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   |
|----:|:----------------------------|:------|:----|:------|----------:|----------:|-----------------:|-----------------:|----------:|:----|
|   1 | VAN DREW, JEFF              | S     | D   | I     |   1600    |  10500    | 119301           | 110239           |   9062.42 | R   |
|   1 | VAN DREW ANDRZEJCZAK & LAND | S/A/A | D   | I/I/I |   2500    |   2000    |  53209.7         |  52709.7         |    500    | R   |
|   2 | BELL, COLIN                 | S     | D   | C     |  11699.2  |    999.23 |  11699.2         |    999.23        |  10700    | R   |
|   2 | BROWN, CHRIS                | S     | R   | C     | 150340    |  45033.7  | 367022           |  86186.1         | 280836    | R   |
|   2 | ARMATO, JOHN                | A     | D   | C     |   2860.65 |      0    |   2860.65        |      0           |   2860.65 | R   |
|   2 | MAZZEO, VINCENT             | A     | D   | I     |   6217.82 |    498    |  39777.9         |  28842.7         |  10935.1  | R   |
|   2 | SERA, VINCENT               | A     | R   | C     |   7579    |   1470.01 |   7579           |   1470.01        |   6108.99 | R   |
|   2 | TAUBE, BRENDA               | A     | R   | C     |   5215    |    690.2  |   5215           |    690.2         |   4524.8  | R   |
|   2 | BELL MAZZEO & ARMATO        | S/A/A | D   | C/I/C |   2832.23 |   2732.23 |   2832.23        |   2732.23        |    100    | R   |
|   3 | GRENIER, FRAN               | S     | R   | C     |    200    |      0    |    200           |      0           |    200    | R   |
|   3 | SWEENEY, STEPHEN M          | S     | D   | I     | 126253    | 183843    |      2.07365e+06 |      1.27017e+06 | 803480    | R   |
|   3 | BURZICHELLI, JOHN J         | A     | D   | I     |  89133.3  |  12246.9  | 205789           |  94196           | 111593    | R   |
|   3 | TALIAFERRO, ADAM            | A     | D   | I     |  23183.3  |   1695.61 |  74027.5         |  17324.1         |  56703.4  | R   |
|   3 | DONELSON & DONOHUE          | A/A   | R   | C/C   |      0    |      0    |      0           |      0           |      0    | R   |
|   4 | MADDEN, FRED H              | S     | D   | I     |  37650    |   5519.81 | 221413           |  62472.7         | 158941    | R   |
|   4 | MORIARTY, PAUL D            | A     | D   | I     |  39050    |  11275.4  | 164828           |  84225.6         |  80602.6  | R   |
|   4 | MOSQUERA, GABRIELA          | A     | D   | I     |  36025    |   9402.84 | 115926           |  68458.8         |  47466.7  | R   |
|   5 | CRUZ PEREZ, NILSA           | S     | D   | I     |  71320    |  16441    | 252728           |  67241.7         | 185486    | R   |
|   5 | BARCLAY, ARTHUR             | A     | D   | I     |  21755    |   9899.83 |  53860.2         |  39724.3         |  14135.9  | R   |
|   5 | EGAN JONES, PATRICIA        | A     | D   | I     |  45174    |  14407.7  | 135208           |  73364.1         |  61843.9  | R   |
|   6 | BEACH, JAMES                | S     | D   | I     |  36229    |  17317.3  | 266454           | 171368           |  95086.2  | R   |
|   6 | GREENWALD, LOUIS D          | A     | D   | I     |  64450    |  29990.7  | 399401           | 241100           | 158301    | R   |
|   6 | LAMPITT, PAMELA R           | A     | D   | I     |  37468    |  17529.4  | 177708           | 103497           |  74210.7  | R   |
|   7 | SINGLETON, TROY E           | S     | D   | C     | 116044    |  70742.2  | 392822           | 304168           |  88653.7  | R   |
|   7 | CHUANG, JENNIFER            | A     | D   | C     |   9460    |   1495.62 |   9460           |   1495.62        |   7964.38 | R   |
|   7 | CONAWAY, HERBERT C MD       | A     | D   | I     |  30350    |  22613.8  | 133786           | 121419           |  12366.8  | R   |
|   7 | MURPHY, CAROL A             | A     | D   | C     |  15638.2  |   7007.63 |  15638.2         |   7007.63        |   8630.56 | R   |
|   7 | PRISCO SCOTT PIPER          | S/A/A | R   | C/C/C |      0    |      0    |      0           |      0           |      0    | R   |
|   8 | ADDIEGO, DAWN               | S     | R   | I     |  26197    |  16474.8  | 187882           | 177115           |  10767.2  | R   |
|   8 | HOWARTH, JOE                | A     | R   | I     |  26050    |  10000    |  56700           |  40500           |  16200    | R   |
|   8 | RODRIGUEZ-GREGG, MARIA      | A     | R   | I     |  19700    |  10000    |  47900           |  36200           |  11700    | R   |
|   8 | RODRIGUEZ-GREGG & HOWARTH   | A/A   | R   | I/I   |  58736    |  48336    |  89036           |  72336           |  16700    | R   |
|   8 | YOUNGKIN MERLINO SCHWARTZ   | S/A/A | D   | C/C/C |   5980    |     56.96 |   5980           |     56.96        |   5923.04 | R   |
|   9 | CONNORS, CHRISTOPHER J      | S     | R   | I     |      0    |      0    |  12919.4         |   2509.9         |  10409.5  | RQ  |
|   9 | DOBROWANSKY, JILL           | A     | D   | C     |    520    |    130.07 |    520           |    130.07        |    389.93 | R   |
|   9 | YOUNG, RYAN                 | A     | D   | C     |    201.62 |     46.28 |    201.62        |     46.28        |    155.34 | R   |
|   9 | CONNORS RUMPF & GOVE        | S/A/A | R   | I/I/I |  10129    |   6622.75 |  54581.8         |  13392.6         |  41189.2  | R   |
|  10 | HOLZAPFEL, JAMES W          | S     | R   | I     |      0    |   4525.78 |  98397.2         |  76911.7         |  21485.5  | R   |
|  10 | MCGUCKIN, GREGORY P         | A     | R   | I     |  14150    |   9597.79 |  69338.9         |  20390.5         |  48948.3  | R   |
|  10 | WOLFE, DAVID W              | A     | R   | I     |      0    |   4435.48 |  27928.5         |  17022.5         |  10906    | R   |
|  11 | BECK, JENNIFER              | S     | R   | I     | 107026    |  51056.8  | 505562           | 394118           | 111445    | R   |
|  11 | GOPAL, VIN                  | S     | D   | C     | 315883    |  14035.5  | 315883           |  14035.5         | 301847    | R   |
|  11 | ACERRA, ROBERT              | A     | R   | C     |   1900    |    750    |   1900           |    750           |   1150    | R   |
|  11 | DOWNEY, JOANN L             | A     | D   | I     |  31102.7  |   1310.71 |  99996.8         |  60157.2         |  39839.6  | R   |
|  11 | HOUGHTALING, ERIC           | A     | D   | I     |  32877.7  |   1310.71 | 141900           |  76324.6         |  65575.2  | R   |
|  11 | WHELAN, MICHAEL             | A     | R   | C     |   1350    |     35.25 |   1350           |     35.25        |   1314.75 | R   |
|  11 | GOPAL HOUGHTALING & DOWNEY  | S/A/A | D   | C/I/I |  35949.3  |  52166.2  | 158595           | 151440           |   7154.93 | R   |
|  12 | THOMPSON, SAMUEL D          | S     | R   | I     |  18050    |  11401.7  | 141770           |  81471.4         |  60298.9  | R   |
|  12 | CLIFTON, ROBERT             | A     | R   | I     |  41250.7  |  27701    |  83788.7         |  59073.9         |  24714.7  | R   |
|  12 | DANCER, RONALD S            | A     | R   | I     |  24750    |  16362.1  | 200431           |  42590.4         | 157841    | R   |
|  12 | DAVIS, GENE                 | A     | D   | C     |   5385    |   2345.16 |   5385           |   2345.16        |   3039.84 | R   |
|  13 | BYRNES, SEAN                | S     | D   | C     |   9910    |   5894.51 |   9910           |   5894.51        |   4015.49 | R   |
|  13 | OSCANLON, DECLAN            | S     | R   | C     |  52150    |  96763.3  | 218112           | 145162           |  72949.9  | R   |
|  13 | DIMASO, SERENA              | A     | R   | C     |  30150    |   6567.75 |  30150           |   6567.75        |  23582.2  | R   |
|  13 | GIAIMO, TOM                 | A     | D   | C     |    600    |      0    |    600           |      0           |    600    | R   |
|  13 | HANDLIN, AMY                | A     | R   | I     | 201275    | 202806    | 276904           | 208827           |  68077.7  | R   |
|  14 | GREENSTEIN, LINDA R         | S     | D   | I     |  60304    |  11468.8  | 154982           |  90968.1         |  64013.7  | R   |
|  14 | SCHIRMER, ILEANA            | S     | R   | C     |  15500    |  10010    |  15500           |  10010           |   5490    | R   |
|  14 | BENSON, DANIEL R            | A     | D   | I     |  51150    |  41568.3  | 248517           | 134846           | 113671    | R   |
|  14 | DEANGELO, WAYNE  P          | A     | D   | I     |  73506    |  49902.2  | 382713           | 126341           | 256372    | R   |
|  14 | STOUT, KRISTIAN             | A     | R   | C     |   3734.75 |   2093.08 |   3734.75        |   2093.08        |   1641.67 | R   |
|  15 | TURNER, SHIRLEY K           | S     | D   | I     |  10277.5  |   7675.54 | 779676           |  96484.7         | 683192    | R   |
|  15 | GUSCIORA, REED              | A     | D   | I     |  13200    |   3585.28 |  80777.6         |  38299.7         |  42477.9  | R   |
|  15 | MUOIO, ELIZABETH M          | A     | D   | I     |  20722    |  11772.2  | 115102           |  42035.6         |  73066.5  | R   |
|  15 | GUSCIORA & MUOIO            | A/A   | D   | I/I   |   2487.2  |    126    |   2487.2         |    126           |   2361.2  | R   |
|  16 | BATEMAN, CHRISTOPHER SPEER  | S     | R   | I     |   9005.31 |  18008.2  | 237097           | 216420           |  20677.1  | R   |
|  16 | POPPE, LAURIE C             | S     | D   | C     |   3035    |      0    |   3035           |      0           |   3035    | R   |
|  16 | CALIGUIRE, MARK             | A     | R   | C     |  41414    |  12863.7  |  41414           |  12863.7         |  28550.3  | R   |
|  16 | FREIMAN, ROY D              | A     | D   | C     |  13587    |   3456.08 |  13587           |   3456.08        |  10130.9  | R   |
|  16 | SIMON, DONNA                | A     | R   | C     |  23330    |  19259.5  |  68979           |  38152           |  30827.1  | R   |
|  16 | ZWICKER, ANDREW             | A     | D   | I     |  57500.1  |  28597.3  | 198897           | 102260           |  96637    | R   |
|  16 | BATEMAN SIMON & CALIGUIRE   | S/A/A | R   | I/C/C |  20580    |  14593    |  20580           |  14593           |   5987.05 | R   |
|  16 | POPPE ZWICKER FREIMAN       | S/A/A | D   | C/I/C |    100    |      0    |    100           |      0           |    100    | R   |
|  17 | KIPNIS, DARYL J             | S     | R   | C     |   3485    |   1976.58 |   5311.56        |   2324.15        |   2987.41 | R   |
|  17 | SMITH, BOB                  | S     | D   | I     |  12700    |  32252.8  | 669513           | 220341           | 449172    | R   |



label: J=H-I
labeled_formulas: J=H-I
output: {"Arithmetic-Relationship": ["J=H-I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_614233___xlsx_161735dc78cdec44b33e84c55cffb64ea73790ee.xlsx___line_66