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       |
|--------:|------:|--------:|:--------|
| 43855.8 | 16.26 | 43872.1 | Job 1   |
| 44193.6 | 12.53 | 44206.2 | Job 2   |
| 44026.6 |  9.95 | 44036.6 | Job 3   |
| 43964.1 | 19.21 | 43983.3 | Job 4   |
| 43922.3 | 11.86 | 43934.2 | Job 5   |
| 43971.2 |  0.21 | 43971.4 | Job 6   |
| 43950.7 | 12.9  | 43963.6 | Job 7   |
| 44139   | 13.87 | 44152.9 | Job 8   |
| 43924   | 17.12 | 43941.2 | Job 9   |
| 44027.5 | 13.68 | 44041.2 | Job 10  |
| 44017.6 | 17.89 | 44035.5 | Job 11  |
| 44037.8 | 16.76 | 44054.5 | Job 12  |
| 44147.7 | 12.13 | 44159.8 | Job 13  |
| 44158.1 |  8.17 | 44166.3 | Job 14  |
| 44119.7 | 10.22 | 44129.9 | Job 15  |
| 43939.1 | 14.7  | 43953.8 | Job 16  |
| 44073.4 |  2.35 | 44075.8 | Job 17  |
| 44002.4 | 12.66 | 44015   | Job 18  |
| 43933.6 |  5.86 | 43939.5 | Job 19  |
| 43855   |  4.99 | 43860   | Job 20  |
| 43893.6 | 18.6  | 43912.2 | Job 21  |
| 43898.3 |  5.12 | 43903.4 | Job 22  |
| 43919.7 |  7.08 | 43926.8 | Job 23  |
| 44110.2 |  5.59 | 44115.8 | Job 24  |
| 44054.5 |  0.23 | 44054.7 | Job 25  |
| 44142.7 |  1.39 | 44144.1 | Job 26  |
| 44086.9 |  4.53 | 44091.5 | Job 27  |
| 44041.4 | 14.77 | 44056.2 | Job 28  |
| 44036.5 |  4.09 | 44040.6 | Job 29  |
| 44026.2 |  7.61 | 44033.8 | Job 30  |
| 43907.4 |  0.39 | 43907.8 | Job 31  |
| 43933.2 | 10.52 | 43943.7 | Job 32  |
| 44088.1 |  3.9  | 44092   | Job 33  |
| 44038.8 |  3.47 | 44042.3 | Job 34  |
| 44185.3 |  4.88 | 44190.2 | Job 35  |
| 44165   |  4.02 | 44169.1 | Job 36  |
| 44011.5 | 17.62 | 44029.1 | Job 37  |
| 44089.3 | 19.24 | 44108.6 | Job 38  |
| 44127.3 |  3.27 | 44130.6 | Job 39  |
| 43864   | 19.77 | 43883.8 | Job 40  |
| 44115.9 |  8.78 | 44124.7 | Job 41  |
| 44153   | 15.92 | 44169   | Job 42  |
| 44061.6 | 13.61 | 44075.2 | Job 43  |
| 44085.8 |  0.66 | 44086.5 | Job 44  |
| 44105.1 |  2.74 | 44107.9 | Job 45  |
| 44104.4 |  6.34 | 44110.8 | Job 46  |
| 44108.8 | 15.04 | 44123.8 | Job 47  |
| 44182   | 15.58 | 44197.5 | Job 48  |
| 44183.6 |  9.83 | 44193.4 | Job 49  |
| 44093.7 |  7.22 | 44101   | Job 50  |
| 44153.8 |  8.5  | 44162.3 | Job 51  |
| 43896   | 12.26 | 43908.2 | Job 52  |
| 44003.6 |  9.11 | 44012.8 | Job 53  |
| 43941.9 | 11.35 | 43953.2 | Job 54  |
| 44192.8 |  7.05 | 44199.9 | Job 55  |
| 44048.4 |  0.61 | 44049   | Job 56  |
| 44186   | 13.69 | 44199.7 | Job 57  |
| 43872.4 |  8.07 | 43880.5 | Job 58  |
| 44191.8 |  9.16 | 44200.9 | Job 59  |
| 44015.9 |  7.89 | 44023.8 | Job 60  |
| 44095.9 | 18.94 | 44114.8 | Job 61  |
| 43839.9 | 11.92 | 43851.8 | Job 62  |
| 43839.7 |  3    | 43842.7 | Job 63  |
| 44144   | 19.36 | 44163.4 | Job 64  |
| 43956   |  1.9  | 43957.9 | Job 65  |
| 44108.8 | 11.49 | 44120.3 | Job 66  |
| 44081.4 |  3.06 | 44084.5 | Job 67  |
| 43949.2 | 18.87 | 43968   | Job 68  |
| 43831.2 | 15.37 | 43846.5 | Job 69  |
| 44132.2 |  7.28 | 44139.5 | Job 70  |
| 43970.8 |  6.99 | 43977.8 | Job 71  |
| 44137.4 |  1.17 | 44138.6 | Job 72  |
| 44130.6 |  9.6  | 44140.2 | Job 73  |
| 43909.7 | 17.91 | 43927.6 | Job 74  |
| 44193.4 | 18.73 | 44212.1 | Job 75  |
| 43865.5 | 16.46 | 43882   | Job 76  |
| 44148.7 | 12.87 | 44161.6 | Job 77  |
| 43920.9 |  6.71 | 43927.6 | Job 78  |
| 43840.8 |  9.63 | 43850.5 | Job 79  |
| 43845.5 | 16.95 | 43862.4 | Job 80  |
| 43895.7 |  6.38 | 43902.1 | Job 81  |
| 44168.2 |  9.55 | 44177.7 | Job 82  |
| 43973.4 |  6.05 | 43979.5 | Job 83  |
| 43968.2 |  5.34 | 43973.5 | Job 84  |
| 43835.8 |  2.93 | 43838.7 | Job 85  |
| 43852.7 | 13.06 | 43865.8 | Job 86  |
| 44108.8 |  2.18 | 44111   | Job 87  |
| 44196.8 |  0.77 | 44197.6 | Job 88  |
| 44156.3 |  3.63 | 44159.9 | Job 89  |
| 44186.2 | 18.77 | 44205   | Job 90  |
| 44032.3 |  9.73 | 44042.1 | Job 91  |
| 44065.6 |  6.74 | 44072.3 | Job 92  |
| 44150.5 |  6.91 | 44157.4 | Job 93  |
| 44081.5 |  1.79 | 44083.3 | Job 94  |
| 44173   | 18.88 | 44191.9 | Job 95  |
| 43836.7 |  2.72 | 43839.4 | Job 96  |
| 44021.1 |  5.76 | 44026.8 | Job 97  |
| 44134.8 | 14.99 | 44149.8 | Job 98  |
| 43840.1 |  9.61 | 43849.7 | Job 99  |
| 44018.2 | 13.12 | 44031.4 | Job 100 |
| 44078.7 |  4.45 | 44083.1 | Job 101 |
| 43862.4 | 14.2  | 43876.6 | Job 102 |
| 43945.9 |  6.72 | 43952.7 | Job 103 |
| 43852.6 | 14.65 | 43867.3 | Job 104 |
| 43859.2 |  8.34 | 43867.5 | Job 105 |
| 44120.2 |  1.85 | 44122.1 | Job 106 |
| 43988.3 | 17.01 | 44005.3 | Job 107 |
| 44148.8 | 11.75 | 44160.6 | Job 108 |
| 44047.7 | 17.77 | 44065.4 | Job 109 |
| 43990.8 | 14.68 | 44005.5 | Job 110 |
| 43949.9 |  6.48 | 43956.4 | Job 111 |
| 44153.6 |  1.02 | 44154.7 | Job 112 |
| 44191.4 |  4.27 | 44195.7 | Job 113 |
| 43900.7 | 15.61 | 43916.3 | Job 114 |
| 43868   |  5.23 | 43873.3 | Job 115 |
| 43979.9 | 11.78 | 43991.7 | Job 116 |
| 44093.2 | 10.38 | 44103.6 | Job 117 |
| 43924.4 |  6.48 | 43930.9 | Job 118 |
| 43914.9 | 10.48 | 43925.4 | Job 119 |
| 43995.3 |  8.7  | 44004   | Job 120 |
| 43991.2 | 11.98 | 44003.2 | Job 121 |
| 44186.5 |  2.91 | 44189.4 | Job 122 |
| 43990.6 | 17.64 | 44008.2 | Job 123 |
| 44030.9 |  5.24 | 44036.1 | Job 124 |
| 44143.9 | 11.53 | 44155.5 | Job 125 |
| 44108.8 | 19.29 | 44128.1 | Job 126 |
| 43917.6 | 15.29 | 43932.9 | Job 127 |
| 43909.8 | 10.2  | 43920   | Job 128 |
| 44117.2 | 17.7  | 44134.9 | Job 129 |
| 43840.5 |  5.72 | 43846.3 | Job 130 |
| 44175.6 | 18.19 | 44193.8 | Job 131 |
| 43890.4 |  7.2  | 43897.6 | Job 132 |
| 43890.1 |  4.18 | 43894.3 | Job 133 |
| 43990.5 | 15.74 | 44006.2 | Job 134 |
| 43942.2 |  3.14 | 43945.4 | Job 135 |
| 44128.6 | 16.41 | 44145   | Job 136 |
| 43987.5 |  9.36 | 43996.8 | Job 137 |
| 43994.7 | 12.15 | 44006.8 | Job 138 |
| 43947.6 |  5.48 | 43953.1 | Job 139 |
| 43953.2 | 10.11 | 43963.3 | Job 140 |
| 43868.6 |  1.39 | 43870   | Job 141 |
| 43995.6 |  9.4  | 44005   | Job 142 |
| 44062.1 |  1.87 | 44063.9 | Job 143 |
| 44047.5 |  1.74 | 44049.3 | Job 144 |
| 44055   | 17.8  | 44072.8 | Job 145 |
| 44117.2 | 15.38 | 44132.6 | Job 146 |
| 44115.5 | 18.45 | 44133.9 | Job 147 |
| 43968.6 |  1.61 | 43970.2 | Job 148 |
| 44111.8 | 12.8  | 44124.6 | Job 149 |
| 43848.2 | 18.83 | 43867   | Job 150 |
| 44009.9 |  2.65 | 44012.6 | Job 151 |
| 44147.8 |  7.06 | 44154.8 | Job 152 |
| 44022.2 |  0.08 | 44022.3 | Job 153 |
| 43893.7 |  7.02 | 43900.7 | Job 154 |
| 44009.5 | 19.68 | 44029.2 | Job 155 |
| 43904.3 | 18.03 | 43922.4 | Job 156 |
| 44128.4 | 11.93 | 44140.3 | Job 157 |
| 43976.9 |  0.31 | 43977.2 | Job 158 |
| 44180   | 18.42 | 44198.5 | Job 159 |
| 43840.8 | 12.21 | 43853   | Job 160 |
| 44149.6 |  4.6  | 44154.2 | Job 161 |
| 43886.1 |  4.64 | 43890.7 | Job 162 |
| 43944.1 | 10.66 | 43954.8 | Job 163 |
| 44081.3 |  0.63 | 44081.9 | Job 164 |
| 43994.3 | 15.62 | 44009.9 | Job 165 |
| 43981   |  4.18 | 43985.2 | Job 166 |
| 43849.1 | 13.66 | 43862.7 | Job 167 |
| 44070.2 |  1.41 | 44071.7 | Job 168 |
| 44159   | 13.04 | 44172   | Job 169 |
| 44116.6 | 10.83 | 44127.5 | Job 170 |
| 43850   |  2.15 | 43852.1 | Job 171 |
| 44180   |  1.2  | 44181.2 | Job 172 |
| 43949.8 |  4.5  | 43954.2 | Job 173 |
| 44060.5 | 16.93 | 44077.4 | Job 174 |
| 43927.4 | 13.89 | 43941.3 | Job 175 |
| 44155.4 | 12.9  | 44168.3 | Job 176 |
| 43841.6 | 15.99 | 43857.6 | Job 177 |
| 43972.7 |  1.35 | 43974   | Job 178 |
| 44125.5 | 16.69 | 44142.2 | Job 179 |
| 43995.5 |  3.57 | 43999.1 | Job 180 |
| 44072.1 | 14.02 | 44086.1 | Job 181 |
| 43959.7 | 19.63 | 43979.3 | Job 182 |
| 44108.6 |  6.98 | 44115.5 | Job 183 |
| 43842.2 |  0.95 | 43843.2 | Job 184 |
| 44164.5 |  9.34 | 44173.8 | Job 185 |
| 43954.5 | 17.23 | 43971.7 | Job 186 |
| 43961.5 | 19.78 | 43981.3 | Job 187 |
| 43901.5 |  7.26 | 43908.8 | Job 188 |
| 43832.3 | 14.16 | 43846.4 | Job 189 |
| 43948.5 | 18.97 | 43967.5 | Job 190 |
| 44161.6 |  8.83 | 44170.4 | Job 191 |
| 44118.2 |  6.95 | 44125.1 | Job 192 |
| 44167.7 | 18.38 | 44186.1 | Job 193 |
| 43935.4 | 12.84 | 43948.2 | Job 194 |
| 44104.8 | 13.73 | 44118.5 | Job 195 |
| 44086.4 | 12.9  | 44099.3 | Job 196 |
| 44141.7 |  4.93 | 44146.7 | Job 197 |
| 43963.7 | 17    | 43980.7 | Job 198 |
| 44128.6 | 18.09 | 44146.7 | Job 199 |
| 44081.5 | 11.94 | 44093.4 | Job 200 |



label: C=B+A
labeled_formulas: C=B+A
output: {"Arithmetic-Relationship": ["C=B+A"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_306651___xlsx_bfa8c8415917cdf850cf234cdc5485c587110ed2.xlsx___line_434