{ "category": "Engineering functions", "display_name": "ERFC.PRECISE", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.ERFC.PRECISE", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "20430", "?" ], "larger_numeric": 0, "last_bit": 801, "matched": 1062, "other_mismatch": 0, "refused": 0, "rows": 1863, "unread": 0, "worst_ulp": 6 }, "detail": "Everything else matches (1,863 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: 802 of 1,866 recorded answers differ in the last bits, worst 6 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#L321-L324" ], "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::erfc_kernel", "ported/special_dist_family::erfc_precise_kernel" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L321-L324", "state": "close", "suite": null, "summary": "Close: 802 of 1,866 recorded answers differ in the last bits, worst 6 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.ERFC.PRECISE.json", "name": "ERFC.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" }, { "basis": "220,000 Excel answers from 0.5 to 26.5 (build 20527) compared with E times the true exp(x*x)*erfc(x). With z = RN(x*x) and E stored, the residual stays within about 10 units of 2^-53 at every x. At x = 24 the exact exp(-x*x) spreads with a standard deviation of 287 units, Cody's and fdlibm's fractional splits of x*x spread the same, and plain binary64 x*x leaves outliers of up to 1,024 units.", "documentation": null, "evidence": [ { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": "Round 4: ERFC above 0.5", "note": "the residual table, what is known about F", "path": "content/notes/evidence/2026-11-04/erf-EVIDENCE-round3.md", "repository": "ExcelFunctionsHandbook" }, { "commit": "d85e5e9b52c601323dacc4369b9edc8146c98357", "locator": "erfc_upper", "note": "the commit stores z and E and uses Cody's rational in place of F; its message carries the row counts", "path": "crates/calc-func/src/ported/normal_dist_common.rs", "repository": "DnaCalc" } ], "functions": [ "FUNC.ERFC", "FUNC.ERFC.PRECISE" ], "inferred": "F is not a closed form: y = RN(E*RN(F)) with any offset matches 40% of answers at best. Its noise tracks about a dozen smooth curves, consistent with two polynomials of degree about 8 in x with shapes near Cephes' erfc P and Q, but that is a reading of shape only, and no table has been matched.", "kind": "excel-differs-from-math", "note_id": "FN-ERFC-001", "open": [ "F, so the last bits: with a stand-in for F, recorded rows match ERFC 234 of 544 and ERFC.PRECISE 1,062 of 1,863, with no answer more than 6 units away.", "The mean of the residual is flat with sharp steps of about 0.4 units, at x = 1.11567925... and 1.1217 among about 80 in [0.5, 27]. No stored polynomial value varies that slowly, and this is unexplained." ], "recorded_on": "2026-11-04", "repros": [ { "call": "ERFC.PRECISE(26.543000000000003)", "correct": { "bits": "0x001038a055f6cfff", "display": "2.2558350220535116e-308", "how": "mpmath erfc at 800 bits from the binary64 input, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x001038a055f6d0d3", "display": "2.2558350220536164e-308", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x403a8b020c49ba5f", "display": "26.543000000000003", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 363, key ERFC.PRECISE|0x403a8b020c49ba5f", "note": null, "path": "cache/oracle/build-20131/ERFC.PRECISE.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ERFC.PRECISE(5.927083333333333)", "correct": { "bits": "0x3c8df497ca9a0a32", "display": "5.1964407001614313e-17", "how": "mpmath erfc at 800 bits from the binary64 input, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x3c8df497ca9a0a49", "display": "5.1964407001614455e-17", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4017b55555555555", "display": "5.927083333333333", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 340, key ERFC.PRECISE|0x4017b55555555555", "note": null, "path": "cache/oracle/build-20131/ERFC.PRECISE.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ERFC.PRECISE(2.0)", "correct": { "bits": "0x3f7328f5ec350e67", "display": "0.004677734981047266", "how": "mpmath erfc at 800 bits from the binary64 input, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x3f7328f5ec350e65", "display": "0.0046777349810472645", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4000000000000000", "display": "2", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 64, key ERFC.PRECISE|0x4000000000000000", "note": null, "path": "cache/oracle/build-20131/ERFC.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, ERFC for x >= 0.5 behaves as Q = E*F with z = RN(x*x) and E = exp(-z) stored to binary64, then multiplied by a factor F that is not identified. So the rounding error of x*x reaches the answer at full size. At x = 26.543000000000003, x*x exceeds z by 4.64E-14, which at the size of this answer is about 212 units, and Excel's answer is 212 units above the correctly rounded erfc. Near x = 5.93 the same effect is 23 units. For small x, where x*x is exact or nearly so, the answer stays within a few units.", "status": "measured", "title": "Above 0.5, ERFC rounds x*x before the exponential, so the tail drifts by hundreds of units" } ], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[ERF](FUNC.ERF.md) computes the central integral; [NORM.S.DIST](FUNC.NORM.S.DIST.md) expresses normal probabilities. Use a scaled complementary error function internally to avoid overflow when designing a mathematical tail algorithm.\n\n\n\n\n", "how-to-implement": "\nLet D denote ordinary binary64 storage and [R](../model/09-staged-arithmetic.md) a 64-bit-significand operation followed by a binary64 store. The current finite-input branch table is:\n\n| Input range | Current computation |\n|---|---|\n| `00.5` | Positive upper-tail candidate below |\n| `x<-0.5` | `R(2-positive_upper_tail(abs(x)))` |\n| `-0.5<=x<=0` | Runtime ERFC fallback |\n\nFor the positive upper stage, store `z=R(x*x)`, obtain the stored public exponential `E=EXP(-z)`, and form `R(E*F(x))`. Excel’s rational factor F is **still open**. The current code uses published Cody coefficients with stored arithmetic as a stand-in; copying that table does not complete an identified Excel tail recipe.\n\nWorked below-half case: the stated ERF reconstruction at 0.25 is `0.276326390168237`, so subtracting it from one gives about `0.723673609831763`. In the upper stage at x=1, z is one and E is about `0.36787944117144233`; the still unresolved F must supply the remaining factor.\n\nApply the current final subnormal-to-zero rule after the chosen branch. In particular, the negative half interval is not routed through the positive small-rational complement by this implementation. The exact half-point ownership in private Excel code is unseparated by the retained equal-answer control. Keep the reconstructed outer stages, current numerical substitutes and unmeasured transfer cases distinct.\n\n\n", "quirks": "\nNonnumeric input gives `#VALUE!`. Subtracting a value rounded to one from one can erase a representable tail. The PRECISE spelling is not a whole-domain accuracy guarantee. The current kernel flushes a final subnormal tail to zero.\n\n\n", "sources": "\n- [Microsoft: ERFC.PRECISE function](https://support.microsoft.com/en-us/excel/functions/erfc-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/special_dist_family.rs); implementation steps and the limits identified in the text.\n- [ERFC stage findings](../notes/evidence/2026-11-04/erf-EVIDENCE-round3.md).\n\n", "try-it": "\n`=ERFC.PRECISE(0.25)` is about `0.723673609831763`; `=ERFC.PRECISE(0)` is `1`. A large positive argument has a small positive tail, whereas a large negative argument approaches two.\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 | 43 |\n| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 935 |\n| 20430 | Windows, 64-bit, CPU not recorded | 928 |\n\n- XC-ERFC.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.ERFC.PRECISE.json).", "what-it-does": "\n`ERFC.PRECISE(x)` is the normalised integral of `exp(-t*t)` from x to infinity. Mathematically it is `1-erf(x)`, but a direct tail calculation retains information when erf is close to one.\n\n\n" }, "signature": { "display": "ERFC.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": "Complementary error function integrated from x to infinity", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the complementary ERF function integrated between x and infinity", "microsoft_url": "https://support.microsoft.com/en-us/office/erfc-precise-function-e90e6bab-f45e-45df-b2ac-cd2eb4d4a273" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "ERFC.PRECISE" }, { "locale": "bg-BG", "name": "ERFC.PRECISE" }, { "locale": "cs-CZ", "name": "ERFC.PRECISE" }, { "locale": "da-DK", "name": "ERFC.PRECISE" }, { "locale": "de-DE", "name": "ERFC.PRECISE" }, { "locale": "el-GR", "name": "ERFC.PRECISE" }, { "locale": "en-AU", "name": "ERFC.PRECISE" }, { "locale": "en-GB", "name": "ERFC.PRECISE" }, { "locale": "en-US", "name": "ERFC.PRECISE" }, { "locale": "es-ES", "name": "FUN.ERROR.COMPL.EXACTO" }, { "locale": "et-EE", "name": "ERFC.PRECISE" }, { "locale": "fi-FI", "name": "VIRHEFUNKTIO.KOMPLEMENTTI.TARKKA" }, { "locale": "fr-FR", "name": "ERFC.PRECIS*" }, { "locale": "he-IL", "name": "ERFC.PRECISE" }, { "locale": "hr-HR", "name": "ERFC.PRECISE" }, { "locale": "hu-HU", "name": "HIBAFKOMPLEMENTER.PONTOS" }, { "locale": "id-ID", "name": "ERFC.PRECISE" }, { "locale": "it-IT", "name": "ERFC.PRECISE" }, { "locale": "ja-JP", "name": "ERFC.PRECISE" }, { "locale": "ko-KR", "name": "ERFC.PRECISE" }, { "locale": "lt-LT", "name": "ERFC.PRECISE" }, { "locale": "lv-LV", "name": "ERFC.PRECISE" }, { "locale": "nb-NO", "name": "ERFC.PRECISE" }, { "locale": "nl-NL", "name": "FOUT.COMPLEMENT.NAUWKEURIG" }, { "locale": "pl-PL", "name": "KOMP.FUNKCJA.BŁ.DOKŁ" }, { "locale": "pt-BR", "name": "ERFC.PRECISE" }, { "locale": "pt-PT", "name": "FUNCERROCOMPL.PRECISO" }, { "locale": "ro-RO", "name": "ERFC.PRECISE" }, { "locale": "ru-RU", "name": "ДФОШ.ТОЧН" }, { "locale": "sk-SK", "name": "ERFC.PRECISE" }, { "locale": "sl-SI", "name": "ERFC.PRECISE" }, { "locale": "sr-Latn-RS", "name": "ERFC.PRECISE" }, { "locale": "sv-SE", "name": "FELFK.EXAKT" }, { "locale": "th-TH", "name": "ERFC.PRECISE" }, { "locale": "tr-TR", "name": "TÜMHATAİŞLEV.DUYARLI" }, { "locale": "uk-UA", "name": "ERFC.PRECISE" }, { "locale": "vi-VN", "name": "ERFC.PRECISE" }, { "locale": "zh-CN", "name": "ERFC.PRECISE" }, { "locale": "zh-HK", "name": "ERFC.PRECISE" }, { "locale": "zh-TW", "name": "ERFC.PRECISE" } ], "signature": { "display": "ERFC.PRECISE(x)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "ERFC.PRECISE", "version_marker": null, "xlcall": { "code": "544", "symbol": "xlfErfc_precise" } }, "microsoft": "https://support.microsoft.com/en-us/office/erfc-precise-function-e90e6bab-f45e-45df-b2ac-cd2eb4d4a273" }, "try_it": { "formula": "=ERFC.PRECISE(0.25)" }, "url": "https://handbook.dnacalc.com/functions/ERFC.PRECISE.html", "variants": [], "versions": [ { "behaviour": "ERFC.PRECISE(26.543000000000003) returned 2.2558350220536164e-308 (0x001038a055f6d0d3). ERFC.PRECISE(5.927083333333333) returned 5.1964407001614455e-17 (0x3c8df497ca9a0a49). 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": "ERFC.PRECISE(26.543000000000003)", "excel": { "bits": "0x001038a055f6d0d3", "display": "2.2558350220536164e-308", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x403a8b020c49ba5f", "display": "26.543000000000003", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H" }, { "call": "ERFC.PRECISE(5.927083333333333)", "excel": { "bits": "0x3c8df497ca9a0a49", "display": "5.1964407001614455e-17", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4017b55555555555", "display": "5.927083333333333", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H" }, { "call": "ERFC.PRECISE(2.0)", "excel": { "bits": "0x3f7328f5ec350e65", "display": "0.0046777349810472645", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4000000000000000", "display": "2", "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-ERFC-001.json" ] }, { "behaviour": "43 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 19929", "platform": "Windows, bitness not recorded, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ERFC.PRECISE.json" ] }, { "behaviour": "935 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.", "excel_build": "16.0 build 20131", "platform": "Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ERFC.PRECISE.json" ] }, { "behaviour": "928 captured inputs are indexed for this environment. Capture dates: 2026-09-29 to 2026-09-29. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20430", "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ERFC.PRECISE.json" ] } ] }