{ "category": "Engineering functions", "display_name": "ERF.PRECISE", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.ERF.PRECISE", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "20527", "?" ], "larger_numeric": 0, "last_bit": 19, "matched": 618418, "other_mismatch": 0, "refused": 0, "rows": 618437, "unread": 0, "worst_ulp": 2 }, "detail": "Everything else matches (618,437 in the answer bank and 3 workbook cells). Last-bit means a finite number within 16 ULP of Excel's.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "close", "state_label": "Close: last-bit deviations remain", "summary": "Close: 20 of 618,440 recorded answers differ in the last bits, worst 2 ULP", "workbook_corpus": { "cells": 3, "last_bit": 1, "matched": 2, "worst_ulp": 1 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L313-L316" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_x87_add", "ported/excel_numeric::excel_x87_sub", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_div", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::add", "ported/excel_numeric/x87::sub", "ported/excel_numeric/x87::div", "ported/normal_dist_common::stored_horner", "ported/normal_dist_common::erf_approx", "ported/normal_dist_common::erfc_upper", "ported/special_dist_family::erf_precise_kernel" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L313-L316", "state": "close", "suite": null, "summary": "Close: 20 of 618,440 recorded answers differ in the last bits, worst 2 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.ERF.PRECISE.json", "name": "ERF.PRECISE", "notes": [ { "basis": "All 618,225 recorded ERF.PRECISE rows with |x| < 0.5 match; they were only scored, never used to read the coefficients, and ERFC and ERFC.PRECISE match every recorded row in that range. Two fresh sets of 60,000 random doubles below 0.5 (Excel build 20527) match 59,996 and 59,982; the second was asked after the constants were fixed, and 17 of its 18 misses are in [0.25, 0.5). With every step stored, 223 of 38,000 rows at 19 sites stay unexplained; the other store placements leave 568 to 1,244. 2,000 consecutive doubles below 0.5 match 1,988, and 2,000 from 0.5 up match 858, chance level, which places the cut.", "documentation": null, "evidence": [ { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": null, "note": "research write-up: how the rational was read, the checks, the final constants", "path": "content/notes/evidence/2026-11-04/erf-EVIDENCE-round3.md", "repository": "ExcelFunctionsHandbook" }, { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": null, "note": "earlier round: the structure, the refutation of Cody, the edge bisection", "path": "content/notes/evidence/2026-11-04/erf-EVIDENCE-round2.md", "repository": "ExcelFunctionsHandbook" }, { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": null, "note": "first write-up; its Cody attribution is withdrawn", "path": "content/notes/evidence/2026-11-04/erf-EVIDENCE.md", "repository": "ExcelFunctionsHandbook" }, { "commit": "36a7f3d7aa607bcea8b75bd65fb352beec657817", "locator": "erf_approx, ERF_N, ERF_D", "note": "the rational in the product; the commit message carries the row counts", "path": "crates/calc-func/src/ported/normal_dist_common.rs", "repository": "DnaCalc" } ], "functions": [ "FUNC.ERF", "FUNC.ERF.PRECISE", "FUNC.ERFC", "FUNC.ERFC.PRECISE", "FUNC.GAUSS" ], "inferred": "That the legacy ERF(x) shares this body is inferred: ERF.PRECISE, ERFC and ERFC.PRECISE rows were scored in full, and for ERF itself the record holds only nine non-zero single-argument inputs below 0.5 (build 19929), all equal to the rational.", "kind": "bit-matching-detail", "note_id": "FN-ERF.PRECISE-001", "open": [ "The last bits of the coefficients of order 3 and above. Orders 0 and 1 are exact: one unit off in a linear term breaks 500 to 1,100 of 160,000 rows. Order 2 sits at the minimum of the same scan. Higher orders are good to the level that shows, about 0.15% of rows above 0.25.", "The source table. Hart's ERF tables remain unchecked.", "Which branch owns x = 0.5: there the rational and a correctly rounded erf give the same bits.", "Subnormal arguments: Excel reads a subnormal written to a cell back as 0, so they cannot be asked that way." ], "recorded_on": "2026-11-04", "repros": [ { "call": "ERF.PRECISE(0.4524739583333333)", "correct": { "bits": "0x3fde939a879e86f3", "display": "0.4777590107351976", "how": "mpmath erf at 800 bits from the binary64 input, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x3fde939a879e86f6", "display": "0.4777590107351978", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x3fdcf55555555555", "display": "0.4524739583333333", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 1219, key ERF.PRECISE|0x3fdcf55555555555", "note": null, "path": "cache/oracle/build-20131/ERF.PRECISE.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ERF.PRECISE(9.094947017729282e-13)", "correct": { "bits": "0x3d720dd750429b6d", "display": "1.0262548740643184e-12", "how": "mpmath erf at 800 bits from the binary64 input, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x3d720dd750429b6e", "display": "1.0262548740643186e-12", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x3d70000000000000", "display": "9.094947017729282e-13", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 2115, key ERF.PRECISE|0x3d70000000000000", "note": null, "path": "cache/oracle/build-20131/ERF.PRECISE.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ERF.PRECISE(9.999999999999998e-11)", "correct": { "bits": "0x3ddf044332d6815f", "display": "1.1283791670955123e-10", "how": "mpmath erf at 800 bits from the binary64 input, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x3ddf044332d68160", "display": "1.1283791670955125e-10", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x3ddb7cdfd9d7bdb9", "display": "9.999999999999998e-11", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 209, key ERF.PRECISE|0x3ddb7cdfd9d7bdb9", "note": null, "path": "cache/oracle/build-20131/ERF.PRECISE.jsonl.gz", "repository": "CalcFunc-Evidence" } } ], "schema": "efh.function-note/v1", "statement": "With RN(v) meaning v rounded to 64 bits on the x87 unit and then stored to binary64, ERF.PRECISE for |x| < 0.5 is x*N(t)/D(t) with t = RN(x*x), p = RN(x*N), y = RN(p/D), and N and D Horner sums in t in which every product and every sum is RN. N has degree 4 and D degree 5, and the coefficients read off Excel's answers, order 0 upward, are N: 0x3ff1df5e70c7956b, 0x3fc201d8627a7d2c, 0x3fa6f289d165b303, 0x3f5d93a5813e372c, 0x3f2932767df264b2; D: 0x3fefada15778ece6, 0x3fdd191aca8d2499, 0x3fb79f85ba68803e, 0x3f856de5da86af12, 0x3f4609751b5b6488, 0x3ef4f20a473a5ab0. The rational stops at 0.5 itself. It equals erf to a flat 9E-17 up to 0.5, and its error climbs at once beyond, so 0.5 is its design interval and not Cody's 0.46875. No published table has been matched: Cody's 1969 rational is refuted by its linear terms, and Cephes has the same shape with different ratios. Evidence record EV-DIST-0026, which predates this note, attributes ERF.PRECISE and ERFC.PRECISE to the a < 1 branches of the NSWC GRATIO routine and says no coefficient table exists; below 0.5 this note replaces that attribution. Because every step rounds, answers need not be correctly rounded: of the 654 recorded rows of build 20131 in [0.25, 0.5), 400 differ from the correctly rounded erf, by up to 3 units, and small arguments can be 1 unit high, as below. ERFC and ERFC.PRECISE below 0.5 are 1 less this value, and GAUSS at tiny arguments takes half of it at its stored z/sqrt(2).", "status": "measured", "title": "Below 0.5, ERF is a stored (4, 5) rational from a table not yet identified" } ], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[ERFC](FUNC.ERFC.md) computes the complementary tail directly. [NORM.S.DIST](FUNC.NORM.S.DIST.md) provides a standard-normal CDF with a different argument transformation.\n\n\n\n\n", "how-to-implement": "\nFor normal `abs(x)<0.5`, use `R(op)=RN53(RN64(op))`: round each operation to a 64-bit significand, then store to binary64. Decode the following hexadecimal strings as **binary64 bit patterns**, not integers converted to floating-point values.\n\n| Power | Numerator coefficient | Denominator coefficient |\n|---:|---|---|\n| 0 | `3ff1df5e70c7956b` | `3fefada15778ece6` |\n| 1 | `3fc201d8627a7d2c` | `3fdd191aca8d2499` |\n| 2 | `3fa6f289d165b303` | `3fb79f85ba68803e` |\n| 3 | `3f5d93a5813e372c` | `3f856de5da86af12` |\n| 4 | `3f2932767df264b2` | `3f4609751b5b6488` |\n| 5 | — | `3ef4f20a473a5ab0` |\n\n1. Store `t=R(x*x)`.\n2. Evaluate each polynomial by Horner, beginning with its highest-power coefficient. Every step is `v=R(R(v*t)+coefficient)`. Keep the multiplication store separate from the addition store; do not use FMA.\n3. Store `p=R(x*N)` and return `R(p/D)`.\n\nWorked `x=0.25`: `t=0.0625`; the staged coefficient evaluation gives `N=1.126001525484713`, `D=1.018724202200851`, `p=0.2815003813711783`, and result `0.276326390168237` (`0x3fd1af54e232d60a`). These are outputs of the stated reconstruction, with all input coefficients retained above.\n\nThe degrees and stores are supported by discriminating readings. The final bits of several higher-order coefficients remain open: the fixed c14 model matched 59,982 of a fresh 60,000-row holdout. Do not extrapolate this ratio above `abs(x)=0.5`. For larger magnitudes the current code uses the signed stored complement `copysign(R(1-upper_ERFC(abs(x))),x)`. At exactly plus or minus 0.5 it instead retains its runtime ERF fallback. The fixed ratio and the mathematical value agree in bits at the positive half point, so that single recorded answer does not identify which private branch owns it. Zero and nonnormal inputs also retain the fallback and their separate transfer/publication rules. The upper ERFC exponential stage is measured, but its remaining rational factor is a stand-in. No published Handbook suite establishes a whole-domain equality claim.\n\n\n", "quirks": "\nNonnumeric arguments give `#VALUE!`. The PRECISE name does not imply correctly rounded results on every input. The measured below-half stage and the unresolved upper stage need separate treatment. Subnormal inputs transferred to worksheet cells can be read back as zero, so the input route is part of a useful reproduction.\n\n\n", "sources": "\n- [Microsoft: ERF.PRECISE function](https://support.microsoft.com/en-us/excel/functions/erf-precise-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/normal_dist_common.rs); implementation steps and the limits identified in the text.\n- [ERF research and holdout results](../notes/evidence/2026-11-04/erf-EVIDENCE-round3.md).\n\n", "try-it": "\n`=ERF.PRECISE(0.25)` is about `0.276326390168237`. `=ERF.PRECISE(-0.25)` has the negative value.\n\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 19929 | Windows, bitness not recorded, CPU not recorded | 42 |\n| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 409,213 |\n\n- XC-ERF.PRECISE-001: build 19929 versus build 20131; 1 same-input pairs, 0 differing answers. Compared axes: excel-build. Numeric answers were compared by their recorded binary64 bits; other answers by typed value.\n\nAgreement on these compared inputs does not establish agreement on unmeasured inputs.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ERF.PRECISE.json).\n\nRetained controls from the indexed captures:\n\n| Build and recorded CPU | Captured call or arguments | Excel result |\n|---|---|---|\n| 19929, CPU not recorded | [`=ERF.PRECISE(0)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/broad-scalar-cycle-011-cellref/comparisons/excel_sample_comparisons.jsonl.gz) | `0.0` (`0x0000000000000000`) |\n| 20131, AMD Ryzen 7 4800H with Radeon Graphics | [`ERF.PRECISE(1)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/oracle/build-20131/ERF.PRECISE.jsonl.gz) | `0.8427007929497149` (`0x3feaf767a741088b`) |\n\nThese are earlier recorded answers, not new Excel runs or an additional cross-build comparison. The function JSON retains each source locator, exact argument bits where available, and input-route status. Call notation does not imply that captured binary64 values were entered as decimal formula literals.", "what-it-does": "\n`ERF.PRECISE(x)` returns the normalised integral of `exp(-t*t)` from zero to x. The normalisation factor is `2/sqrt(pi)`. It is odd: negating x negates the mathematical result.\n\n\n" }, "signature": { "display": "ERF.PRECISE(x)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 1, "min": 1 }, "category": "Engineering functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Error function integrated from 0 to x", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the error function", "microsoft_url": "https://support.microsoft.com/en-us/office/erf-precise-function-9a349593-705c-4278-9a98-e4122831a8e0" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "ERF.PRECISE" }, { "locale": "bg-BG", "name": "ERF.PRECISE" }, { "locale": "cs-CZ", "name": "ERF.PRECISE" }, { "locale": "da-DK", "name": "ERF.PRECISE" }, { "locale": "de-DE", "name": "ERF.PRECISE" }, { "locale": "el-GR", "name": "ERF.PRECISE" }, { "locale": "en-AU", "name": "ERF.PRECISE" }, { "locale": "en-GB", "name": "ERF.PRECISE" }, { "locale": "en-US", "name": "ERF.PRECISE" }, { "locale": "es-ES", "name": "FUN.ERROR.EXACTO" }, { "locale": "et-EE", "name": "ERF.PRECISE" }, { "locale": "fi-FI", "name": "VIRHEFUNKTIO.TARKKA" }, { "locale": "fr-FR", "name": "ERF.PRECIS*" }, { "locale": "he-IL", "name": "ERF.PRECISE" }, { "locale": "hr-HR", "name": "ERF.PRECISE" }, { "locale": "hu-HU", "name": "HIBAF.PONTOS" }, { "locale": "id-ID", "name": "ERF.PRECISE" }, { "locale": "it-IT", "name": "ERF.PRECISE" }, { "locale": "ja-JP", "name": "ERF.PRECISE" }, { "locale": "ko-KR", "name": "ERF.PRECISE" }, { "locale": "lt-LT", "name": "ERF.PRECISE" }, { "locale": "lv-LV", "name": "ERF.PRECISE" }, { "locale": "nb-NO", "name": "FEILF.PRESIS" }, { "locale": "nl-NL", "name": "FOUTFUNCTIE.NAUWKEURIG" }, { "locale": "pl-PL", "name": "FUNKCJA.BŁ.DOKŁ" }, { "locale": "pt-BR", "name": "ERF.PRECISE" }, { "locale": "pt-PT", "name": "FUNCERRO.PRECISO" }, { "locale": "ro-RO", "name": "ERF.PRECISE" }, { "locale": "ru-RU", "name": "ФОШ.ТОЧН" }, { "locale": "sk-SK", "name": "ERF.PRECISE" }, { "locale": "sl-SI", "name": "ERF.PRECISE" }, { "locale": "sr-Latn-RS", "name": "ERF.PRECISE" }, { "locale": "sv-SE", "name": "FELF.EXAKT" }, { "locale": "th-TH", "name": "ERF.PRECISE" }, { "locale": "tr-TR", "name": "HATAİŞLEV.DUYARLI" }, { "locale": "uk-UA", "name": "ERF.PRECISE" }, { "locale": "vi-VN", "name": "ERF.PRECISE" }, { "locale": "zh-CN", "name": "ERF.PRECISE" }, { "locale": "zh-HK", "name": "ERF.PRECISE" }, { "locale": "zh-TW", "name": "ERF.PRECISE" } ], "signature": { "display": "ERF.PRECISE(x)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "ERF.PRECISE", "version_marker": null, "xlcall": { "code": "543", "symbol": "xlfErf_precise" } }, "microsoft": "https://support.microsoft.com/en-us/office/erf-precise-function-9a349593-705c-4278-9a98-e4122831a8e0" }, "try_it": { "formula": "=ERF.PRECISE(0.25)" }, "url": "https://handbook.dnacalc.com/functions/ERF.PRECISE.html", "variants": [], "versions": [ { "behaviour": "ERF.PRECISE(0.4524739583333333) returned 0.4777590107351978 (0x3fde939a879e86f6). ERF.PRECISE(9.094947017729282e-13) returned 1.0262548740643186e-12 (0x3d720dd750429b6e). 1 further recorded control is attached. Inputs were supplied through cells using Value2. These are controls from this environment, not a same-input comparison with another build.", "excel_build": "16.0 build 20131", "observations": [ { "call": "ERF.PRECISE(0.4524739583333333)", "excel": { "bits": "0x3fde939a879e86f6", "display": "0.4777590107351978", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x3fdcf55555555555", "display": "0.4524739583333333", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H" }, { "call": "ERF.PRECISE(9.094947017729282e-13)", "excel": { "bits": "0x3d720dd750429b6e", "display": "1.0262548740643186e-12", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x3d70000000000000", "display": "9.094947017729282e-13", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H" }, { "call": "ERF.PRECISE(9.999999999999998e-11)", "excel": { "bits": "0x3ddf044332d68160", "display": "1.1283791670955125e-10", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x3ddb7cdfd9d7bdb9", "display": "9.999999999999998e-11", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H" } ], "platform": null, "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-ERF.PRECISE-001.json" ] }, { "behaviour": "42 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build. Retained control =ERF.PRECISE(0) returned 0.0 (0x0000000000000000). The selected archive row does not record its input plumbing; no input route is inferred.", "excel_build": "16.0 build 19929", "observations": [ { "call": "=ERF.PRECISE(0)", "excel": { "bits": "0x0000000000000000", "display": "0.0", "kind": "number" }, "input_route": "not-recorded", "inputs": [], "recorded_in": "Excel 16.0 build 19929, Windows, bitness not recorded, CPU not recorded.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "BSE-000000133", "path": "runs/broad-scalar-cycle-011-cellref/comparisons/excel_sample_comparisons.jsonl.gz", "repository": "CalcFunc-Evidence" } } ], "platform": "Windows, bitness not recorded, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ERF.PRECISE.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/broad-scalar-cycle-011-cellref/comparisons/excel_sample_comparisons.jsonl.gz" ] }, { "behaviour": "409,213 captured inputs are indexed for this environment. Capture dates: 2026-07-16 to 2026-07-17. This is a reading count, not a comparison with another build. Retained control ERF.PRECISE(1) returned 0.8427007929497149 (0x3feaf767a741088b). The selected archive row does not record its input plumbing; no input route is inferred.", "excel_build": "16.0 build 20131", "observations": [ { "call": "ERF.PRECISE(1)", "excel": { "bits": "0x3feaf767a741088b", "display": "0.8427007929497149", "kind": "number" }, "input_route": "not-recorded", "inputs": [ { "name": "argument1", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "ERF.PRECISE|0x3ff0000000000000", "path": "cache/oracle/build-20131/ERF.PRECISE.jsonl.gz", "repository": "CalcFunc-Evidence" } } ], "platform": "Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ERF.PRECISE.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/oracle/build-20131/ERF.PRECISE.jsonl.gz" ] } ] }