{ "category": "Statistical functions", "display_name": "GAUSS", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.GAUSS", "implementation_state": { "answer_bank": { "excel_builds": [ "20228", "20430" ], "larger_numeric": 0, "last_bit": 357, "matched": 9371, "other_mismatch": 0, "refused": 0, "rows": 9728, "unread": 0, "worst_ulp": 3 }, "detail": "Everything else matches (9,728 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: 357 of 9,731 recorded answers differ in the last bits, worst 3 ULP", "workbook_corpus": { "cells": 3, "matched": 3 } }, "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#L109-L109", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/gauss_fn.rs#L4-L9", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/normal_dist_common.rs#L193-L198", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/normal_log_family.rs#L19-L28", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/normal_log_family.rs#L54-L64" ], "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/normal_log_family::flush_subnormal", "ported/normal_log_family::identified_std_normal_cdf", "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#L109-L109", "state": "close", "suite": null, "summary": "Close: 357 of 9,731 recorded answers differ in the last bits, worst 3 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.GAUSS.json", "name": "GAUSS", "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### Relationships\n\n\n- **`NORM.S.DIST(z, TRUE)`** — the unshifted standard normal CDF. `GAUSS(z)` and\n `NORM.S.DIST(z, TRUE) − 0.5` are the same number mathematically. They are *not* the same\n computation in general, and the difference matters: forming Φ(z) and then subtracting ½ loses\n precision for small z, because Φ(z) ≈ ½ + small and the subtraction cancels the leading digits\n of the answer. `GAUSS` exists so that the small quantity never has to be recovered from a\n difference. Below 0.5 Excel's `GAUSS` uses the ERF rational of FN-ERF.PRECISE-001; from 0.5 up,\n whether it avoids that path is an open question here.\n- **`PHI(z)`** — the standard normal *density*, not a probability. Naming collision with the\n common notation Φ for the CDF; Excel's `PHI` is φ, the derivative of `NORM.S.DIST`. The two\n were introduced together in Excel 2013 and are documented on separate pages.\n- **`NORM.DIST` / `NORM.INV` / `NORM.S.INV`** — the general and inverse normal surfaces.\n- **`ERF` and `ERF.PRECISE`** — the substrate. GAUSS(z) = ½·erf(z/√2) exactly, so any statement\n about `GAUSS`'s last bits is a statement about the error function Excel provides. The\n Handbook's own evidence names this dependency explicitly.\n- **`STANDARDIZE`** — the usual preprocessing step, (x − μ)/σ.\n- **`CONFIDENCE.NORM`, `Z.TEST`** — consumers of the same normal-tail machinery.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\n**The whole function is one erf evaluation, and erf is a solved problem.** The classical\nimplementation is Cody's rational Chebyshev approximation (1969), refined into ACM Algorithm 715\n(`CALERF`), which splits the line into three regions — a small-argument rational in z², a middle\nregion computing erfc directly, and a large-argument asymptotic form — and is the ancestor of\nfdlibm's `erf`/`erfc` and of most library implementations. Boost.Math and Cephes are in the same\nlineage with different coefficient sets. The mathematics has been settled for fifty years; what\ndiffers between implementations is coefficients, region boundaries, and the order of the final\narithmetic.\n\n**The reason `GAUSS` is a separate function is cancellation.** Writing GAUSS(z) as Φ(z) − ½ is\nthe obvious implementation and the wrong one for small z: the true answer is small, Φ(z) is close\nto ½, and the subtraction discards the leading significant digits. Computing ½·erf(z/√2) instead\nkeeps the small quantity small throughout. This is the same lesson as `log1p` versus\n`LN(1+x)` and `expm1` versus `EXP(x)−1`, applied to the normal integral — and it is the reason\nthe function has a name of its own rather than being left to the reader to spell out. An\nimplementation that quietly routes `GAUSS` through the CDF has thrown away the function's\npurpose while returning plausible answers everywhere except where it matters.\n\n**The scaling by √2 is not free.** z/√2 must be computed with a correctly rounded division (or by\nmultiplying by a correctly rounded 1/√2 — which is *not* the same, and the two differ in the last\nbit for many z). For a compatibility-oriented implementation this is a specification detail, not\nan optimisation: the choice is observable.\n\n**Saturation.** The threshold beyond which the result is exactly ±½ is an implementation\nfingerprint, determined by where erf(z/√2) rounds to 1 rather than by any mathematical boundary.\n\n**What the Handbook's evidence says about the substrate.** The open-discrepancy record for this\nsurface diagnoses the disagreement as needing the error-function/CDF substrate. That is an\nunusually specific statement of *why* a surface is unresolved: not \"we have not looked\", but \"the\nlayer beneath it has not been identified\". FN-ERF.PRECISE-001 has since identified that layer below\n0.5: a stored (4, 5) rational, which `GAUSS` uses too, with coefficients read off Excel's answers\nand no published table matched. A separate record in the same family identifies the `.PRECISE`\nerror-function surfaces as branches of an incomplete-gamma routine rather than as a standalone\ncoefficient table; below 0.5 that note finds a coefficient table.\n\n\n", "quirks": "\n### Result and edge cases\n\n\nReturns `Number`, always in [−½, ½].\n\n- **z = 0** gives exactly 0, and the signed zero is worth preserving.\n- **Small z** gives z/√(2π) to within a rounding. Subnormals cannot be asked through a cell,\n which reads them back as 0 (FN-ERF.PRECISE-001). There is no cancellation here, unlike in the\n ½-subtracted form discussed below — which is the point.\n- **Large |z|** saturates at ±½. In binary64 the difference between Φ(z) and 1 falls below the\n representable spacing at ½ once |z| exceeds roughly 8.3, so beyond that the function returns\n exactly ±½ and carries no further information.\n- **Odd symmetry** is a free self-check: `GAUSS(z) + GAUSS(−z)` should be exactly zero for every\n z. An implementation that computes Φ(z) − ½ separately for each sign will generally fail this,\n and failing it is a defect provable without any oracle.\n- **Array arguments** lift elementwise.\n\n", "sources": "- Abramowitz & Stegun, *Handbook of Mathematical Functions*, §7.1 (error function) and §26.2\n (the normal probability function and its erf representation).\n- W. J. Cody, \"Rational Chebyshev approximation for the error function\", *Math. Comp.* 23 (1969);\n ACM Algorithm 715 `CALERF`; fdlibm `s_erf.c`; Boost.Math; Cephes — the implementation lineage\n discussed under **Numerical notes**.\n- Handbook evidence records `EV-DIST-0023` (the single witness, the absence of any count, and the\n erf-substrate diagnosis) and `EV-DIST-0018` (the ten-witness re-sweep, explicitly one pinned\n row per surface rather than a corpus rate).\n- Handbook, [Coercion and lifting](../model/02-coercion-and-lifting.md).\n- Handbook projections `data/functions/FUNC.GAUSS.json` (arity, `NumToNum` kernel class, unary\n numeric scalar-or-array lift, `arg_domain_guard=none`) and `data/presence/FUNC.GAUSS.json`\n (the `gauss_fn` module, with no sibling surfaces).\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| 20228 | Windows, 64-bit, CPU not recorded | 9,216 |\n| 20430 | Windows, 64-bit, CPU not recorded | 512 |\n\n- XC-GAUSS-001: build 19929 versus build 20228; 3 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.GAUSS.json).", "what-it-does": "\n`GAUSS(z)` returns the probability that a standard normal variable falls between 0 and z —\nthat is, the standard normal cumulative distribution function shifted so that the origin maps to\nzero. Microsoft's one-line description says it exactly: \"Returns 0.5 less than the standard\nnormal cumulative distribution.\"\n\n*The quoted one-line description is Microsoft's text, from its support article and the VBA reference .*\n\n GAUSS(z) = Φ(z) − ½ = (1/√(2π)) ∫₀^z e^{−t²/2} dt = ½ · erf( z / √2 )\n\n- **Domain:** the whole real line.\n- **Range:** the open interval (−½, ½). The bounds are approached but never attained\n mathematically, and are attained in floating point once |z| is beyond about 8.3.\n- **Symmetry:** odd. GAUSS(−z) = −GAUSS(z), and GAUSS(0) = 0 exactly. This is the structural\n reason the function exists: Φ itself is not odd, and the ½ subtraction is precisely what makes\n the symmetry manifest.\n- **Derivative:** the standard normal density φ(z) = e^{−z²/2}/√(2π), which is 1/√(2π) ≈ 0.3989\n at the origin and decays super-exponentially.\n- **Series at the origin:** GAUSS(z) = φ(0)·(z − z³/6 + z⁵/40 − …), so for small z the function is\n z/√(2π) to first order.\n\nThis is the function classically tabulated in the back of statistics textbooks — the \"area under\nthe normal curve from 0 to z\" table — and that is the whole reason it has a worksheet surface of\nits own. A&S §26.2 defines the same object and relates it to the error function of §7.1.\n\n**The identity that governs the implementation** is the last one above: GAUSS is half an error\nfunction of a scaled argument. Everything numerical about this surface is therefore a statement\nabout erf, and the Handbook's evidence for it says so in as many words.\n\n\n\n### Arguments\n\n\n| Argument | Meaning | Default |\n|---|---|---|\n| `z` | The value for which you want the distribution. Required. | — |\n\nThere is no mean, no standard deviation, and no cumulative flag. `GAUSS` is the standardised\nform only; a non-standard normal must be standardised first — `GAUSS((x − μ)/σ)` — or computed\nwith `NORM.DIST`.\n\n\n" }, "signature": { "display": "GAUSS(z)", "parameters": [ { "description": null, "name": "z", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 1, "min": 1 }, "category": "Statistical functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "UnaryNumericScalarOrArrayElementwise", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "NumToNum", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Probability that a standard normal value lies between 0 and z", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns 0.5 less than the standard normal cumulative distribution", "microsoft_url": "https://support.microsoft.com/en-us/office/gauss-function-069f1b4e-7dee-4d6a-a71f-4b69044a6b33" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "GAUSS" }, { "locale": "bg-BG", "name": "GAUSS" }, { "locale": "cs-CZ", "name": "GAUSS" }, { "locale": "da-DK", "name": "GAUSS" }, { "locale": "de-DE", "name": "GAUSS" }, { "locale": "el-GR", "name": "GAUSS" }, { "locale": "en-AU", "name": "GAUSS" }, { "locale": "en-GB", "name": "GAUSS" }, { "locale": "en-US", "name": "GAUSS" }, { "locale": "es-ES", "name": "GAUSS" }, { "locale": "et-EE", "name": "GAUSS" }, { "locale": "fi-FI", "name": "GAUSS" }, { "locale": "fr-FR", "name": "GAUSS*" }, { "locale": "he-IL", "name": "GAUSS" }, { "locale": "hr-HR", "name": "GAUSS" }, { "locale": "hu-HU", "name": "GAUSS" }, { "locale": "id-ID", "name": "GAUSS" }, { "locale": "it-IT", "name": "GAUSS" }, { "locale": "ja-JP", "name": "GAUSS" }, { "locale": "ko-KR", "name": "GAUSS" }, { "locale": "lt-LT", "name": "GAUSS" }, { "locale": "lv-LV", "name": "GAUSS" }, { "locale": "nb-NO", "name": "GAUSS" }, { "locale": "nl-NL", "name": "GAUSS" }, { "locale": "pl-PL", "name": "GAUSS" }, { "locale": "pt-BR", "name": "GAUSS" }, { "locale": "pt-PT", "name": "GAUSS" }, { "locale": "ro-RO", "name": "GAUSS" }, { "locale": "ru-RU", "name": "ГАУСС" }, { "locale": "sk-SK", "name": "GAUSS" }, { "locale": "sl-SI", "name": "GAUSS" }, { "locale": "sr-Latn-RS", "name": "GAUSS" }, { "locale": "sv-SE", "name": "GAUSS" }, { "locale": "th-TH", "name": "GAUSS" }, { "locale": "tr-TR", "name": "GAUSS" }, { "locale": "uk-UA", "name": "GAUSS" }, { "locale": "vi-VN", "name": "GAUSS" }, { "locale": "zh-CN", "name": "GAUSS" }, { "locale": "zh-HK", "name": "GAUSS" }, { "locale": "zh-TW", "name": "GAUSS" } ], "signature": { "display": "GAUSS(z)", "parameters": [ { "description": null, "name": "z", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "GAUSS", "version_marker": null, "xlcall": { "code": "577", "symbol": "xlfGauss" } }, "microsoft": "https://support.microsoft.com/en-us/office/gauss-function-069f1b4e-7dee-4d6a-a71f-4b69044a6b33" }, "try_it": { "formula": "=GAUSS(\"1\")" }, "url": "https://handbook.dnacalc.com/functions/GAUSS.html", "variants": [], "versions": [ { "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.", "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.GAUSS.json" ] }, { "behaviour": "9,216 captured inputs are indexed for this environment. Capture dates: 2026-08-09 to 2026-08-09. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20228", "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.GAUSS.json" ] }, { "behaviour": "512 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.GAUSS.json" ] } ] }