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 |
|:--------------------------------------------------------------------------------------------------------------------------------------|----:|------:|----:|----:|-------:|----:|----:|----:|----:|
| /tools/device-display/tablet.html                                                                                                     |  11 |   481 |   0 |   0 |  16.08 |   2 |  15 |   1 |   0 |
| /tools/device-display/phone.html                                                                                                      |  13 |   357 |   0 |   0 |  55.38 |   2 |   4 |   0 |   1 |
| /tools/device-display/desk.html                                                                                                       |   5 |   347 |   0 |   0 |  13.12 |   3 |   7 |   0 |   1 |
| /subscribe/                                                                                                                           |   1 |    13 |   0 |   0 |   6    |   0 |   1 |   0 |   0 |
| /site-map/                                                                                                                            |   3 |  1194 |   0 |   0 |  35.92 |   0 |   1 |   1 |   0 |
| /services/website-review-and-competitive-analysis-html/                                                                               |  38 |  2653 |   0 |   0 |  90.1  |   0 |   0 |   0 |   1 |
| /services/web-content-marketing-strategy/                                                                                             |  25 |  1076 |   0 |   0 |  70.2  |   1 |   2 |   0 |   0 |
| /services/search-engine-optimization/                                                                                                 |  62 |  3097 |   0 |   0 |  76.35 |   5 |   8 |   6 |   0 |
| /services/search-engine-advertising/                                                                                                  | 106 |  2062 |   0 |   0 |  60.18 |   7 |   9 |   4 |  11 |
| /services/pricing-information/                                                                                                        |  36 |  2877 |   0 |   0 |  54.42 |   0 |   2 |   0 |   9 |
| /services/increase-website-lead-generation/                                                                                           |  73 |  2167 |   0 |   0 |  60.09 |   7 |   9 |   3 |   7 |
| /services/building-search-engine-link-popularity/                                                                                     |  35 |  1105 |   0 |   0 |  45.16 |   0 |   8 |   6 |   1 |
| /services/b2b-marketing-get-social/                                                                                                   |  17 |   513 |   0 |   0 |  66.71 |   0 |   0 |   0 |   3 |
| /services/b2b-account-based-marketing/                                                                                                |  47 |  1942 |   0 |   0 |  56.24 |   2 |   4 |  12 |   5 |
| /services/                                                                                                                            |  34 |  3067 |   0 |   0 |  65.23 |   4 |  13 |   0 |   1 |
| /pdfs/TTW-Video-Optimization-Best-Practices-Oct-2015.pdf                                                                              |  44 |   849 |   0 |   0 |  64.36 |   1 |   2 |   0 |   0 |
| /pdfs/ToTheWeb-Why-Search-Optimize-PDFs-SEO-PDFs-Increase-Downloads.pdf                                                               |  13 |   139 |   0 |   0 |  67.27 |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-Site-Architecture-sitemap-example.pdf                                                                                  |  41 |   873 |   0 |   0 |  81.05 |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-SEO-PDFs-Search-Optimize-PDFs-to-Increase-Downloads-from-Search-Engines.pdf                                            |  20 |    71 |   0 |   0 |  73.45 |   0 |   0 |   0 |   1 |
| /pdfs/ToTheWeb-Sample-Relaunch-Content-Guidelines.pdf                                                                                 |  21 |   730 |   0 |   0 |  58.98 |   0 |   1 |   1 |   5 |
| /pdfs/ToTheWeb-Sample-Content-Document-Word-Template.docx                                                                             |   3 |     3 |   0 |   0 |  63    |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-PPC-Campaign%20Playbook-Guide-to-Successful-B2B-Marketing-Campaign-Launch-eBook.pdf                                    |   6 |   127 |   0 |   0 |  84.1  |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-Meru-Search-Optimization-PPC-Case-Study.pdf                                                                            |   5 |    23 |   0 |   0 |  73.37 |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-Keyword-Research-Selection-Implementation-Best-Practices-Guide.pdf                                                     | 116 |  5395 |   0 |   0 |  71.55 |   0 |   1 |   0 |   4 |
| /pdfs/totheweb-infographic-channels-smart-marketers-use-to-drive-b2b-leads.pdf                                                        |   1 |     1 |   0 |   0 |  32    |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-How-to-Create-Awesome-Blog-Posts-that-Generate-Traffic.pdf                                                             |   5 |    23 |   0 |   0 |  74.61 |   0 |   0 |   1 |   0 |
| /pdfs/totheweb-how-much-should-you-pay-for-a-b2b-ppc-lead.pdf                                                                         |  20 |   525 |   0 |   0 |  66.13 |   0 |   0 |   1 |   2 |
| /pdfs/ToTheWeb-GWMT-SEO-Tracking.xlsx                                                                                                 |  48 |   179 |   0 |   0 |  75.04 |   0 |   1 |   2 |   4 |
| /pdfs/ToTheWeb-Every-PDF-Deserves-a-Great-Title.pdf                                                                                   |   4 |     6 |   0 |   0 |  82.1  |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-Ensighten-PPC-Landing-Page-Optimization-Case-Study.pdf                                                                 |   2 |    28 |   0 |   0 |  76.76 |   0 |   0 |   0 |   0 |
| /pdfs/totheweb-data-driven-approach-to-fast-track-b2b-lead-generation.pdf                                                             |   2 |    38 |   0 |   0 |  82    |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb-Complete-Guide-to-Keyword-and-Search-Optimization-for-B2B-Lead-Generation.pdf                                          |  72 |  1617 |   0 |   0 |  69.09 |   0 |   3 |   1 |   2 |
| /pdfs/totheweb-9-quick-wins-to-instantly-boost-b2b-web-leads-sales.pdf                                                                |   1 |     2 |   0 |   0 |  27    |   0 |   0 |   0 |   1 |
| /pdfs/totheweb-2018-SEO-Myths-12-Common-SEO-Myths-Shattered.pdf                                                                       |  11 |   396 |   0 |   0 |  55.4  |   0 |   0 |   3 |   1 |
| /pdfs/ToTheWeb_Keyword-Research-Selection-for-Modern-SEO-infographic.pdf                                                              |   2 |    45 |   0 |   0 |  87.76 |   0 |   0 |   0 |   0 |
| /pdfs/ToTheWeb_Competitive_Research_PDF.pdf                                                                                           |   1 |    62 |   0 |   0 |  18.9  |   0 |   0 |   1 |   0 |
| /pdfs/Technical-SEO-Audit-10-Point-Checklist-to-Improve-Google-Search-Infographic.pdf                                                 |  20 |   213 |   0 |   0 |  79.33 |   0 |   0 |   0 |   0 |
| /pdfs/SCALIX_CaseStudy-ToTheWeb.pdf                                                                                                   |   2 |   332 |   0 |   0 |  76.26 |   0 |   0 |   0 |   0 |
| /pdfs/Omni-ID-CaseStudy-w-Logo.pdf                                                                                                    |   1 |   275 |   0 |   0 |  90.46 |   0 |   0 |   0 |   0 |
| /pdfs/MDV_CaseStudy-ToTheWeb.pdf                                                                                                      |   5 |   294 |   0 |   0 |  40.37 |   0 |   1 |   1 |   0 |
| /pdfs/LitePoint_CaseStudy-ToTheWeb.pdf                                                                                                |   1 |   275 |   0 |   0 |  72.22 |   0 |   0 |   0 |   0 |
| /pdfs/How_Search_Engines_Work.pdf                                                                                                     |  44 |   370 |   0 |   0 |  64.47 |   0 |   0 |   3 |   3 |
| /pdfs/Digital_Divide_White_Paper.pdf                                                                                                  |   2 |   275 |   0 |   0 |  67.87 |   0 |   0 |   0 |   0 |
| /pdfs/10-Minute-B2B-Website%20Make-Overs-Content-Marketing-MeetingUP-Apr%2026-2017-For-Event-Distribution.pdf                         |   1 |    28 |   0 |   0 |  44.79 |   0 |   0 |   0 |   0 |
| /our_clients/case-studies/case-studies-3/                                                                                             |   1 |   133 |   0 |   0 |  63.03 |   0 |   0 |   0 |   0 |
| /our_clients/case-studies/case-studies-2/                                                                                             |   7 |   310 |   0 |   0 |  42.49 |   0 |   0 |   3 |   1 |
| /our_clients/case-studies/case-studies-1/                                                                                             |   1 |   275 |   0 |   0 |  63.9  |   0 |   0 |   0 |   0 |
| /our_clients/case-studies/                                                                                                            |  54 |  4332 |   0 |   0 |  67.99 |   1 |   2 |   5 |   2 |
| /our_clients/all-clients/                                                                                                             |  12 |   569 |   0 |   0 |  52.79 |   0 |   3 |   1 |   0 |
| /our_clients/                                                                                                                         |   9 |  1255 |   0 |   0 |  22.09 |   4 |   7 |   0 |   0 |
| /learning_center/website-stats-analysis/                                                                                              |  32 |   523 |   0 |   0 |  73.73 |   0 |   0 |   1 |   3 |
| /learning_center/website-search-strategy/                                                                                             |  87 |  4910 |   0 |   0 |  74.11 |   0 |   4 |   6 |  10 |
| /learning_center/website-evaluation/                                                                                                  |  17 |   815 |   0 |   0 |  39.15 |   1 |   3 |   1 |   3 |
| /learning_center/website-content-creation/                                                                                            |  23 |  2296 |   0 |   0 |  76.48 |   0 |   1 |   2 |   0 |
| /learning_center/tool-calculate-ad-campaign-lead-cost-return-ad-spend-roas-cost-per-sale/                                             |  54 |  2080 |   0 |   0 |  74.7  |   0 |   3 |   1 |   1 |
| /learning_center/search-engine-marketing/                                                                                             |   1 |   328 |   0 |   0 |  29.68 |   0 |   0 |   0 |   1 |
| /learning_center/search-engine-guide/                                                                                                 |  21 |   652 |   0 |   0 |  77.63 |   0 |   0 |   0 |   0 |
| /learning_center/search-engine-evaluation/                                                                                            |   3 |   339 |   0 |   0 |  72.51 |   0 |   0 |   0 |   0 |
| /learning_center/project-life-cycle-guide/                                                                                            |   9 |   348 |   0 |   0 |  57.58 |   0 |   1 |   2 |   1 |
| /learning_center/improve-lead-generation/                                                                                             |   5 |   413 |   0 |   0 |  77.81 |   0 |   0 |   0 |   0 |
| /learning_center/defining-goals-for-lead-generation/                                                                                  |  11 |   416 |   0 |   0 |  67.5  |   0 |   0 |   0 |   2 |
| /learning_center/defend-brand-name/                                                                                                   |  22 |  1266 |   0 |   0 |  58.12 |   0 |   0 |   2 |   2 |
| /learning_center/campaign-tracking-url-builder/                                                                                       |  57 |  1354 |   0 |   0 |  62.65 |   0 |   6 |   7 |   3 |
| /blog/sem-ppc-paid-advertising/how-much-should-you-pay-for-a-ppc-lead/                                                                |  12 |   341 |   0 |   0 | 100.27 |   0 |   0 |   0 |   0 |
| /blog/page/4/                                                                                                                         |   1 |   266 |   0 |   0 |  12.95 |   0 |   0 |   1 |   0 |
| /blog/page/3/                                                                                                                         |   1 |   162 |   0 |   0 |  18.96 |   0 |   0 |   1 |   0 |
| /blog/page/2/                                                                                                                         |   1 |   364 |   0 |   0 |  16.16 |   0 |   0 |   1 |   0 |
| /blog/category/sem-ppc-paid-advertising/                                                                                              |   1 |    92 |   0 |   0 |  63.54 |   0 |   0 |   0 |   0 |
| /blog/category/b2b-organic-search-marketing-technical-seo/                                                                            |   3 |   128 |   0 |   0 |  44.57 |   0 |   0 |   0 |   0 |
| /blog/category/b2b-lead-generation-strategy/                                                                                          |   1 |   100 |   0 |   0 |  62    |   0 |   0 |   0 |   0 |
| /blog/category/b2b-content-marketing/                                                                                                 |   4 |   335 |   0 |   0 |  33.37 |   0 |   0 |   0 |   3 |
| /blog/b2b-website-usability/noahscom-should-learn-how-to-serve-bagels-to-the-online-visitor/                                          |   5 |   299 |   0 |   0 |  58.07 |   0 |   0 |   0 |   1 |
| /blog/b2b-website-usability/increase-website-engagement-with-more-prominent-internal-onsite-search-field/                             |  92 |  3200 |   0 |   0 |  58.06 |   0 |   0 |   9 |  15 |
| /blog/b2b-website-usability/i-use-crazyegg-heat-mapping-software-for-all-my-clients/                                                  |   4 |   284 |   0 |   0 |  82.29 |   0 |   0 |   0 |   0 |
| /blog/b2b-organic-search-marketing-technical-seo/what-new-google-privacy-policy-changes-really-mean/                                  |   4 |   278 |   0 |   0 |  71.66 |   0 |   0 |   0 |   0 |
| /blog/b2b-organic-search-marketing-technical-seo/seo-best-practices-for-optimizing-pdf-files/                                         |  82 |  2876 |   0 |   0 |  70.56 |   0 |   2 |   9 |   8 |
| /blog/b2b-organic-search-marketing-technical-seo/keyword-research-simplified-free-tools-to-jumpstart-the-keyword-research-process/    |  60 |   459 |   0 |   0 |  83.35 |   1 |   4 |   1 |   0 |
| /blog/b2b-organic-search-marketing-technical-seo/is-your-site-suffering-from-the-most-common-technical-seo-problems/                  |  25 |   251 |   0 |   0 |  98.42 |   0 |   0 |   1 |   0 |
| /blog/b2b-organic-search-marketing-technical-seo/googles-top-10-best-practices-for-mobile-landing-pages-lead-conversion/              |  38 |   750 |   0 |   0 |  81.89 |   0 |   0 |   0 |   0 |
| /blog/b2b-organic-search-marketing-technical-seo/getting-high-on-google-search-the-3-secrets-to-success-in-organic-rankings/          |  14 |   111 |   0 |   0 |  76.18 |   0 |   1 |   0 |   1 |
| /blog/b2b-organic-search-marketing-technical-seo/get-high-on-google-the-foundation-of-search-engine-optimization-seo-and-keyword-use/ |   3 |     3 |   0 |   0 |  89    |   0 |   0 |   0 |   0 |
| /blog/b2b-organic-search-marketing-technical-seo/everything-seo-starts-smart-keyword-selection-best-practice-guide-modern-seo/        | 115 |  1550 |   0 |   0 |  82.12 |   1 |   8 |   1 |   7 |
| /blog/b2b-organic-search-marketing-technical-seo/everyone-should-be-using-google-webmaster-tools/                                     |  13 |   344 |   0 |   0 |  62.52 |   0 |   0 |   0 |   1 |
| /blog/b2b-organic-search-marketing-technical-seo/build-your-own-seo-reporting-dashboard-for-clients-management/                       | 424 | 31861 |   0 |   0 |  86.01 |   0 |   1 |  12 |  21 |
| /blog/b2b-organic-search-marketing-technical-seo/b2b-social-media-a-review-of-applications-that-can-be-measured/                      |   1 |    23 |   0 |   0 |  92.35 |   0 |   0 |   0 |   0 |
| /blog/b2b-organic-search-marketing-technical-seo/5-steps-to-optimize-images-for-google-image-search/                                  |   5 |   234 |   0 |   0 |  87.74 |   0 |   0 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/which-media-channels-do-smart-b2b-marketers-use-to-drive-leads/                                    |   6 |   297 |   0 |   0 | 110.86 |   0 |   0 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/top-ten-tools-to-run-our-web-agency/                                                               |   1 |   275 |   0 |   0 |  79.48 |   0 |   0 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/ten-tips-get-31-percent-more-youtube-video-views-in-3-months-a-case-study/                         |  16 |   144 |   0 |   0 |  83.29 |   0 |   0 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/ten-quick-wins-to-immediately-improve-your-b2b-website-lead-generation-opportunities/              |   8 |    26 |   0 |   0 |  84.41 |   0 |   0 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/simple-data-driven-strategies-fast-track-lead-generation/                                          |   8 |   304 |   0 |   0 |  83.67 |   0 |   1 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/google-survey-suggests-itprofessionals-will-watch-video-during-purchase-process/                   |   3 |   281 |   0 |   0 |  91.62 |   0 |   0 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/b2b-lead-generation-the-power-of-online-tools-to-drive-targeted-web-traffic-year-over-year/        |  18 |   233 |   0 |   0 | 112.87 |   0 |   0 |   0 |   0 |
| /blog/b2b-lead-generation-strategy/3-common-mistakes-that-slash-website-lead-generation/                                              |   1 |   275 |   0 |   0 |  80.48 |   0 |   0 |   0 |   0 |
| /blog/b2b-content-marketing/wikipedia-part-one-what-wikipedia-can-and-cannot-do-for-your-business/                                    |  22 |   340 |   0 |   0 |  55.55 |   0 |   2 |   0 |   2 |
| /blog/b2b-content-marketing/wikipedia-part-2-how-to-get-your-company-onto-wikipedia/                                                  |  21 |   313 |   0 |   0 |  69.62 |   0 |   1 |   1 |   0 |
| /blog/b2b-content-marketing/quick-wins-what-makes-a-great-b2b-blog-post/                                                              |   6 |   315 |   0 |   0 |  87.99 |   0 |   0 |   0 |   0 |
| /blog/b2b-content-marketing/content-marketing-seo-strategy/                                                                           |   2 |   281 |   0 |   0 | 119.33 |   0 |   0 |   0 |   0 |
| /blog/2019/                                                                                                                           |   1 |   986 |   0 |   0 |   9.04 |   0 |   1 |   0 |   0 |
| /blog/2018/04/                                                                                                                        |   1 |   367 |   0 |   0 |  12.44 |   0 |   0 |   1 |   0 |
| /blog/2016/                                                                                                                           |   1 |   101 |   0 |   0 |   9.68 |   0 |   1 |   0 |   0 |
| /blog/2015/                                                                                                                           |   1 |   462 |   0 |   0 |   8.63 |   0 |   1 |   0 |   0 |
| /blog/2013/07/                                                                                                                        |   1 |     5 |   0 |   0 |  14    |   0 |   0 |   1 |   0 |
| /blog/2013/02/                                                                                                                        |   1 |   346 |   0 |   0 |  15.22 |   0 |   0 |   1 |   0 |
| /blog/2013/                                                                                                                           |   1 |   263 |   0 |   0 |   6    |   0 |   1 |   0 |   0 |
| /blog/2012/03/                                                                                                                        |   1 |   334 |   0 |   0 |  20.76 |   0 |   0 |   1 |   0 |
| /blog/2012/                                                                                                                           |   1 |   222 |   0 |   0 |   6.04 |   0 |   1 |   0 |   0 |
| /blog/2009/03/                                                                                                                        |   1 |   361 |   0 |   0 |  17.2  |   0 |   0 |   1 |   0 |
| /blog/2009/01/                                                                                                                        |   1 |    10 |   0 |   0 |  16.9  |   0 |   0 |   1 |   0 |
| /blog/2009/                                                                                                                           |   1 |   275 |   0 |   0 |   7.99 |   0 |   1 |   0 |   0 |
| /blog/2008/                                                                                                                           |   1 |   400 |   0 |   0 |   6.03 |   0 |   1 |   0 |   0 |
| /about-us/search-engine-ethical-practices/                                                                                            |  22 |  1320 |   0 |   0 |  62.18 |   0 |   0 |   3 |   6 |
| /about-us/rosemary-brisco/                                                                                                            |   8 |   356 |   0 |   0 |  54.48 |   0 |   1 |   0 |   1 |
| /about-us/michele-grey/                                                                                                               |   2 |   303 |   0 |   0 |  20.45 |   0 |   0 |   1 |   1 |
| /about-us/michael-menduno/                                                                                                            |   3 |   352 |   0 |   0 |  30.69 |   0 |   1 |   1 |   1 |
| /about-us/john-mcaulay/                                                                                                               |   2 |   353 |   0 |   0 |  16.48 |   0 |   3 |   0 |   0 |
| /about-us/john-koh/                                                                                                                   |   7 |   460 |   0 |   0 |  37.51 |   0 |   3 |   0 |   1 |
| /about-us/dirk-frandsen/                                                                                                              |   4 |   334 |   0 |   0 |  36.32 |   0 |   1 |   0 |   1 |
| /about-us/contact-us/                                                                                                                 |   2 |   332 |   0 |   0 |  56.64 |   0 |   0 |   0 |   1 |
| /about-us/chad-klingensmith/                                                                                                          |   2 |   391 |   0 |   0 |  70.23 |   0 |   0 |   0 |   0 |
| /about-us/brandon-loya/                                                                                                               |   6 |   457 |   0 |   0 |  78.43 |   0 |   0 |   0 |   0 |



label: E=D/C
labeled_formulas: E=D/C
E=B*D
E=D*F
E=D*G
E=D*H
E=D*I
E=D*J
E=(B+C)*D
E=(B*D)*F
E=(B*D)*G
E=(B*D)*H
E=(B*D)*I
E=(B*D)*J
E=(C*D)*F
D=(C+G)*E
D=(C*E)*H
D=(C+I)*E
D=(C+J)*E
E=(D*F)*G
E=(D*F)*H
E=(D*F)*I
E=(D*F)*J
E=(D*G)*H
E=(D*G)*I
E=(D*G)*J
E=(D*H)*I
E=(D*H)*J
E=(D*I)*J
output: {"Arithmetic-Relationship": ["E=D/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_133063___xlsx_d3470f417ad1c1d5e9f1786c9d1f21f3f084f628.xlsx___line_760