73  |    0    | 16635    | 5796 | 19137.3  |  920 | 2.0801363000000021E-2 |
|  940000 | 235000 | 322228    | 325593    | 14098.8  | 25174.6  | 6660 | 7049.4 | 7049.4 | 14098.8 | 4089 | 4089 | 8178 | 738 |  940000 | -3365.33  |    0    | 16996.6  | 5922 | 19553.3  |  940 | 2.0801363000000021E-2 |
|  960000 | 240000 | 330042    | 333478    | 14098.8  | 25710.2  | 6840 | 7049.4 | 7049.4 | 14098.8 | 4176 | 4176 | 8352 | 792 |  960000 | -3436.93  |    0    | 17358.2  | 6048 | 19969.3  |  960 | 2.0801362999999958E-2 |
|  980000 | 245000 | 337856    | 341364    | 14098.8  | 26245.9  | 7020 | 7049.4 | 7049.4 | 14098.8 | 4263 | 4263 | 8526 | 846 |  980000 | -3508.53  |    0    | 17719.9  | 6174 | 20385.3  |  980 | 2.0801363000000017E-2 |
| 1000000 | 250000 | 345669    | 349250    | 14098.8  | 26781.5  | 7200 | 7049.4 | 7049.4 | 14098.8 | 4350 | 4350 | 8700 | 900 | 1000000 | -3580.14  |    0    | 18081.5  | 6300 | 20801.4  | 1000 | 2.0801363000000014E-2 |



label: J=H+I
M=K+L
P=C-D
Q=E-J
R=F-M
S=G-N
labeled_formulas: J=H+I
M=K+L
P=C-D
Q=E-J
R=F-M
S=G-N
O=(G*Q)+A
output: {"Arithmetic-Relationship": ["J=H+I", "M=K+L", "P=C-D", "Q=E-J", "R=F-M", "S=G-N"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_209002___xlsx_203c1896144d520f235bdf18220d14028e27bb4e.xlsx___line_175