diff --git a/.trinity/seals/t27f_T27fFormulaTable.json b/.trinity/seals/t27f_T27fFormulaTable.json new file mode 100644 index 0000000000..e72ec89d2a --- /dev/null +++ b/.trinity/seals/t27f_T27fFormulaTable.json @@ -0,0 +1,28 @@ +{ + "built_by": "t27c-bootstrap@0.5.2+72ddaf7ac", + "closure": [], + "config": "gen=c,rust,verilog,zig;tests=zig", + "gen_hash_c": "sha256:6634050ae732df97c0f82b12dc33507bbaad64e0f756a483a01f0ee3b895142a", + "gen_hash_rust": "sha256:4c55e68190df1eac153777d665ed137da934bc782eb27c920b5a33db796a8627", + "gen_hash_verilog": "sha256:b1512da42459deb04c3eef8a612e1f1f6140d7158cfb5fb194fe34303c8065a7", + "gen_hash_zig": "sha256:f97bf28a419159210910c0de2174d662b9a135a3b4c8d73d9a5f4a642ecf8261", + "module": "T27fFormulaTable", + "ring": 12, + "seal_schema": 2, + "sealed_at": "2026-10-20T17:35:40Z", + "sealed_by": "t27c-bootstrap@0.5.2", + "spec_hash": "sha256:86fa1a3bdbc03a80e988e9f5417f16ed01a868d0634d6815d8dd57fb38a2b84b", + "spec_path": "specs/t27f/formula_table.t27", + "tests": { + "failed": 0, + "failing": [], + "forced": false, + "passed": 9, + "total": 9, + "vacuous": 0 + }, + "toolchain": { + "test_runner": "sha256:8512b80da533b79289110fca4a65f3336abd7a059ca4b72ea595d5e33ff8ad10", + "zig": "0.16.0" + } +} \ No newline at end of file diff --git a/.trinity/seals/t27os_T27osOrbitView.json b/.trinity/seals/t27os_T27osOrbitView.json index 3aad2d12be..9da37f5c41 100644 --- a/.trinity/seals/t27os_T27osOrbitView.json +++ b/.trinity/seals/t27os_T27osOrbitView.json @@ -7,7 +7,7 @@ }, { "spec": "specs/t27f/formula_table.t27", - "spec_hash": "sha256:59d968f6cfd27ba742a07208fd7f0cb25c1cabf4052c9526f8fd9058e1721053" + "spec_hash": "sha256:86fa1a3bdbc03a80e988e9f5417f16ed01a868d0634d6815d8dd57fb38a2b84b" }, { "spec": "specs/t27os/lanes_view.t27", @@ -15,23 +15,23 @@ } ], "config": "gen=c,rust,verilog,zig;tests=zig", - "gen_hash_c": "sha256:c2b1381bc6b2b2221f83af364002486db06ef77ad188b9643304e005777fa016", - "gen_hash_rust": "sha256:9f0309d52837cc73ade2f9f740e688b7c3813a682d2c4189260736e64e977e47", - "gen_hash_verilog": "sha256:82ec427976d9d02dbf454147ba713f83ba4f66395fc7ac8c92484318822a31f8", - "gen_hash_zig": "sha256:62ac52e15bc276614fb59ffcdf60cb688454f02183cb7b6393438ac8639ec215", + "gen_hash_c": "sha256:960027342e19795cd625d4dbde86c152cb75e508d87555a7441eb0bd290b099f", + "gen_hash_rust": "sha256:68a5142ac223bd3c6a3416d6eb3b3641cc7e8fd4f9af27eb3c97c5fb428583fb", + "gen_hash_verilog": "sha256:01b1aa964c2ad8d0fa5392a971aad42d7e63d1d0a3f11e79f5c6124f6ec3bb14", + "gen_hash_zig": "sha256:e7f27f968326b00002f83170724c71c5a68037c126306f16bafc92b43ee7d296", "module": "T27osOrbitView", "ring": 12, "seal_schema": 2, - "sealed_at": "2026-10-20T17:11:19Z", + "sealed_at": "2026-10-20T17:35:29Z", "sealed_by": "t27c-bootstrap@0.5.2", - "spec_hash": "sha256:b8a41ef1b4d052045fc52b25536c7edeca99cfadf32fb2c53f85d79313d43c66", + "spec_hash": "sha256:92912f044a00945a9443479d367b83ad0f7a60be0290f59edaa03ac4cac42d8c", "spec_path": "specs/t27os/orbit_view.t27", "tests": { "failed": 0, "failing": [], "forced": false, - "passed": 10, - "total": 10, + "passed": 12, + "total": 12, "vacuous": 1 }, "toolchain": { diff --git a/specs/t27f/formula_table.t27 b/specs/t27f/formula_table.t27 index 71155bb1f4..0e6e328ead 100644 --- a/specs/t27f/formula_table.t27 +++ b/specs/t27f/formula_table.t27 @@ -1,44 +1,772 @@ -; GENERATED from specs/physics/formula_registry.t27 -- do not hand-edit (DRY: the registry is the SSOT). -; Regenerate: extract every fn preceded by a "[VERIFIED] sector= cx= delta=" tag line; each fn's return expression, -; its value evaluated in f64 (phi, pi, e as in the registry), its sector, and the tag's deviation in thousandths of a percent. -; Only VERIFIED rows are emitted: conjectures and failures never reach the brand visual (AGENTS.md "Brand visual"). -; Source of every row: the Pellis/Vasilev/Olsen "Sacred Formula" paper (research/trinity-pellis-paper/), compared with CODATA/PDG. +; GENERATED from specs/physics/formula_registry.t27 (rows 0..31) and harvested from the sources named below (rows 32..) -- do not hand-edit (DRY: the registry is the SSOT for rows 0..31). +; Rows 0..31 are the registry's [VERIFIED] functions exactly as before: each fn's return expression, its value evaluated in f64 (phi, pi, e as in the +; registry), its sector, and the tag's deviation in thousandths of a percent (ERR_MILLI_PCT, the registry's own claim, unchanged so the orbit shows what it showed). +; Rows 32.. (owner 2026-10-21, "find them ALL"): every other formula of the owner's family that lands within 1 percent of the measured value its source cites, +; harvested from formula_registry.t27, the FORMULA_TABLE archives v03..v09, FORMULA_TABLE.md, the paper tables (G2_TRINITY_V1.0 .tex), pellis-formulas.t27, +; sacred_physics.t27, sacred_lattice.t27, the DISCOVERY_*.md and formula-matrix search dumps, and gHashTag/trinity (formulas-catalog-2026.md, +; PELLIS_TRINITY_COMPARISON.md, sacred_constants.csv). Each value was recomputed in float math; a row is kept only when |error| <= 1 percent against the +; measured value the source cites (CODATA 2022 / PDG 2024 / NuFIT / Planck 2018 / lattice QCD). Source and measured value of every row: the report of the PR. +; TAG column: VERIFIED = a registry [VERIFIED] row (rows 0..31, first); candidate = a small-coefficient formula from a catalog table, spec or paper that recomputes +; within 1 percent; conjecture = a large-coefficient search fit (n >= 100), a lattice fit of sacred_constants.csv, or a row whose measured value is contested. +; REPRO_MILLI_PCT is the error recomputed against the cited measured value, for every row; for rows 32.. it equals ERR_MILLI_PCT. Twelve of the 32 registry rows +; are NOT within 1 percent when recomputed (their registry tag claims 0.03 percent): they stay, tagged VERIFIED as the registry tags them, with the real error here. +; FORMULA_COUNT stays 32: the orbit (orbit_view.t27, glass_window.t27) reads the registry prefix, capped at OV_MAX = 32; ROW_COUNT is the whole table. +; Everything in a row is recomputed by the tests below from its recipe (n * 3^k * pi^m * phi^p * e^q, or one of eight named closed forms). module T27fFormulaTable; pub const FORMULA_COUNT : u32 = 32; -pub const SECTOR_COUNT : u32 = 9; +pub const ROW_COUNT : u32 = 358; +pub const SECTOR_COUNT : u32 = 16; +pub const TAG_VERIFIED : u32 = 0; +pub const TAG_CANDIDATE : u32 = 1; +pub const TAG_CONJECTURE : u32 = 2; +pub const CLOSE_MILLI_PCT : i64 = 1000; /// Four fields per formula (name, expression, value, sector), packed in FORMULA_TEXT; field f of formula i is at slot i * 4 + f. -pub const FORMULA_TEXT : str = "gamma_phipow(PHI, -3.0)0.236067977gauge-couplingln2_over_piln(2.0) / PI0.2206356gauge-couplingln3_over_piln(3.0) / PI0.349699153gauge-couplingalpha_inv_pellis_exactGA - 2.0 / pow(PHI, 3.0) + pow(3.0 * PHI, -5.0)137.035999gauge-couplingalpha_s1.0 / (pow(PHI, 4.0) + PHI)0.118033989gauge-couplingtc_qcd156.5156.5gauge-couplingneutron_proton_ratio1.0 + alpha_em * gamma_phi()1.00172267electroweakmuon_electron_ratio8.0 * pow(PHI, 2.0) * pow(PI, 2.0)206.711678electroweakelectron_mass_mev1.0 / (E * PHI)0.227361998leptonmuon_mass_mev2.0 * pow(PHI, 2.0) * pow(PI, 2.0)51.6779196leptontau_mass_mev4.0 / (PHI * PHI)1.52786405leptonkoide_q2.0 / 3.00.666666667leptonbottom_mass_gev5.0 * PI * pow(PHI, -2.0) * pow(E, -1.0)2.20724283quarktop_mass_gev4.0 * 9.0 * PI * pow(PHI, 4.0) * pow(E, 2.0)5727.85346quarkstrange_down_ratio2.0 * PI * PHI / 3.03.38880246quarktheta_cabibboGA / 16.08.59423525ckmv_cb1.0 / (7.0 * pow(PHI, 2.0) * pow(PI, 2.0) * pow(E, 2.0))0.000748234916ckmv_us1.0 / (E * PHI)0.227361998ckmsin2theta23_pmns3.0 * pow(PHI, -8.0) * PI * E0.545336401pmnsdelta_cp_pmns9.0 / (PHI * PHI)3.4376941pmnssin2theta12_pmns4.0 / (pow(PHI, 2.0) * pow(PI, 4.0) * pow(E, 4.0))0.000287281257pmnslambda_exponent122122cosmologyhiggs_z_ratio(1.0 / 8.0) * pow(PHI, 2.0) * pow(PI, 3.0) * pow(E, -2.0)1.37323843higgsv_ud_chimera7.0 * pow(PHI, -5.0) * pow(PI, 3.0) * pow(E, -3.0)0.974374728ckmv_cs_chimera7.0 * pow(PHI, -5.0) * pow(PI, 3.0) * pow(E, -3.0)0.974374728ckmv_td_chimera2.0 * pow(PHI, -4.0) * pow(PI, -4.0) * E0.00814281233ckmsin2theta12_chimera8.0 * pow(PHI, -5.0) * PI * pow(E, -2.0)0.306699236pmnsdelta_cp_rad9.0 * pow(PHI, -2.0)3.4376941pmnsstrange_muon_ratiopow(PHI, -2.0) * pow(PI, -1.0) * pow(E, 2.0)0.898387728leptonbottom_top_ratio4.0 * pow(PHI, -2.0) * pow(PI, -1.0) * pow(E, -3.0)0.0242131556qcdomega_b_chimera4.0 * pow(PHI, -2.0) * pow(PI, -3.0)0.0492759599cosmologyns_chimera3.0 * pow(PHI, 3.0) * pow(PI, -4.0) * pow(E, 2.0)0.963992485cosmology"; -pub const FIELD_START : [128]u32 = [0, 9, 23, 34, 48, 59, 71, 80, 94, 105, 117, 128, 142, 164, 211, 221, 235, 242, 269, 280, 294, 300, 305, 310, 324, 344, 372, 382, 393, 412, 446, 456, 467, 484, 499, 510, 516, 529, 563, 573, 579, 591, 608, 618, 624, 631, 640, 651, 657, 672, 712, 722, 727, 739, 783, 793, 798, 816, 836, 846, 851, 864, 873, 883, 886, 890, 946, 960, 963, 967, 982, 993, 996, 1012, 1041, 1052, 1056, 1069, 1086, 1095, 1099, 1115, 1165, 1179, 1183, 1198, 1201, 1204, 1213, 1226, 1283, 1293, 1298, 1310, 1360, 1371, 1374, 1386, 1436, 1447, 1450, 1462, 1502, 1515, 1518, 1537, 1577, 1588, 1592, 1604, 1624, 1633, 1637, 1655, 1699, 1710, 1716, 1732, 1783, 1795, 1798, 1813, 1849, 1861, 1870, 1880, 1929, 1940]; -pub const FIELD_LEN : [128]u32 = [9, 14, 11, 14, 11, 12, 9, 14, 11, 12, 11, 14, 22, 47, 10, 14, 7, 27, 11, 14, 6, 5, 5, 14, 20, 28, 10, 11, 19, 34, 10, 11, 17, 15, 11, 6, 13, 34, 10, 6, 12, 17, 10, 6, 7, 9, 11, 6, 15, 40, 10, 5, 12, 44, 10, 5, 18, 20, 10, 5, 13, 9, 10, 3, 4, 56, 14, 3, 4, 15, 11, 3, 16, 29, 11, 4, 13, 17, 9, 4, 16, 50, 14, 4, 15, 3, 3, 9, 13, 57, 10, 5, 12, 50, 11, 3, 12, 50, 11, 3, 12, 40, 13, 3, 19, 40, 11, 4, 12, 20, 9, 4, 18, 44, 11, 6, 16, 51, 12, 3, 15, 36, 12, 9, 10, 49, 11, 9]; -/// Deviation from the measured value, in thousandths of a percent, signed (-0.62 percent = -620). -pub const ERR_MILLI_PCT : [32]i64 = [-620, 0, 0, 29, 29, 0, 34, 27, 29, 29, 28, 0, 34, 43, 0, 96, 43, 1360, 62, 18, 36, 0, 22, 17, 80, 37, 98, 17, 78, 21, 41, 94]; -/// Complexity of the expression (registry cx). -pub const COMPLEXITY : [32]u32 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 6, 6, 2, 5, 6, 5, 6]; -/// Sector names in order of first appearance: gauge-coupling, electroweak, lepton, quark, ckm, pmns, cosmology, higgs, qcd. -pub const SECTOR_OF : [32]u32 = [0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 4, 4, 4, 5, 5, 2, 8, 6, 6]; +pub const FORMULA_TEXT : str = "gamma_phipow(PHI, -3.0)0.236067977gauge-couplingln2_over_piln(2.0) / PI0.2206356gauge-couplingln3_over_piln(3.0) / PI0.349699153gauge-couplingalpha_inv_pellis_exactGA - 2.0 / pow(PHI, 3.0) + pow(3.0 * PHI, -5.0)137.035999gauge-couplingalpha_s1.0 / (pow(PHI, 4.0) + PHI)0.118033989gauge-couplingtc_qcd156.5156.5gauge-couplingneutron_proton_ratio1.0 + alpha_em * gamma_phi()1.00172267electroweakmuon_electron_ratio8.0 * pow(PHI, 2.0) * pow(PI, 2.0)206.711678electroweakelectron_mass_mev1.0 / (E * PHI)0.227361998leptonmuon_mass_mev2.0 * pow(PHI, 2.0) * pow(PI, 2.0)51.6779196leptontau_mass_mev4.0 / (PHI * PHI)1.52786405leptonkoide_q2.0 / 3.00.666666667leptonbottom_mass_gev5.0 * PI * pow(PHI, -2.0) * pow(E, -1.0)2.20724283quarktop_mass_gev4.0 * 9.0 * PI * pow(PHI, 4.0) * pow(E, 2.0)5727.85346quarkstrange_down_ratio2.0 * PI * PHI / 3.03.38880246quarktheta_cabibboGA / 16.08.59423525ckmv_cb1.0 / (7.0 * pow(PHI, 2.0) * pow(PI, 2.0) * pow(E, 2.0))0.000748234916ckmv_us1.0 / (E * PHI)0.227361998ckmsin2theta23_pmns3.0 * pow(PHI, -8.0) * PI * E0.545336401pmnsdelta_cp_pmns9.0 / (PHI * PHI)3.4376941pmnssin2theta12_pmns4.0 / (pow(PHI, 2.0) * pow(PI, 4.0) * pow(E, 4.0))0.000287281257pmnslambda_exponent122122cosmologyhiggs_z_ratio(1.0 / 8.0) * pow(PHI, 2.0) * pow(PI, 3.0) * pow(E, -2.0)1.37323843higgsv_ud_chimera7.0 * pow(PHI, -5.0) * pow(PI, 3.0) * pow(E, -3.0)0.974374728ckmv_cs_chimera7.0 * pow(PHI, -5.0) * pow(PI, 3.0) * pow(E, -3.0)0.974374728ckmv_td_chimera2.0 * pow(PHI, -4.0) * pow(PI, -4.0) * E0.00814281233ckmsin2theta12_chimera8.0 * pow(PHI, -5.0) * PI * pow(E, -2.0)0.306699236pmnsdelta_cp_rad9.0 * pow(PHI, -2.0)3.4376941pmnsstrange_muon_ratiopow(PHI, -2.0) * pow(PI, -1.0) * pow(E, 2.0)0.898387728leptonbottom_top_ratio4.0 * pow(PHI, -2.0) * pow(PI, -1.0) * pow(E, -3.0)0.0242131556qcdomega_b_chimera4.0 * pow(PHI, -2.0) * pow(PI, -3.0)0.0492759599cosmologyns_chimera3.0 * pow(PHI, 3.0) * pow(PI, -4.0) * pow(E, 2.0)0.963992485cosmologyG01_alpha_inv4.0 * pow(3.0, 2.0) * pow(PI, -1.0) * pow(PHI, 1.0) * pow(E, 2.0)137.002733gauge-couplingPM1_alpha_inv_GA360.0 * pow(PHI, -2.0)137.507764gauge-couplingG06_alpha_running3.0 * pow(PHI, 2.0) * pow(E, -2.0)1.06293711gauge-couplingP13_alpha_s_4phi2_9pi24.0 * pow(3.0, -2.0) * pow(PI, -2.0) * pow(PHI, 2.0)0.117894357gauge-couplingP11_alpha_s_v03(1.0 / 3.0) * pow(PHI, 2.0) * pow(E, -2.0)0.118104124gauge-couplingG05_alphas_over_alpha22.0 * pow(PI, 1.0) * pow(PHI, 1.0) * pow(E, -1.0)3.74001227gauge-couplingP14_sin2thW_2pi3e_729(2.0 / 729.0) * pow(PI, 3.0) * pow(E, 1.0)0.231231272gauge-couplingG03_sin2thWpow(3.0, -2.0) * pow(PI, 2.0) * pow(PHI, 3.0) * pow(E, -3.0)0.231279272gauge-couplingH04_Gamma_Z(4.0 / 3.0) * pow(PI, 1.0) * pow(PHI, 1.0) * pow(E, -1.0)2.49334151electroweakmW_over_mZ_108phi4.0 * pow(3.0, 3.0) * pow(PI, -2.0) * pow(PHI, 1.0) * pow(E, -3.0)0.881511951electroweakP13_mW_162phi3_pi_e2.0 * pow(3.0, 4.0) * pow(PI, -1.0) * pow(PHI, 3.0) * pow(E, -1.0)80.3588255electroweakEW5_Z_5_over_phi_4pow(5.0 / PHI, 4.0)91.1862711electroweakP12_mZ_7pi4_phi_e3_243(7.0 / 243.0) * pow(PI, 4.0) * pow(PHI, 1.0) * pow(E, 3.0)91.1931764electroweakH06_mt_over_mW7.0 * pow(PI, -1.0) * pow(PHI, 2.0) * pow(E, -1.0)2.14599629electroweakH07_sigma_had_nb3.0 * pow(PI, 1.0) * pow(PHI, 1.0) * pow(E, 1.0)41.4527407electroweaktau_n_8pi_phi8_e3_27(8.0 / 27.0) * pow(PI, 1.0) * pow(PHI, 8.0) * pow(E, 3.0)878.335959electroweakvHiggs_4_3p6_phi2_pi34.0 * pow(3.0, 6.0) * pow(PI, -3.0) * pow(PHI, 2.0)246.214248electroweakK03_koide_cbt8.0 * pow(PHI, -1.0) * pow(E, -2.0)0.669134439leptonK01_koide_leptons8.0 * pow(PHI, -1.0) * pow(E, -2.0)0.669134439leptonK02_koide_uds4.0 * pow(PHI, -2.0) * pow(E, -1.0)0.562069771leptonL01_m_e2.0 * pow(PI, -2.0) * pow(PHI, 4.0) * pow(E, -1.0)0.510959325leptonL02_m_mu72.0 * pow(PI, -4.0) * pow(PHI, 2.0) * pow(E, 4.0)105.654066leptonP13_me_over_mmu_v03(8.0 / 9.0) * pow(PI, -2.0) * pow(PHI, -4.0) * pow(E, -1.0)0.00483395596leptonL4_mmu_me_alt8.0 * pow(PI, 2.0) * pow(PHI, 2.0)206.711678leptonr_e_54phi_pi354.0 * pow(PI, -3.0) * pow(PHI, 1.0)2.81794026leptonL04_ymu_ytaupow(3.0, -2.0) * pow(PI, -1.0) * pow(PHI, -1.0) * pow(E, 1.0)0.0594175116leptonQ02_m_d3.0 * pow(PHI, 3.0) * pow(E, -1.0)4.67508696quarkQ03_m_s7.0 * pow(PI, 1.0) * pow(PHI, 3.0)93.1560003quarkQ01_m_upow(PI, 2.0) * pow(PHI, 1.0) * pow(E, -2.0)2.16121723quarkP15_ms_over_mb_v03(4.0 / 9.0) * pow(PI, -3.0) * pow(PHI, 3.0) * pow(E, -1.0)0.0223375893quarkP16_mc_over_mt_v03(7.0 / 3.0) * pow(PI, -2.0) * pow(PHI, -1.0) * pow(E, -3.0)0.007274547quarkQ08_md_mupow(PI, 2.0) * pow(PHI, 1.0) * pow(E, -2.0)2.16121723quarkQ07_ms_md24.0 * pow(PI, -1.0) * pow(PHI, 2.0)20.0003064quarkC05_A_wolfenstein2.0 * pow(3.0, -1.0) * pow(PI, 2.0) * pow(PHI, 4.0) * pow(E, -4.0)0.82600204ckmJ_21gamma521.0 * pow(PI, -2.0) * pow(PHI, -19.0) * pow(E, -2.0)3.08010428e-05ckmV_cb_closest_v03(4.0 / 3.0) * pow(PHI, -1.0) * pow(E, -3.0)0.0410268006ckmP16_Vcb_gamma3_pipow(PI, 1.0) * pow(PHI, -9.0)0.0413295913ckmC2_Vcs_Vud_pow_nspow(7.0 * pow(PHI, -5.0) * pow(PI, 3.0) * pow(E, -3.0), 3.0 * pow(PHI, 3.0) * pow(PI, -4.0) * pow(E, 2.0))0.975285931ckmP8_Vtd_e3_81phi7(1.0 / 81.0) * pow(PHI, -7.0) * pow(E, 3.0)0.00854053241ckmP9_Vts_29164.0 * pow(3.0, 6.0) * pow(PI, -5.0) * pow(PHI, -3.0) * pow(E, -4.0)0.0412000087ckmP09_V_ts_v03(4.0 / 9.0) * pow(PI, -2.0) * pow(PHI, 4.0) * pow(E, -2.0)0.0417714291ckmP10_Vub_7_729phi2(7.0 / 729.0) * pow(PHI, -2.0)0.00366771204ckmC1_Vud_cos_thetaCcos(0.22673)0.974406675ckmC01_V_us2.0 * pow(3.0, -2.0) * pow(PI, -3.0) * pow(PHI, 3.0) * pow(E, 2.0)0.224331238ckmP6_Vus_3gamma_pi3.0 * pow(PI, -1.0) * pow(PHI, -3.0)0.225428313ckmC07_etabar3.0 * pow(PI, 2.0) * pow(PHI, -3.0) * pow(E, -3.0)0.347996306ckmC06_rhobar15.0 * pow(PI, -3.0) * pow(PHI, 6.0) * pow(E, -4.0)0.158997229ckmP04_dcp_over_2pi_v036.0 * pow(PHI, -5.0)0.541019662pmnsN06_dm31_1e3eV28.0 * pow(PI, -1.0) * pow(PHI, 2.0) * pow(E, -1.0)2.45256718pmnsN05_sin2_2th233.0 * pow(PI, -1.0) * pow(PHI, 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pow(PHI, -16.0) * pow(E, -21.0)80.3770011electroweakbf_W_mass_3636_phi4_pi_12_e83636.0 * pow(PI, -12.0) * pow(PHI, 4.0) * pow(E, 8.0)80.3770048electroweakbf_W_mass_86_phi12_pi8_e_1586.0 * pow(PI, 8.0) * pow(PHI, 12.0) * pow(E, -15.0)80.3770175electroweakbf_W_mass_320_phi_7_pi_7_e10320.0 * pow(PI, -7.0) * pow(PHI, -7.0) * pow(E, 10.0)80.3770767electroweakbf_W_mass_91_phi_13_pi_6_e1391.0 * pow(PI, -6.0) * pow(PHI, -13.0) * pow(E, 13.0)80.3768714electroweakbf_W_mass_104_phi_8_pi11_e_9104.0 * pow(PI, 11.0) * pow(PHI, -8.0) * pow(E, -9.0)80.3767571electroweakbf_W_mass_32_phi_7_pi2_e232.0 * pow(PI, 2.0) * pow(PHI, -7.0) * pow(E, 2.0)80.375781electroweakbf_W_mass_83_phi_6_pi_1_e483.0 * pow(PI, -1.0) * pow(PHI, -6.0) * pow(E, 4.0)80.3859791electroweakbf_W_mass_4_phi0_pi0_e34.0 * pow(E, 3.0)80.3421477electroweakbf_W_mass_1_phi_1_pi6_e_2pow(PI, 6.0) * pow(PHI, -1.0) * pow(E, -2.0)80.4123274electroweakbf_W_mass_14_phi_2_pi_2_e514.0 * pow(PI, -2.0) * pow(PHI, -2.0) * pow(E, 5.0)80.4128434electroweakbf_W_mass_10_phi_1_pi_3_e610.0 * pow(PI, -3.0) * pow(PHI, -1.0) * pow(E, 6.0)80.4136237electroweakbf_W_mass_12_phi1_pi_4_e612.0 * pow(PI, -4.0) * pow(PHI, 1.0) * pow(E, 6.0)80.4148557electroweakbf_Z_mass_10288_phi_30_pi_2_e1210288.0 * pow(PI, -2.0) * pow(PHI, -30.0) * pow(E, 12.0)91.1876electroweakbf_Z_mass_49979_phi_11_pi_7_e749979.0 * pow(PI, -7.0) * pow(PHI, -11.0) * pow(E, 7.0)91.1875997electroweakbf_Z_mass_37555_phi_8_pi_15_e1537555.0 * pow(PI, -15.0) * pow(PHI, -8.0) * pow(E, 15.0)91.1875994electroweakbf_Z_mass_24974_phi_8_pi_26_e2824974.0 * pow(PI, -26.0) * pow(PHI, -8.0) * pow(E, 28.0)91.1876007electroweakbf_Z_mass_18174_phi22_pi_13_e_118174.0 * pow(PI, -13.0) * pow(PHI, 22.0) * pow(E, -1.0)91.1875993electroweakbf_Z_mass_16956_phi12_pi0_e_1116956.0 * pow(PHI, 12.0) * pow(E, -11.0)91.1876009electroweakbf_Z_mass_22991_phi17_pi2_e_1622991.0 * pow(PI, 2.0) * pow(PHI, 17.0) * pow(E, -16.0)91.187599electroweakbf_Z_mass_4027_phi_26_pi5_e34027.0 * pow(PI, 5.0) * pow(PHI, -26.0) * pow(E, 3.0)91.1876014electroweakbf_Z_mass_6905_phi_19_pi_22_e306905.0 * pow(PI, -22.0) * pow(PHI, -19.0) * pow(E, 30.0)91.187598electroweakbf_Z_mass_3522_phi18_pi_16_e63522.0 * pow(PI, -16.0) * pow(PHI, 18.0) * pow(E, 6.0)91.187604electroweakbf_Z_mass_90_phi0_pi7_e_890.0 * pow(PI, 7.0) * pow(E, -8.0)91.1875953electroweakbf_Z_mass_163_phi5_pi7_e_11163.0 * pow(PI, 7.0) * pow(PHI, 5.0) * pow(E, -11.0)91.1875639electroweakbf_Z_mass_583_phi0_pi1_e_3583.0 * pow(PI, 1.0) * pow(E, -3.0)91.1874312electroweakbf_Z_mass_570_phi3_pi5_e_9570.0 * pow(PI, 5.0) * pow(PHI, 3.0) * pow(E, -9.0)91.1878136electroweakbf_Z_mass_357_phi_10_pi10_e_8357.0 * pow(PI, 10.0) * pow(PHI, -10.0) * pow(E, -8.0)91.187369electroweakbf_Z_mass_87_phi1_pi_3_e387.0 * pow(PI, -3.0) * pow(PHI, 1.0) * pow(E, 3.0)91.1886362electroweakbf_Z_mass_1_phi_7_pi13_e_7pow(PI, 13.0) * pow(PHI, -7.0) * pow(E, -7.0)91.195517electroweakbf_Z_mass_14_phi_8_pi5_e014.0 * pow(PI, 5.0) * pow(PHI, -8.0)91.1961023electroweakbf_Z_mass_12_phi_5_pi3_e112.0 * pow(PI, 3.0) * pow(PHI, -5.0) * pow(E, 1.0)91.1983844electroweakbf_Z_mass_8_phi0_pi3_e_18.0 * pow(PI, 3.0) * pow(E, -1.0)91.2525739electroweakbf_electron_mass_1_phi_14_pi8_e_10pow(PI, 8.0) * pow(PHI, -14.0) * pow(E, -10.0)0.000511007411leptonbf_electron_mass_10_phi_14_pi_1_e_210.0 * pow(PI, -1.0) * pow(PHI, -14.0) * pow(E, -2.0)0.000511015649leptonbf_electron_mass_12_phi_12_pi_2_e_212.0 * pow(PI, -2.0) * pow(PHI, -12.0) * pow(E, -2.0)0.000511023479leptonbf_muon_mass_17_phi12_pi1_e_1217.0 * pow(PI, 1.0) * pow(PHI, 12.0) * pow(E, -12.0)0.105661481leptonbf_muon_mass_8_phi2_pi_2_e_38.0 * pow(PI, -2.0) * pow(PHI, 2.0) * pow(E, -3.0)0.105653059leptonbf_tau_mass_31_phi_11_pi3_e_131.0 * pow(PI, 3.0) * pow(PHI, -11.0) * pow(E, -1.0)1.77685827leptonbf_tau_mass_28_phi13_pi_7_e_128.0 * pow(PI, -7.0) * pow(PHI, 13.0) * pow(E, -1.0)1.77686226leptonbf_tau_mass_46_phi3_pi9_e_1546.0 * pow(PI, 9.0) * pow(PHI, 3.0) * pow(E, -15.0)1.77685659leptonbf_tau_mass_2_phi14_pi1_e_82.0 * pow(PI, 1.0) * pow(PHI, 14.0) * pow(E, -8.0)1.77685086leptonbf_tau_mass_74_phi8_pi_4_e_374.0 * pow(PI, -4.0) * pow(PHI, 8.0) * pow(E, -3.0)1.77684648leptonbf_tau_mass_9_phi_4_pi9_e_109.0 * pow(PI, 9.0) * pow(PHI, -4.0) * pow(E, -10.0)1.77703501leptonbf_bottom_mass_1_phi_11_pi5_e1pow(PI, 5.0) * pow(PHI, -11.0) * pow(E, 1.0)4.18003389quarkbf_bottom_mass_10_phi_11_pi_4_e910.0 * pow(PI, -4.0) * pow(PHI, -11.0) * pow(E, 9.0)4.18010127quarkbf_bottom_mass_12_phi_9_pi_5_e912.0 * pow(PI, -5.0) * pow(PHI, -9.0) * pow(E, 9.0)4.18016532quarkbf_bottom_mass_9_phi_4_pi8_e_89.0 * pow(PI, 8.0) * pow(PHI, -4.0) * pow(E, -8.0)4.17960341quarkbf_charm_mass_7_phi_3_pi12_e_147.0 * pow(PI, 12.0) * pow(PHI, -3.0) * pow(E, -14.0)1.27002083quarkbf_charm_mass_5_phi_2_pi11_e_135.0 * pow(PI, 11.0) * pow(PHI, -2.0) * pow(E, -13.0)1.27003316quarkbf_charm_mass_6_phi0_pi10_e_136.0 * pow(PI, 10.0) * pow(E, -13.0)1.27005261quarkbf_charm_mass_17_phi_9_pi12_e_1217.0 * pow(PI, 12.0) * pow(PHI, -9.0) * pow(E, -12.0)1.27006178quarkbf_strange_mass_74_phi_7_pi_2_e_174.0 * pow(PI, -2.0) * pow(PHI, -7.0) * pow(E, -1.0)0.0950000887quarkbf_strange_mass_2_phi_1_pi3_e_62.0 * pow(PI, 3.0) * pow(PHI, -1.0) * pow(E, -6.0)0.095000323quarkbf_strange_mass_11_phi5_pi_8_e211.0 * pow(PI, -8.0) * pow(PHI, 5.0) * pow(E, 2.0)0.0949994014quarkbf_strange_mass_62_phi13_pi_12_e162.0 * pow(PI, -12.0) * pow(PHI, 13.0) * pow(E, 1.0)0.0950007475quarkbf_strange_mass_28_phi_2_pi_5_e128.0 * pow(PI, -5.0) * pow(PHI, -2.0) * pow(E, 1.0)0.0950009327quarkbf_top_mass_18_phi_9_pi11_e_618.0 * pow(PI, 11.0) * pow(PHI, -9.0) * pow(E, -6.0)172.689309quarkbf_top_mass_15_phi_11_pi12_e_615.0 * pow(PI, 12.0) * pow(PHI, -11.0) * pow(E, -6.0)172.686663quarkbf_top_mass_11_phi_10_pi_3_e1111.0 * pow(PI, -3.0) * pow(PHI, -10.0) * pow(E, 11.0)172.705419quarkbf_top_mass_13_phi8_pi12_e_1513.0 * pow(PI, 12.0) * pow(PHI, 8.0) * pow(E, -15.0)172.67351quarkbf_top_mass_15_phi3_pi0_e115.0 * pow(PHI, 3.0) * pow(E, 1.0)172.722399quarkbf_top_mass_6_phi4_pi3_e_26.0 * pow(PI, 3.0) * pow(PHI, 4.0) * pow(E, -2.0)172.568874quarkbf_top_mass_5_phi2_pi4_e_25.0 * pow(PI, 4.0) * pow(PHI, 2.0) * pow(E, -2.0)172.56623quarkbf_top_mass_7_phi1_pi5_e_37.0 * pow(PI, 5.0) * pow(PHI, 1.0) * pow(E, -3.0)172.564556quarkbf_V_cb_2_phi_6_pi0_e_12.0 * pow(PHI, -6.0) * pow(E, -1.0)0.0410024372ckmbf_V_cb_8_phi_5_pi_6_e48.0 * pow(PI, -6.0) * pow(PHI, -5.0) * pow(E, 4.0)0.0409666524ckmbf_V_cb_6_phi_5_pi_4_e26.0 * pow(PI, -4.0) * pow(PHI, -5.0) * pow(E, 2.0)0.0410395436ckmbf_V_cb_6_phi_11_pi9_e_106.0 * pow(PI, 9.0) * pow(PHI, -11.0) * pow(E, -10.0)0.0408029199ckmbf_V_cb_5_phi_13_pi10_e_105.0 * pow(PI, 10.0) * pow(PHI, -13.0) * pow(E, -10.0)0.0408022948ckmbf_V_cb_7_phi_14_pi11_e_117.0 * pow(PI, 11.0) * pow(PHI, -14.0) * pow(E, -11.0)0.0408018989ckmbf_V_cb_16_phi9_pi_9_e016.0 * pow(PI, -9.0) * pow(PHI, 9.0)0.0407999744ckmbf_V_cb_23_phi_6_pi_10_e823.0 * pow(PI, -10.0) * pow(PHI, -6.0) * pow(E, 8.0)0.0407999023ckmbf_V_cs_15_phi_3_pi_2_e115.0 * pow(PI, -2.0) * pow(PHI, -3.0) * pow(E, 1.0)0.975265979ckmbf_V_cs_14_phi1_pi_1_e_214.0 * pow(PI, -1.0) * pow(PHI, 1.0) * pow(E, -2.0)0.975836008ckmbf_V_cs_10_phi2_pi_2_e_110.0 * pow(PI, -2.0) * pow(PHI, 2.0) * pow(E, -1.0)0.975845476ckmbf_V_cs_12_phi4_pi_3_e_112.0 * pow(PI, -3.0) * pow(PHI, 4.0) * pow(E, -1.0)0.975860427ckmbf_V_cs_4_phi3_pi1_e_44.0 * pow(PI, 1.0) * pow(PHI, 3.0) * pow(E, -4.0)0.974978092ckmbf_V_td_11_phi0_pi_1_e_611.0 * pow(PI, -1.0) * pow(E, -6.0)0.00867912456ckmbf_V_td_13_phi_3_pi_6_e113.0 * pow(PI, -6.0) * pow(PHI, -3.0) * pow(E, 1.0)0.00867712147ckmbf_V_td_9_phi4_pi_6_e_29.0 * pow(PI, -6.0) * pow(PHI, 4.0) * pow(E, -2.0)0.00868370118ckmbf_V_td_3_phi3_pi_2_e_53.0 * pow(PI, -2.0) * pow(PHI, 3.0) * pow(E, -5.0)0.00867584972ckmbf_V_td_7_phi6_pi_4_e_57.0 * pow(PI, -4.0) * pow(PHI, 6.0) * pow(E, -5.0)0.00868864356ckmbf_V_ub_12_phi15_pi_9_e_512.0 * pow(PI, -9.0) * pow(PHI, 15.0) * pow(E, -5.0)0.0036997688ckmbf_V_ub_10_phi13_pi_8_e_510.0 * pow(PI, -8.0) * pow(PHI, 13.0) * pow(E, -5.0)0.00369971212ckmbf_V_ub_14_phi12_pi_7_e_614.0 * pow(PI, -7.0) * pow(PHI, 12.0) * pow(E, -6.0)0.00369967622ckmbf_V_ub_1_phi13_pi1_e_13pow(PI, 1.0) * pow(PHI, 13.0) * pow(E, -13.0)0.00369965248ckmbf_V_ub_4_phi_5_pi_4_e04.0 * pow(PI, -4.0) * pow(PHI, -5.0)0.00370273217ckmbf_V_ud_5_phi_4_pi2_e_25.0 * pow(PI, 2.0) * pow(PHI, -4.0) * pow(E, -2.0)0.974384182ckmbf_V_ud_6_phi_2_pi1_e_26.0 * pow(PI, 1.0) * pow(PHI, -2.0) * pow(E, -2.0)0.97439911ckmbf_V_ud_16_phi4_pi_5_e116.0 * pow(PI, -5.0) * pow(PHI, 4.0) * pow(E, 1.0)0.974127182ckmbf_V_ud_4_phi3_pi1_e_44.0 * pow(PI, 1.0) * pow(PHI, 3.0) * pow(E, -4.0)0.974978092ckmbf_V_ud_2_phi_3_pi5_e_52.0 * pow(PI, 5.0) * pow(PHI, -3.0) * pow(E, -5.0)0.973518096ckmbf_V_us_28_phi9_pi_8_e028.0 * pow(PI, -8.0) * pow(PHI, 9.0)0.224309575ckmbf_V_us_31_phi_15_pi2_e031.0 * pow(PI, 2.0) * pow(PHI, -15.0)0.22430907ckmbf_V_us_46_phi_1_pi8_e_1446.0 * pow(PI, 8.0) * pow(PHI, -1.0) * pow(E, -14.0)0.224308859ckmbf_V_us_20_phi10_pi_9_e120.0 * pow(PI, -9.0) * pow(PHI, 10.0) * pow(E, 1.0)0.224311751ckmbf_V_us_2_phi10_pi0_e_72.0 * pow(PHI, 10.0) * pow(E, -7.0)0.224308135ckmbf_V_us_9_phi_8_pi8_e_99.0 * pow(PI, 8.0) * pow(PHI, -8.0) * pow(E, -9.0)0.224331382ckmbf_V_us_11_phi2_pi1_e_611.0 * pow(PI, 1.0) * pow(PHI, 2.0) * pow(E, -6.0)0.22425955ckmbf_V_us_9_phi6_pi_4_e_29.0 * pow(PI, -4.0) * pow(PHI, 6.0) * pow(E, -2.0)0.224377806ckmbf_V_us_13_phi_1_pi_4_e113.0 * pow(PI, -4.0) * pow(PHI, -1.0) * pow(E, 1.0)0.224207793ckmbf_V_us_3_phi5_pi0_e_53.0 * pow(PHI, 5.0) * pow(E, -5.0)0.224174932ckmbf_theta_C_16_phi6_pi_1_e_616.0 * pow(PI, -1.0) * pow(PHI, 6.0) * pow(E, -6.0)0.22653174ckmbf_delta_CP_rad_16_phi_5_pi6_e_616.0 * pow(PI, 6.0) * pow(PHI, -5.0) * pow(E, -6.0)3.43806534pmnsbf_delta_CP_rad_7_phi0_pi2_e_37.0 * pow(PI, 2.0) * pow(E, -3.0)3.43965068pmnsbf_delta_CP_rad_5_phi1_pi1_e_25.0 * pow(PI, 1.0) * pow(PHI, 1.0) * pow(E, -2.0)3.43968406pmnsbf_delta_CP_rad_6_phi3_pi0_e_26.0 * pow(PHI, 3.0) * pow(E, -2.0)3.43973676pmnsbf_delta_CP_rad_2_phi2_pi4_e_52.0 * pow(PI, 4.0) * pow(PHI, 2.0) * pow(E, -5.0)3.43662668pmnsbf_delta_CP_6_phi4_pi_3_e56.0 * pow(PI, -3.0) * pow(PHI, 4.0) * pow(E, 5.0)196.845097pmnsbf_delta_CP_5_phi2_pi_2_e55.0 * pow(PI, -2.0) * pow(PHI, 2.0) * pow(E, 5.0)196.842082pmnsbf_delta_CP_7_phi1_pi_1_e47.0 * pow(PI, -1.0) * pow(PHI, 1.0) * pow(E, 4.0)196.840172pmnsbf_delta_CP_10_phi_6_pi6_e_110.0 * pow(PI, 6.0) * pow(PHI, -6.0) * pow(E, -1.0)197.0965pmnsbf_delta_CP_12_phi_4_pi5_e_112.0 * pow(PI, 5.0) * pow(PHI, -4.0) * pow(E, -1.0)197.09952pmnsbf_sin2theta12_11_phi0_pi_4_e111.0 * pow(PI, -4.0) * pow(E, 1.0)0.306964163pmnsbf_sin2theta12_3_phi3_pi_5_e23.0 * pow(PI, -5.0) * pow(PHI, 3.0) * pow(E, 2.0)0.306848338pmnsbf_sin2theta12_16_phi1_pi_3_e_116.0 * pow(PI, -3.0) * pow(PHI, 1.0) * pow(E, -1.0)0.307159197pmnsbf_sin2theta12_6_phi_5_pi3_e_46.0 * pow(PI, 3.0) * pow(PHI, -5.0) * pow(E, -4.0)0.30724494pmnsbf_sin2theta13_6_phi_6_pi_5_e36.0 * pow(PI, -5.0) * pow(PHI, -6.0) * pow(E, 3.0)0.021946208pmnsbf_sin2theta13_4_phi_1_pi_5_e14.0 * pow(PI, -5.0) * pow(PHI, -1.0) * pow(E, 1.0)0.0219592483pmnsbf_sin2theta23_10_phi2_pi_6_e310.0 * pow(PI, -6.0) * pow(PHI, 2.0) * pow(E, 3.0)0.546964941pmnsbf_sin2theta23_14_phi1_pi_5_e214.0 * pow(PI, -5.0) * pow(PHI, 1.0) * pow(E, 2.0)0.546959634pmnsbf_sin2theta23_1_phi2_pi3_e_5pow(PI, 3.0) * pow(PHI, 2.0) * pow(E, -5.0)0.546956124pmnsbf_sin2theta23_8_phi_5_pi5_e_68.0 * pow(PI, 5.0) * pow(PHI, -5.0) * pow(E, -6.0)0.547185094pmnsbf_sin2theta23_3_phi3_pi_1_e_23.0 * pow(PI, -1.0) * pow(PHI, 3.0) * pow(E, -2.0)0.547451108pmnsbf_sin2theta23_4_phi3_pi_3_e04.0 * pow(PI, -3.0) * pow(PHI, 3.0)0.546478769pmnsbf_theta13_2_phi_3_pi_1_e02.0 * pow(PI, -1.0) * pow(PHI, -3.0)0.150285542pmnsbf_theta13_11_phi3_pi_12_e811.0 * pow(PI, -12.0) * pow(PHI, 3.0) * pow(E, 8.0)0.150284084pmnsbf_theta13_15_phi2_pi3_e_915.0 * pow(PI, 3.0) * pow(PHI, 2.0) * pow(E, -9.0)0.150267763pmnsbf_theta12_13_phi_5_pi9_e_1113.0 * pow(PI, 9.0) * pow(PHI, -5.0) * pow(E, -11.0)0.583599222pmnsbf_theta12_4_phi_4_pi0_e04.0 * pow(PHI, -4.0)0.583592135pmnsbf_theta12_3_phi15_pi1_e_103.0 * pow(PI, 1.0) * pow(PHI, 15.0) * pow(E, -10.0)0.583634441pmnsbf_theta12_25_phi13_pi_7_e_225.0 * pow(PI, -7.0) * pow(PHI, 13.0) * pow(E, -2.0)0.583634907pmnsbf_theta12_42_phi14_pi_7_e_342.0 * pow(PI, -7.0) * pow(PHI, 14.0) * pow(E, -3.0)0.583638186pmnsbf_theta12_30_phi15_pi_8_e_230.0 * pow(PI, -8.0) * pow(PHI, 15.0) * pow(E, -2.0)0.583643849pmnsbf_theta23_37_phi2_pi_5_e137.0 * pow(PI, -5.0) * pow(PHI, 2.0) * pow(E, 1.0)0.860443034pmnsbf_theta23_1_phi8_pi0_e_4pow(PHI, 8.0) * pow(E, -4.0)0.860445157pmnsbf_theta23_23_phi_3_pi8_e_1123.0 * pow(PI, 8.0) * pow(PHI, -3.0) * pow(E, -11.0)0.860447933pmnsbf_theta23_14_phi7_pi_8_e314.0 * pow(PI, -8.0) * pow(PHI, 7.0) * pow(E, 3.0)0.860450679pmnsbf_theta23_10_phi8_pi_9_e410.0 * pow(PI, -9.0) * pow(PHI, 8.0) * pow(E, 4.0)0.860459028pmnsbf_theta23_12_phi10_pi_10_e412.0 * pow(PI, -10.0) * pow(PHI, 10.0) * pow(E, 4.0)0.860472211pmnsbf_Omega_b_7_phi_2_pi0_e_47.0 * pow(PHI, -2.0) * pow(E, -4.0)0.0489716607cosmologybf_Omega_b_6_phi1_pi_2_e_36.0 * pow(PI, -2.0) * pow(PHI, 1.0) * pow(E, -3.0)0.0489728862cosmologybf_Omega_b_9_phi_4_pi_2_e_19.0 * pow(PI, -2.0) * pow(PHI, -4.0) * pow(E, -1.0)0.0489438041cosmologybf_Omega_b_4_phi6_pi_2_e_54.0 * pow(PI, -2.0) * pow(PHI, 6.0) * pow(E, -5.0)0.0490019856cosmologybf_Omega_b_2_phi0_pi2_e_62.0 * pow(PI, 2.0) * pow(E, -6.0)0.0489286068cosmologybf_ns_16_phi1_pi_2_e_116.0 * pow(PI, -2.0) * pow(PHI, 1.0) * pow(E, -1.0)0.964969075cosmologybf_ns_6_phi_5_pi4_e_46.0 * pow(PI, 4.0) * pow(PHI, -5.0) * pow(E, -4.0)0.965238447cosmologybf_ns_7_phi6_pi_6_e27.0 * pow(PI, -6.0) * pow(PHI, 6.0) * pow(E, 2.0)0.965414037cosmologybf_ns_4_phi0_pi4_e_64.0 * pow(PI, 4.0) * pow(E, -6.0)0.965811986cosmologybf_mH_mZ_1_phi_5_pi5_e_3pow(PI, 5.0) * pow(PHI, -5.0) * pow(E, -3.0)1.3738133higgsbf_mH_mZ_14_phi_6_pi_3_e414.0 * pow(PI, -3.0) * pow(PHI, -6.0) * pow(E, 4.0)1.37382212higgsbf_mH_mZ_10_phi_5_pi_4_e510.0 * pow(PI, -4.0) * pow(PHI, -5.0) * pow(E, 5.0)1.37383545higgsbf_mH_mZ_12_phi_3_pi_5_e512.0 * pow(PI, -5.0) * pow(PHI, -3.0) * pow(E, 5.0)1.3738565higgsbf_mH_mZ_4_phi_4_pi_1_e24.0 * pow(PI, -1.0) * pow(PHI, -4.0) * pow(E, 2.0)1.37261431higgsbf_mH_mZ_8_phi2_pi_5_e38.0 * pow(PI, -5.0) * pow(PHI, 2.0) * pow(E, 3.0)1.37467283higgsbf_H_mass_15_phi_3_pi_3_e715.0 * pow(PI, -3.0) * pow(PHI, -3.0) * pow(E, 7.0)125.239145higgsbf_Tc_7_phi2_pi1_e17.0 * pow(PI, 1.0) * pow(PHI, 2.0) * pow(E, 1.0)156.501201qcdbf_Tc_5_phi3_pi0_e25.0 * pow(PHI, 3.0) * pow(E, 2.0)156.50272qcdbf_Tc_6_phi5_pi_1_e26.0 * pow(PI, -1.0) * pow(PHI, 5.0) * pow(E, 2.0)156.505117qcdbf_Tc_16_phi_3_pi5_e_216.0 * pow(PI, 5.0) * pow(PHI, -3.0) * pow(E, -2.0)156.429069qcdbf_Tc_9_phi0_pi_1_e49.0 * pow(PI, -1.0) * pow(E, 4.0)156.412178qcdbf_Tc_2_phi4_pi3_e_12.0 * pow(PI, 3.0) * pow(PHI, 4.0) * pow(E, -1.0)156.363612qcd"; +/// Start of each field in FORMULA_TEXT. +pub const FIELD_START : [1432]u32 = [ + 0, 9, 23, 34, 48, 59, 71, 80, 94, 105, 117, 128, 142, 164, 211, 221, + 235, 242, 269, 280, 294, 300, 305, 310, 324, 344, 372, 382, 393, 412, 446, 456, + 467, 484, 499, 510, 516, 529, 563, 573, 579, 591, 608, 618, 624, 631, 640, 651, + 657, 672, 712, 722, 727, 739, 783, 793, 798, 816, 836, 846, 851, 864, 873, 883, + 886, 890, 946, 960, 963, 967, 982, 993, 996, 1012, 1041, 1052, 1056, 1069, 1086, 1095, + 1099, 1115, 1165, 1179, 1183, 1198, 1201, 1204, 1213, 1226, 1283, 1293, 1298, 1310, 1360, 1371, + 1374, 1386, 1436, 1447, 1450, 1462, 1502, 1515, 1518, 1537, 1577, 1588, 1592, 1604, 1624, 1633, + 1637, 1655, 1699, 1710, 1716, 1732, 1783, 1795, 1798, 1813, 1849, 1861, 1870, 1880, 1929, 1940, + 1949, 1962, 2027, 2037, 2051, 2067, 2089, 2099, 2113, 2130, 2164, 2174, 2188, 2210, 2262, 2273, + 2287, 2302, 2344, 2355, 2369, 2391, 2440, 2450, 2464, 2485, 2527, 2538, 2552, 2563, 2623, 2634, + 2648, 2659, 2716, 2726, 2737, 2754, 2820, 2831, 2842, 2861, 2927, 2937, 2948, 2966, 2985, 2995, + 3006, 3028, 3086, 3096, 3107, 3121, 3171, 3181, 3192, 3208, 3256, 3266, 3277, 3297, 3354, 3364, + 3375, 3396, 3447, 3457, 3468, 3481, 3516, 3527, 3533, 3550, 3585, 3596, 3602, 3615, 3650, 3661, + 3667, 3674, 3724, 3735, 3741, 3749, 3799, 3809, 3815, 3834, 3893, 3906, 3912, 3925, 3959, 3969, + 3975, 3988, 4024, 4034, 4040, 4052, 4113, 4125, 4131, 4138, 4172, 4182, 4187, 4194, 4228, 4238, + 4243, 4250, 4293, 4303, 4308, 4326, 4384, 4396, 4401, 4419, 4478, 4489, 4494, 4503, 4546, 4556, + 4561, 4570, 4606, 4616, 4621, 4638, 4704, 4714, 4717, 4727, 4780, 4794, 4797, 4813, 4856, 4868, + 4871, 4888, 4917, 4929, 4932, 4949, 5055, 5066, 5069, 5085, 5128, 5141, 5144, 5155, 5222, 5234, + 5237, 5249, 5307, 5319, 5322, 5339, 5369, 5382, 5385, 5402, 5414, 5425, 5428, 5436, 5502, 5513, + 5516, 5532, 5568, 5579, 5582, 5592, 5642, 5653, 5656, 5666, 5717, 5728, 5731, 5751, 5771, 5782, + 5786, 5801, 5851, 5861, 5865, 5879, 5929, 5940, 5944, 5960, 6018, 6029, 6033, 6050, 6094, 6105, + 6109, 6125, 6177, 6189, 6193, 6205, 6250, 6262, 6266, 6278, 6344, 6355, 6359, 6376, 6405, 6415, + 6419, 6432, 6474, 6484, 6493, 6499, 6549, 6559, 6568, 6580, 6630, 6640, 6649, 6665, 6699, 6710, + 6719, 6734, 6785, 6797, 6806, 6814, 6873, 6882, 6891, 6901, 6959, 6970, 6979, 6986, 7019, 7029, + 7034, 7051, 7101, 7111, 7116, 7130, 7166, 7175, 7180, 7198, 7240, 7251, 7254, 7261, 7289, 7298, + 7301, 7309, 7357, 7367, 7370, 7385, 7428, 7438, 7441, 7454, 7472, 7482, 7485, 7511, 7531, 7541, + 7555, 7568, 7621, 7630, 7641, 7654, 7707, 7717, 7728, 7741, 7794, 7804, 7815, 7828, 7881, 7891, + 7902, 7915, 7954, 7964, 7975, 7988, 8026, 8036, 8047, 8060, 8114, 8124, 8135, 8147, 8212, 8222, + 8228, 8242, 8308, 8318, 8324, 8336, 8386, 8398, 8401, 8413, 8466, 8479, 8482, 8494, 8561, 8574, + 8577, 8589, 8639, 8650, 8653, 8666, 8727, 8740, 8744, 8758, 8792, 8802, 8806, 8822, 8873, 8883, + 8887, 8901, 8952, 8961, 8965, 8983, 9043, 9053, 9062, 9083, 9149, 9159, 9168, 9183, 9248, 9258, + 9267, 9281, 9348, 9359, 9368, 9379, 9445, 9455, 9464, 9480, 9546, 9557, 9566, 9579, 9646, 9658, + 9667, 9680, 9731, 9741, 9750, 9758, 9809, 9820, 9829, 9845, 9906, 9917, 9926, 9943, 9946, 9947, + 9956, 9974, 10033, 10043, 10050, 10065, 10115, 10125, 10132, 10146, 10195, 10205, 10212, 10226, 10276, 10286, + 10293, 10313, 10363, 10374, 10381, 10404, 10437, 10447, 10454, 10475, 10526, 10536, 10543, 10559, 10624, 10633, + 10640, 10656, 10675, 10678, 10685, 10711, 10776, 10786, 10794, 10814, 10880, 10889, 10897, 10914, 10949, 10959, + 10967, 10982, 11002, 11013, 11021, 11036, 11086, 11096, 11104, 11115, 11181, 11191, 11199, 11210, 11261, 11271, + 11279, 11296, 11345, 11355, 11363, 11374, 11424, 11435, 11443, 11454, 11504, 11514, 11522, 11534, 11583, 11593, + 11601, 11621, 11667, 11678, 11686, 11707, 11753, 11764, 11772, 11785, 11837, 11848, 11856, 11868, 11914, 11925, + 11933, 11947, 11993, 12004, 12012, 12026, 12092, 12102, 12110, 12128, 12180, 12191, 12199, 12218, 12269, 12279, + 12285, 12307, 12357, 12367, 12373, 12397, 12463, 12473, 12479, 12497, 12563, 12572, 12581, 12609, 12659, 12669, + 12678, 12709, 12768, 12778, 12787, 12813, 12879, 12889, 12898, 12922, 12973, 12983, 12988, 13009, 13059, 13069, + 13084, 13111, 13114, 13115, 13130, 13152, 13165, 13166, 13181, 13194, 13259, 13269, 13284, 13313, 13365, 13378, + 13392, 13421, 13473, 13486, 13500, 13528, 13579, 13592, 13606, 13634, 13685, 13698, 13712, 13739, 13788, 13798, + 13812, 13839, 13872, 13882, 13896, 13922, 13972, 13983, 13997, 14022, 14071, 14082, 14096, 14121, 14141, 14152, + 14166, 14194, 14246, 14257, 14271, 14299, 14351, 14362, 14376, 14404, 14456, 14469, 14483, 14511, 14563, 14576, + 14590, 14618, 14670, 14683, 14697, 14723, 14773, 14786, 14800, 14824, 14874, 14884, 14898, 14922, 14972, 14983, + 14997, 15021, 15073, 15087, 15098, 15122, 15174, 15188, 15199, 15222, 15267, 15281, 15292, 15316, 15368, 15382, + 15393, 15423, 15478, 15488, 15499, 15528, 15582, 15592, 15603, 15634, 15690, 15700, 15711, 15743, 15800, 15810, + 15821, 15849, 15902, 15912, 15923, 15950, 16002, 16012, 16023, 16051, 16104, 16114, 16125, 16153, 16206, 16216, + 16227, 16255, 16308, 16318, 16329, 16354, 16404, 16413, 16424, 16450, 16501, 16511, 16522, 16545, 16562, 16572, + 16583, 16608, 16652, 16662, 16673, 16699, 16750, 16760, 16771, 16797, 16848, 16858, 16869, 16894, 16944, 16954, + 16965, 16996, 17052, 17059, 17070, 17100, 17155, 17165, 17176, 17207, 17263, 17273, 17284, 17315, 17371, 17381, + 17392, 17423, 17479, 17489, 17500, 17530, 17570, 17580, 17591, 17621, 17676, 17685, 17696, 17724, 17777, 17787, + 17798, 17829, 17885, 17894, 17905, 17934, 17988, 17997, 18008, 18033, 18067, 18077, 18088, 18115, 18167, 18177, + 18188, 18214, 18249, 18259, 18270, 18296, 18347, 18357, 18368, 18397, 18451, 18460, 18471, 18496, 18546, 18556, + 18567, 18593, 18638, 18647, 18658, 18683, 18719, 18729, 18740, 18765, 18815, 18825, 18836, 18860, 18893, 18903, + 18914, 18948, 18994, 19008, 19014, 19049, 19102, 19116, 19122, 19157, 19210, 19224, 19230, 19260, 19312, 19323, + 19329, 19357, 19407, 19418, 19424, 19453, 19505, 19515, 19521, 19550, 19602, 19612, 19618, 19646, 19697, 19707, + 19713, 19740, 19790, 19800, 19806, 19834, 19885, 19895, 19901, 19929, 19980, 19990, 19996, 20026, 20070, 20080, + 20085, 20117, 20169, 20179, 20184, 20215, 20266, 20276, 20281, 20311, 20361, 20371, 20376, 20407, 20459, 20469, + 20474, 20505, 20557, 20567, 20572, 20602, 20637, 20647, 20652, 20684, 20737, 20747, 20752, 20785, 20837, 20849, + 20854, 20885, 20935, 20946, 20951, 20982, 21032, 21044, 21049, 21082, 21134, 21146, 21151, 21183, 21234, 21246, + 21251, 21280, 21332, 21342, 21347, 21377, 21430, 21440, 21445, 21475, 21528, 21538, 21543, 21572, 21624, 21633, + 21638, 21664, 21698, 21708, 21713, 21739, 21788, 21798, 21803, 21829, 21878, 21887, 21892, 21918, 21967, 21977, + 21982, 22005, 22040, 22052, 22055, 22078, 22128, 22140, 22143, 22166, 22216, 22228, 22231, 22256, 22308, 22320, + 22323, 22349, 22402, 22414, 22417, 22443, 22496, 22508, 22511, 22534, 22570, 22582, 22585, 22610, 22662, 22674, + 22677, 22701, 22752, 22763, 22766, 22790, 22841, 22852, 22855, 22879, 22930, 22941, 22944, 22968, 23019, 23030, + 23033, 23055, 23104, 23115, 23118, 23142, 23177, 23190, 23193, 23217, 23268, 23281, 23284, 23307, 23357, 23370, + 23373, 23396, 23446, 23459, 23462, 23485, 23535, 23548, 23551, 23576, 23628, 23640, 23643, 23668, 23720, 23733, + 23736, 23761, 23813, 23826, 23829, 23853, 23898, 23911, 23914, 23937, 23973, 23986, 23989, 24012, 24062, 24073, + 24076, 24099, 24149, 24159, 24162, 24185, 24235, 24246, 24249, 24271, 24320, 24331, 24334, 24357, 24407, 24418, + 24421, 24444, 24480, 24491, 24494, 24518, 24555, 24565, 24568, 24593, 24645, 24656, 24659, 24683, 24734, 24745, + 24748, 24771, 24806, 24817, 24820, 24843, 24893, 24904, 24907, 24930, 24980, 24990, 24993, 25016, 25066, 25077, + 25080, 25104, 25155, 25166, 25169, 25191, 25225, 25236, 25239, 25266, 25317, 25327, 25330, 25362, 25413, 25423, + 25427, 25457, 25490, 25500, 25504, 25534, 25583, 25593, 25597, 25627, 25661, 25671, 25675, 25705, 25754, 25764, + 25768, 25794, 25843, 25853, 25857, 25883, 25932, 25942, 25946, 25972, 26021, 26031, 26035, 26063, 26114, 26122, + 26126, 26154, 26205, 26214, 26218, 26248, 26282, 26293, 26297, 26326, 26375, 26386, 26390, 26421, 26472, 26483, + 26487, 26517, 26567, 26577, 26581, 26611, 26661, 26672, 26676, 26706, 26756, 26768, 26772, 26802, 26852, 26863, + 26867, 26897, 26947, 26958, 26962, 26991, 27034, 27045, 27049, 27079, 27129, 27140, 27144, 27174, 27224, 27235, + 27239, 27268, 27303, 27314, 27318, 27344, 27380, 27391, 27395, 27422, 27473, 27484, 27488, 27514, 27564, 27575, + 27579, 27607, 27659, 27670, 27674, 27699, 27719, 27730, 27734, 27761, 27812, 27823, 27827, 27855, 27907, 27918, + 27922, 27950, 28002, 28013, 28017, 28045, 28097, 28108, 28112, 28138, 28188, 28199, 28203, 28228, 28256, 28267, + 28271, 28299, 28351, 28362, 28366, 28392, 28442, 28453, 28457, 28483, 28533, 28544, 28548, 28576, 28628, 28639, + 28643, 28669, 28704, 28716, 28725, 28751, 28801, 28813, 28822, 28849, 28900, 28912, 28921, 28947, 28997, 29009, + 29018, 29043, 29076, 29088, 29097, 29119, 29170, 29181, 29190, 29211, 29261, 29272, 29281, 29301, 29350, 29361, + 29370, 29390, 29423, 29434, 29443, 29467, 29511, 29520, 29525, 29550, 29601, 29611, 29616, 29641, 29692, 29702, + 29707, 29732, 29783, 29792, 29797, 29821, 29871, 29881, 29886, 29909, 29958, 29968, 29973, 29999, 30050, 30060, + 30065, 30084, 30132, 30142, 30145, 30164, 30197, 30206, 30209, 30229, 30278, 30288, 30291, 30313, 30364, 30374, + 30377, 30397, 30430, 30440, 30443, 30463, 30512, 30522 +]; +/// Length of each field. +pub const FIELD_LEN : [1432]u32 = [ + 9, 14, 11, 14, 11, 12, 9, 14, 11, 12, 11, 14, 22, 47, 10, 14, + 7, 27, 11, 14, 6, 5, 5, 14, 20, 28, 10, 11, 19, 34, 10, 11, + 17, 15, 11, 6, 13, 34, 10, 6, 12, 17, 10, 6, 7, 9, 11, 6, + 15, 40, 10, 5, 12, 44, 10, 5, 18, 20, 10, 5, 13, 9, 10, 3, + 4, 56, 14, 3, 4, 15, 11, 3, 16, 29, 11, 4, 13, 17, 9, 4, + 16, 50, 14, 4, 15, 3, 3, 9, 13, 57, 10, 5, 12, 50, 11, 3, + 12, 50, 11, 3, 12, 40, 13, 3, 19, 40, 11, 4, 12, 20, 9, 4, + 18, 44, 11, 6, 16, 51, 12, 3, 15, 36, 12, 9, 10, 49, 11, 9, + 13, 65, 10, 14, 16, 22, 10, 14, 17, 34, 10, 14, 22, 52, 11, 14, + 15, 42, 11, 14, 22, 49, 10, 14, 21, 42, 11, 14, 11, 60, 11, 14, + 11, 57, 10, 11, 17, 66, 11, 11, 19, 66, 10, 11, 18, 19, 10, 11, + 22, 58, 10, 11, 14, 50, 10, 11, 16, 48, 10, 11, 20, 57, 10, 11, + 21, 51, 10, 11, 13, 35, 11, 6, 17, 35, 11, 6, 13, 35, 11, 6, + 7, 50, 11, 6, 8, 50, 10, 6, 19, 59, 13, 6, 13, 34, 10, 6, + 13, 36, 10, 6, 12, 61, 12, 6, 7, 34, 10, 5, 7, 34, 10, 5, + 7, 43, 10, 5, 18, 58, 12, 5, 18, 59, 11, 5, 9, 43, 10, 5, + 9, 36, 10, 5, 17, 66, 10, 3, 10, 53, 14, 3, 16, 43, 12, 3, + 17, 29, 12, 3, 17, 106, 11, 3, 16, 43, 13, 3, 11, 67, 12, 3, + 12, 58, 12, 3, 17, 30, 13, 3, 17, 12, 11, 3, 8, 66, 11, 3, + 16, 36, 11, 3, 10, 50, 11, 3, 10, 51, 11, 3, 20, 20, 11, 4, + 15, 50, 10, 4, 14, 50, 11, 4, 16, 58, 11, 4, 17, 44, 11, 4, + 16, 52, 12, 4, 12, 45, 12, 4, 12, 66, 11, 4, 17, 29, 10, 4, + 13, 42, 10, 9, 6, 50, 10, 9, 12, 50, 10, 9, 16, 34, 11, 9, + 15, 51, 12, 9, 8, 59, 9, 9, 10, 58, 11, 9, 7, 33, 10, 5, + 17, 50, 10, 5, 14, 36, 9, 5, 18, 42, 11, 3, 7, 28, 9, 3, + 8, 48, 10, 3, 15, 43, 10, 3, 13, 18, 10, 3, 26, 20, 10, 14, + 13, 53, 9, 11, 13, 53, 10, 11, 13, 53, 10, 11, 13, 53, 10, 11, + 13, 39, 10, 11, 13, 38, 10, 11, 13, 54, 10, 11, 12, 65, 10, 6, + 14, 66, 10, 6, 12, 50, 12, 3, 12, 53, 13, 3, 12, 67, 13, 3, + 12, 50, 11, 3, 13, 61, 13, 4, 14, 34, 10, 4, 16, 51, 10, 4, + 14, 51, 9, 4, 18, 60, 10, 9, 21, 66, 10, 9, 15, 65, 10, 9, + 14, 67, 11, 9, 11, 66, 10, 9, 16, 66, 11, 9, 13, 67, 12, 9, + 13, 51, 10, 9, 8, 51, 11, 9, 16, 61, 11, 9, 17, 3, 1, 9, + 18, 59, 10, 7, 15, 50, 10, 7, 14, 49, 10, 7, 14, 50, 10, 7, + 20, 50, 11, 7, 23, 33, 10, 7, 21, 51, 10, 7, 16, 65, 9, 7, + 16, 19, 3, 7, 26, 65, 10, 8, 20, 66, 9, 8, 17, 35, 10, 8, + 15, 20, 11, 8, 15, 50, 10, 8, 11, 66, 10, 8, 11, 51, 10, 8, + 17, 49, 10, 8, 11, 50, 11, 8, 11, 50, 10, 8, 12, 49, 10, 8, + 20, 46, 11, 8, 21, 46, 11, 8, 13, 52, 11, 8, 12, 46, 11, 8, + 14, 46, 11, 8, 14, 66, 10, 8, 18, 52, 11, 8, 19, 51, 10, 6, + 22, 50, 10, 6, 24, 66, 10, 6, 18, 66, 9, 9, 28, 50, 10, 9, + 31, 59, 10, 9, 26, 66, 10, 9, 24, 51, 10, 5, 21, 50, 10, 15, + 27, 3, 1, 15, 22, 13, 1, 15, 13, 65, 10, 15, 29, 52, 13, 14, + 29, 52, 13, 14, 28, 51, 13, 14, 28, 51, 13, 14, 27, 49, 10, 14, + 27, 33, 10, 14, 26, 50, 11, 14, 25, 49, 11, 14, 25, 20, 11, 14, + 28, 52, 11, 14, 28, 52, 11, 14, 28, 52, 13, 14, 28, 52, 13, 14, + 28, 52, 13, 14, 26, 50, 13, 14, 24, 50, 10, 14, 24, 50, 11, 14, + 24, 52, 14, 11, 24, 52, 14, 11, 23, 45, 14, 11, 24, 52, 14, 11, + 30, 55, 10, 11, 29, 54, 10, 11, 31, 56, 10, 11, 32, 57, 10, 11, + 28, 53, 10, 11, 27, 52, 10, 11, 28, 53, 10, 11, 28, 53, 10, 11, + 28, 53, 10, 11, 25, 50, 9, 11, 26, 51, 10, 11, 23, 17, 10, 11, + 25, 44, 10, 11, 26, 51, 10, 11, 26, 51, 10, 11, 25, 50, 10, 11, + 31, 56, 7, 11, 30, 55, 10, 11, 31, 56, 10, 11, 31, 56, 10, 11, + 31, 56, 10, 11, 30, 40, 10, 11, 30, 55, 9, 11, 28, 53, 10, 11, + 31, 56, 9, 11, 29, 54, 9, 11, 25, 34, 10, 11, 27, 52, 10, 11, + 26, 35, 10, 11, 26, 51, 10, 11, 29, 54, 9, 11, 25, 50, 10, 11, + 26, 45, 9, 11, 25, 36, 10, 11, 25, 50, 10, 11, 24, 33, 10, 11, + 34, 46, 14, 6, 35, 53, 14, 6, 35, 53, 14, 6, 30, 52, 11, 6, + 28, 50, 11, 6, 29, 52, 10, 6, 29, 52, 10, 6, 28, 51, 10, 6, + 27, 50, 10, 6, 28, 51, 10, 6, 28, 51, 10, 6, 30, 44, 10, 5, + 32, 52, 10, 5, 31, 51, 10, 5, 30, 50, 10, 5, 31, 52, 10, 5, + 31, 52, 10, 5, 30, 35, 10, 5, 32, 53, 10, 5, 33, 52, 12, 5, + 31, 50, 11, 5, 31, 50, 12, 5, 33, 52, 12, 5, 32, 51, 12, 5, + 29, 52, 10, 5, 30, 53, 10, 5, 30, 53, 10, 5, 29, 52, 9, 5, + 26, 34, 10, 5, 26, 49, 10, 5, 26, 49, 9, 5, 26, 49, 10, 5, + 23, 35, 12, 3, 23, 50, 12, 3, 23, 50, 12, 3, 25, 52, 12, 3, + 26, 53, 12, 3, 26, 53, 12, 3, 23, 36, 12, 3, 25, 52, 12, 3, + 24, 51, 11, 3, 24, 51, 11, 3, 24, 51, 11, 3, 24, 51, 11, 3, + 22, 49, 11, 3, 24, 35, 13, 3, 24, 51, 13, 3, 23, 50, 13, 3, + 23, 50, 13, 3, 23, 50, 13, 3, 25, 52, 12, 3, 25, 52, 13, 3, + 25, 52, 13, 3, 24, 45, 13, 3, 23, 36, 13, 3, 23, 50, 11, 3, + 23, 50, 10, 3, 23, 50, 11, 3, 22, 49, 11, 3, 23, 50, 11, 3, + 23, 36, 11, 3, 24, 37, 10, 3, 25, 52, 11, 3, 24, 51, 11, 3, + 23, 35, 11, 3, 23, 50, 11, 3, 23, 50, 10, 3, 23, 50, 11, 3, + 24, 51, 11, 3, 22, 34, 11, 3, 27, 51, 10, 3, 32, 51, 10, 4, + 30, 33, 10, 4, 30, 49, 10, 4, 30, 34, 10, 4, 30, 49, 10, 4, + 26, 49, 10, 4, 26, 49, 10, 4, 26, 49, 10, 4, 28, 51, 8, 4, + 28, 51, 9, 4, 30, 34, 11, 4, 29, 49, 11, 4, 31, 51, 11, 4, + 30, 50, 10, 4, 30, 50, 11, 4, 30, 50, 12, 4, 30, 50, 11, 4, + 30, 50, 11, 4, 29, 43, 11, 4, 30, 50, 11, 4, 30, 50, 11, 4, + 29, 35, 11, 4, 26, 36, 11, 4, 27, 51, 11, 4, 26, 50, 11, 4, + 28, 52, 11, 4, 25, 20, 11, 4, 27, 51, 11, 4, 28, 52, 11, 4, + 28, 52, 11, 4, 28, 52, 11, 4, 26, 50, 11, 4, 25, 28, 11, 4, + 28, 52, 11, 4, 26, 50, 11, 4, 26, 50, 11, 4, 28, 52, 11, 4, + 26, 35, 12, 9, 26, 50, 12, 9, 27, 51, 12, 9, 26, 50, 12, 9, + 25, 33, 12, 9, 22, 51, 11, 9, 21, 50, 11, 9, 20, 49, 11, 9, + 20, 33, 11, 9, 24, 44, 9, 5, 25, 51, 10, 5, 25, 51, 10, 5, + 25, 51, 9, 5, 24, 50, 10, 5, 23, 49, 10, 5, 26, 51, 10, 5, + 19, 48, 10, 3, 19, 33, 9, 3, 20, 49, 10, 3, 22, 51, 10, 3, + 20, 33, 10, 3, 20, 49, 10, 3 +]; +/// Deviation from the measured value, in thousandths of a percent, signed (-0.62 percent = -620). Rows 0..31: the registry claim; rows 32..: recomputed. +pub const ERR_MILLI_PCT : [358]i64 = [ + -620, 0, 0, 29, 29, 0, 34, 27, 29, 29, 28, 0, 34, 43, 0, 96, + 43, 1360, 62, 18, 36, 0, 22, 17, 80, 37, 98, 17, 78, 21, 41, 94, + -24, 344, -15, -5, 88, 35, 5, 30, -86, 7, -13, -1, 6, -56, -66, -7, + -2, 20, 371, 12, -8, -4, -125, -27, 0, -71, 109, -261, 56, -11, -212, -36, + 2, 0, 3, -178, 559, -20, 6, 0, -68, -604, 6, 9, 499, -1, -2, -120, + -18, 0, 7, -140, 27, 40, -3, 283, -11, 0, -84, -4, 4, 9, -37, 2, + 101, -95, -21, 39, -140, 86, -2, 62, 0, 0, 0, 0, 0, 0, 0, -7, + 3, 7, 2, 23, 11, -586, 107, -23, 83, 5, -6, -28, -115, -53, -52, 11, + -18, -57, 33, 0, 6, -2, -16, -27, 8, 23, 2, 83, 17, -24, -19, -37, + 0, -19, -23, -145, -22, -8, 110, -94, 57, -18, 65, 405, 503, -79, -5, 1, + -8, 4, 8, 3, 2, 16, 2, -42, 0, 0, 111, 0, -1, -4, 10, -55, + 63, -87, 300, 311, 311, 311, 1, 1, 1, -9, -88, 90, 0, -1, -2, 2, + 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 11, -43, 44, 45, 46, 47, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, + 9, 9, 12, 71, 1, 3, 5, 1, -7, 0, 0, 0, -1, -1, 10, 1, + 2, 4, -9, 2, 3, 4, 5, 0, 0, -1, 1, 1, 0, -2, 9, -10, + 19, -70, -72, -73, 6, -81, 96, -481, -482, -483, -488, -488, -22, 36, 37, 39, + -51, -10, -33, 43, -48, 100, -6, -8, -9, -9, 74, 4, 5, -23, 64, -85, + 0, 0, -1, 1, -1, 10, -22, 30, -46, -60, 10, -7, 39, 40, 42, -49, + -61, -62, -63, 67, 68, -12, -49, 52, 80, -17, 42, -6, -7, -8, 34, 82, + -95, -10, -11, -21, 0, -1, 6, 6, 7, 8, 5, 5, 6, 6, 7, 8, + 3, 6, -53, 65, -85, 7, 35, 53, 95, 20, 21, 22, 23, -67, 82, 31, + 1, 2, 3, -45, -56, -87 +]; +/// The same deviation recomputed against the measured value the source cites, for every row. +pub const REPRO_MILLI_PCT : [358]i64 = [ + -616, 0, 0, 0, 29, 0, 34, -27, -55506, -51090, -99914, 1, -47233, 3219148, -83056, 3694197, + -98175, 1361, 62, -18, -99906, 0, -22, 3, -113, -6189, -98, -18, 1592, -193, 625, -94, + -24, 344, -15, -5, 88, 35, 5, 30, -86, 7, -13, -1, 6, -56, -66, -7, + -2, 20, 371, 12, -8, -4, -125, -27, 0, -71, 109, -261, 56, -11, -212, -36, + 2, 0, 3, -178, 559, -20, 6, 0, -68, -604, 6, 9, 499, -1, -2, -120, + -18, 0, 7, -140, 27, 40, -3, 283, -11, 0, -84, -4, 4, 9, -37, 2, + 101, -95, -21, 39, -140, 86, -2, 62, 0, 0, 0, 0, 0, 0, 0, -7, + 3, 7, 2, 23, 11, -586, 107, -23, 83, 5, -6, -28, -115, -53, -52, 11, + -18, -57, 33, 0, 6, -2, -16, -27, 8, 23, 2, 83, 17, -24, -19, -37, + 0, -19, -23, -145, -22, -8, 110, -94, 57, -18, 65, 405, 503, -79, -5, 1, + -8, 4, 8, 3, 2, 16, 2, -42, 0, 0, 111, 0, -1, -4, 10, -55, + 63, -87, 300, 311, 311, 311, 1, 1, 1, -9, -88, 90, 0, -1, -2, 2, + 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 11, -43, 44, 45, 46, 47, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, + 9, 9, 12, 71, 1, 3, 5, 1, -7, 0, 0, 0, -1, -1, 10, 1, + 2, 4, -9, 2, 3, 4, 5, 0, 0, -1, 1, 1, 0, -2, 9, -10, + 19, -70, -72, -73, 6, -81, 96, -481, -482, -483, -488, -488, -22, 36, 37, 39, + -51, -10, -33, 43, -48, 100, -6, -8, -9, -9, 74, 4, 5, -23, 64, -85, + 0, 0, -1, 1, -1, 10, -22, 30, -46, -60, 10, -7, 39, 40, 42, -49, + -61, -62, -63, 67, 68, -12, -49, 52, 80, -17, 42, -6, -7, -8, 34, 82, + -95, -10, -11, -21, 0, -1, 6, 6, 7, 8, 5, 5, 6, 6, 7, 8, + 3, 6, -53, 65, -85, 7, 35, 53, 95, 20, 21, 22, 23, -67, 82, 31, + 1, 2, 3, -45, -56, -87 +]; +/// Complexity of the expression (registry cx for rows 0..31; |k|+|m|+|p|+|q| plus one for a coefficient other than 1 for the rest; 9 for a closed form). +pub const COMPLEXITY : [358]u32 = [ + 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 6, 6, 2, 5, 6, 5, 6, + 7, 3, 5, 7, 5, 4, 5, 10, 4, 10, 10, 9, 9, 5, 4, 13, 12, 4, 4, 4, 8, 11, 8, 5, 5, 5, 5, 5, 5, 8, 7, 5, + 4, 12, 24, 5, 10, 9, 11, 19, 9, 3, 9, 11, 5, 9, 14, 6, 5, 5, 10, 4, 10, 5, 8, 3, 4, 11, 5, 6, 6, 11, 9, 6, + 10, 3, 8, 5, 5, 3, 6, 2, 10, 15, 15, 13, 8, 4, 19, 15, 13, 7, 9, 11, 6, 12, 5, 11, 9, 8, 10, 11, 12, 13, 9, 10, + 7, 8, 9, 0, 9, 10, 8, 8, 7, 3, 8, 9, 4, 7, 10, 7, 2, 10, 10, 8, 6, 8, 10, 4, 5, 7, 5, 5, 5, 9, 7, 6, + 12, 10, 18, 9, 8, 17, 9, 10, 1, 1, 7, 11, 28, 23, 26, 12, 9, 14, 20, 10, 28, 10, 15, 27, 15, 19, 14, 10, 19, 18, 13, 18, + 42, 15, 48, 58, 25, 36, 25, 33, 29, 12, 12, 4, 9, 10, 11, 12, 45, 26, 39, 63, 37, 24, 36, 35, 72, 41, 16, 24, 5, 18, 29, 8, + 27, 14, 10, 5, 32, 18, 17, 26, 8, 16, 22, 28, 24, 16, 24, 17, 25, 24, 21, 30, 27, 24, 34, 11, 11, 16, 27, 9, 27, 30, 25, 36, + 5, 10, 9, 10, 8, 16, 12, 31, 34, 37, 19, 25, 7, 5, 6, 9, 9, 8, 11, 13, 11, 16, 30, 27, 26, 27, 10, 9, 6, 11, 9, 14, + 18, 18, 24, 21, 18, 26, 10, 13, 7, 11, 14, 18, 6, 5, 6, 12, 13, 10, 7, 14, 11, 6, 11, 6, 13, 15, 8, 12, 9, 10, 17, 7, + 7, 5, 24, 15, 26, 5, 27, 23, 25, 26, 9, 12, 23, 19, 22, 25, 7, 7, 8, 14, 9, 5, 14, 15, 11, 13, 14, 15, 14, 8, 11, 14, + 5, 6, 9, 11, 6, 9 +]; +/// Sector index. Sector names in order: gauge-coupling, electroweak, lepton, quark, ckm, pmns, cosmology, higgs, qcd, quantum, nuclear, particle, planck, condensed, astro, quantum-gravity. +pub const SECTOR_OF : [358]u32 = [ + 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 4, 4, 4, 5, 5, 2, 8, 6, 6, + 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, + 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, + 7, 7, 8, 8, 8, 8, 8, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, + 6, 6, 6, 6, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, + 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, + 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, + 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, + 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, + 8, 8, 8, 8, 8, 8 +]; +/// 0 VERIFIED, 1 candidate, 2 conjecture. VERIFIED rows come first, then candidates, then conjectures. +pub const TAG_OF : [358]u32 = [ + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, + 2, 2, 2, 2, 2, 2 +]; +/// 0 = monomial n * 3^k * pi^m * phi^p * e^q; 1 ln2/pi, 2 ln3/pi, 3 alpha_inv Pellis, 4 1/(phi^4+phi), 5 1+alpha*phi^-3, 6 (5/phi)^4, 7 cos(0.22673), 8 (7 phi^-5 pi^3 e^-3)^(3 phi^3 pi^-4 e^2). +pub const RECIPE_KIND : [358]u32 = [ + 0, 1, 2, 3, 4, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0 +]; +/// The coefficient n of a monomial recipe. +pub const RECIPE_N : [358]f64 = [ + 1.0, 0.0, 0.0, 0.0, 0.0, 156.5, 0.0, 8.0, + 1.0, 2.0, 4.0, 2.0, 5.0, 36.0, 0.6666666666666666, 22.5, + 0.14285714285714285, 1.0, 3.0, 9.0, 4.0, 122.0, 0.125, 7.0, + 7.0, 2.0, 8.0, 9.0, 1.0, 4.0, 4.0, 3.0, + 4.0, 360.0, 3.0, 4.0, 0.3333333333333333, 2.0, 0.0027434842249657062, 1.0, + 1.3333333333333333, 4.0, 2.0, 0.0, 0.02880658436213992, 7.0, 3.0, 0.2962962962962963, + 4.0, 8.0, 8.0, 4.0, 2.0, 72.0, 0.8888888888888888, 8.0, + 54.0, 1.0, 3.0, 7.0, 1.0, 0.4444444444444444, 2.3333333333333335, 1.0, + 24.0, 2.0, 21.0, 1.3333333333333333, 1.0, 0.0, 0.012345679012345678, 4.0, + 0.4444444444444444, 0.009602194787379973, 0.0, 2.0, 3.0, 3.0, 15.0, 6.0, + 8.0, 3.0, 2.3333333333333335, 1.0, 18.0, 0.03, 4.0, 22.5, + 0.3333333333333333, 24.0, 5.0, 2.0, 5.0, 0.006858710562414266, 2.3333333333333335, 4.0, + 5.0, 7.0, 0.1111111111111111, 1.0, 3.0, 0.6666666666666666, 6.0, 10.0, + 8715.0, 4055.0, 9433.0, 5722.0, 9981.0, 750.0, 6087.0, 4.0, + 7.0, 4.0, 5.0, 2.0, 7.0, 1.0, 5.0, 9.0, + 7.0, 1.0, 5.0, 4.0, 4.0, 8.0, 8.0, 8.0, + 8.0, 4.0, 1.0, 1.0, 1.0, 8.0, 7.0, 5.0, + 2.0, 2.0, 3.0, 4.0, 5.0, 4.0, 8.0, 8.0, + 2.0, 5.0, 2.0, 8.0, 5.0, 2.0, 9.0, 8.0, + 1.0, 1.0, 8.0, 1.0, 1.0, 4.0, 4.0, 8.0, + 8.0, 3.0, 4.0, 8.0, 1.0, 8.0, 7.0, 4.0, + 2.0, 1.0, 7.0, 36.0, 29.0, 3.0, 4.0, 8.0, + 9.0, 2.0, 2.0, 9.0, 75.0, 57.0, 9.0, 75.0, + 57.0, 2.0, 4.0, 3.0, 10.0, 14.0, 1.0, 12.0, + 15316.0, 35289.0, 6441.0, 26676.0, 3636.0, 86.0, 320.0, 91.0, + 104.0, 32.0, 83.0, 4.0, 1.0, 14.0, 10.0, 12.0, + 10288.0, 49979.0, 37555.0, 24974.0, 18174.0, 16956.0, 22991.0, 4027.0, + 6905.0, 3522.0, 90.0, 163.0, 583.0, 570.0, 357.0, 87.0, + 1.0, 14.0, 12.0, 8.0, 1.0, 10.0, 12.0, 17.0, + 8.0, 31.0, 28.0, 46.0, 2.0, 74.0, 9.0, 1.0, + 10.0, 12.0, 9.0, 7.0, 5.0, 6.0, 17.0, 74.0, + 2.0, 11.0, 62.0, 28.0, 18.0, 15.0, 11.0, 13.0, + 15.0, 6.0, 5.0, 7.0, 2.0, 8.0, 6.0, 6.0, + 5.0, 7.0, 16.0, 23.0, 15.0, 14.0, 10.0, 12.0, + 4.0, 11.0, 13.0, 9.0, 3.0, 7.0, 12.0, 10.0, + 14.0, 1.0, 4.0, 5.0, 6.0, 16.0, 4.0, 2.0, + 28.0, 31.0, 46.0, 20.0, 2.0, 9.0, 11.0, 9.0, + 13.0, 3.0, 16.0, 16.0, 7.0, 5.0, 6.0, 2.0, + 6.0, 5.0, 7.0, 10.0, 12.0, 11.0, 3.0, 16.0, + 6.0, 6.0, 4.0, 10.0, 14.0, 1.0, 8.0, 3.0, + 4.0, 2.0, 11.0, 15.0, 13.0, 4.0, 3.0, 25.0, + 42.0, 30.0, 37.0, 1.0, 23.0, 14.0, 10.0, 12.0, + 7.0, 6.0, 9.0, 4.0, 2.0, 16.0, 6.0, 7.0, + 4.0, 1.0, 14.0, 10.0, 12.0, 4.0, 8.0, 15.0, + 7.0, 5.0, 6.0, 16.0, 9.0, 2.0 +]; +/// Exponent of 3. +pub const RECIPE_K : [358]i64 = [ + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 2, 0, 0, -2, 0, 0, 0, -2, 0, 3, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, + 0, -1, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 5, -3, -3, 1, -3, -3, -1, 4, 4, 4, -1, 3, 3, 4, 1, -1, + -2, 2, 3, 0, 3, 4, 1, 0, 1, 0, 4, 4, 3, 2, 2, 2, -1, 3, 4, 4, 1, 0, 4, 1, 1, -1, -1, 1, 1, 2, -2, 2, + -4, 4, -6, -3, -3, 5, -3, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0 +]; +/// Exponent of pi. +pub const RECIPE_M : [358]i64 = [ + 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 1, 1, 0, -2, 0, 1, 0, -4, 0, 3, 3, 3, -4, 1, 0, -1, -1, -3, -4, + -1, 0, 0, -2, 0, 1, 3, 2, 1, -2, -1, 0, 4, -1, 1, 1, -3, 0, 0, 0, -2, -4, -2, 2, -3, -1, 0, 1, 2, -3, -2, 2, + -1, 2, -2, 0, 1, 0, 0, -5, -2, 0, 0, -3, -1, 2, -3, 0, -1, -1, -3, -1, -2, 1, 1, 0, 2, 1, 1, 0, -1, 4, -2, 0, + 0, -1, 0, 4, 2, 1, 5, 0, -5, -2, -8, -2, -2, -1, -7, 1, -4, -2, -1, -3, -1, -2, 0, 0, 0, -2, -1, -3, -1, -3, -2, -3, + 0, 0, -2, 0, -2, -3, -3, -3, 0, 0, -1, -1, 0, -1, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, -2, 0, -1, -1, -2, -2, 0, + 0, -2, 4, 0, 3, -3, 0, 0, 0, 0, -1, -4, -13, 6, -7, 3, 5, -6, -8, 0, -8, -2, -1, -9, -3, -9, -6, -4, -12, -11, -3, -13, + 7, 3, 16, 20, -12, 8, -7, -6, 11, 2, -1, 0, 6, -2, -3, -4, -2, -7, -15, -26, -13, 0, 2, 5, -22, -16, 7, 7, 1, 5, 10, -3, + 13, 5, 3, 3, 8, -1, -2, 1, -2, 3, -7, 9, 1, -4, 9, 5, -4, -5, 8, 12, 11, 10, 12, -2, 3, -8, -12, -5, 11, 12, -3, 12, + 0, 3, 4, 5, 0, -6, -4, 9, 10, 11, -9, -10, -2, -1, -2, -3, 1, -1, -6, -6, -2, -4, -9, -8, -7, 1, -4, 2, 1, -5, 1, 5, + -8, 2, 8, -9, 0, 8, 1, -4, -4, 0, -1, 6, 2, 1, 0, 4, -3, -2, -1, 6, 5, -4, -5, -3, 3, -5, -5, -6, -5, 3, 5, -1, + -3, -1, -12, 3, 9, 0, 1, -7, -7, -8, -5, 0, 8, -8, -9, -10, 0, -2, -2, -2, 2, -2, 4, -6, 4, 5, -3, -4, -5, -1, -5, -3, + 1, 0, -1, 5, -1, 3 +]; +/// Exponent of phi. +pub const RECIPE_P : [358]i64 = [ + -3, 0, 0, 0, 0, 0, 0, 2, -1, 2, -2, 0, -2, 4, 1, -2, -2, -1, -8, -2, -2, 0, 2, -5, -5, -4, -5, -2, -2, -2, -2, 3, + 1, -2, 2, 2, 2, 1, 0, 3, 1, 1, 3, 0, 1, 2, 1, 8, 2, -1, -1, -2, 4, 2, -4, 2, 1, -1, 3, 3, 1, 3, -1, 1, + 2, 4, -19, -1, -9, 0, -7, -3, 4, -2, 0, 3, -3, -3, 6, -5, 2, -2, 5, 2, -5, -3, 2, -2, 1, 6, -2, 2, -1, 5, 5, 3, + 4, -1, 5, 1, 1, -1, 0, 1, -2, 7, -1, -8, -5, -2, 10, 5, 2, 0, -4, -4, 0, -5, 0, -3, -3, -1, 4, 2, -4, 2, -4, 3, + 2, -2, -3, 0, 2, 0, 0, -1, 2, 1, 2, 1, 0, 1, 3, 4, 0, 4, 3, -2, 3, 4, 4, 1, -3, 4, -1, -3, -3, 2, 2, -1, + 4, 1, 6, 3, 1, -6, -2, 4, 0, 0, 1, -4, -5, -6, -11, 5, 0, -2, 9, -9, -11, -6, -10, -12, -7, 8, -2, -2, -4, -5, -4, -2, + 14, 1, -16, -16, 4, 12, -7, -13, -8, -7, -6, 0, -1, -2, -1, 1, -30, -11, -8, -8, 22, 12, 17, -26, -19, 18, 0, 5, 0, 3, -10, 1, + -7, -8, -5, 0, -14, -14, -12, 12, 2, -11, 13, 3, 14, 8, -4, -11, -11, -9, -4, -3, -2, 0, -9, -7, -1, 5, 13, -2, -9, -11, -10, 8, + 3, 4, 2, 1, -6, -5, -5, -11, -13, -14, 9, -6, -3, 1, 2, 4, 3, 0, -3, 4, 3, 6, 15, 13, 12, 13, -5, -4, -2, 4, 3, -3, + 9, -15, -1, 10, 10, -8, 2, 6, -1, 5, 6, -5, 0, 1, 3, 2, 4, 2, 1, -6, -4, 0, 3, 1, -5, -6, -1, 2, 1, 2, -5, 3, + 3, -3, 3, 2, -5, -4, 15, 13, 14, 15, 2, 8, -3, 7, 8, 10, -2, 1, -4, 6, 0, 1, -5, 6, 0, -5, -6, -5, -3, -4, 2, -3, + 2, 3, 5, -3, 0, 4 +]; +/// Exponent of e. +pub const RECIPE_Q : [358]i64 = [ + 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 2, 0, 0, -2, -1, 1, 0, -4, 0, -2, -3, -3, 1, -2, 0, 2, -3, 0, 2, + 2, 0, -2, 0, -2, -1, 1, -3, -1, -3, -1, 0, 3, -1, 1, 3, 0, -2, -2, -1, -1, 4, -1, 0, 0, 1, -1, 0, -2, -1, -3, -2, + 0, -4, -2, -3, 0, 0, 3, -4, -2, 0, 0, 2, 0, -3, -4, 0, -1, 1, -1, -1, -2, 0, -3, 0, 0, -3, -1, -3, -3, -1, -1, 2, + -2, 0, -2, 0, 1, 0, 0, 0, 2, -5, 5, 2, 0, 0, -1, -4, -1, 1, 0, -2, 1, 2, 3, -3, -1, 1, 3, 2, -3, -3, 1, -2, + -2, -3, -1, 0, 2, -2, 3, 3, -3, 1, 0, 2, 0, 2, -2, 0, 0, -2, -1, -1, 1, -1, -1, 1, 0, 0, -2, 0, 0, -2, 0, -2, + 3, -2, -1, 2, 1, 2, 3, -1, 0, 0, 3, -2, 9, -10, 7, -3, -3, 5, 2, 0, 8, -1, -3, 5, -4, -1, 5, 3, 2, 1, -6, 2, + -20, -10, -15, -21, 8, -15, 10, 13, -9, 2, 4, 3, -2, 5, 6, 6, 12, 7, 15, 28, -1, -11, -16, 3, 30, 6, -8, -11, -3, -9, -8, 3, + -7, 0, 1, -1, -10, -2, -2, -12, -3, -1, -1, -15, -8, -3, -10, 1, 9, 9, -8, -14, -13, -13, -12, -1, -6, 2, 1, 1, -6, -6, 11, -15, + 1, -2, -2, -3, -1, 4, 2, -10, -10, -11, 0, 8, 1, -2, -1, -1, -4, -6, 1, -2, -5, -5, -5, -5, -6, -13, 0, -2, -2, 1, -4, -5, + 0, 0, -14, 1, -7, -9, -6, -2, 1, -5, -6, -6, -3, -2, -2, -5, 5, 5, 4, -1, -1, 1, 2, -1, -4, 3, 1, 3, 2, -5, -6, -2, + 0, 0, 8, -9, -11, 0, -10, -2, -3, -2, 1, -4, -11, 3, 4, 4, -4, -3, -1, -5, -6, -1, -4, 2, -6, -3, 4, 5, 5, 2, 3, 7, + 1, 2, 2, -2, 4, -1 +]; +/// The value of the formula as recomputed in float math when the table was built. +pub const VALUE : [358]f64 = [ + 0.23606797749978967, 0.2206356001526516, 0.3496991525660598, 137.03599916476563, + 0.11803398874989485, 156.5, 1.0017226712621337, 206.7116782205399, + 0.22736199840626878, 51.67791955513498, 1.5278640450004206, 0.6666666666666666, + 2.207242829461467, 5727.853456169522, 3.388802461543506, 8.594235253127366, + 0.0007482349157000298, 0.22736199840626878, 0.5453364005846908, 3.4376941012509463, + 0.0002872812570393472, 122.0, 1.3732384273235516, 0.9743747276384436, + 0.9743747276384436, 0.00814281233387034, 0.3066992363465198, 3.4376941012509463, + 0.8983877275708474, 0.024213155572004822, 0.04927595985657853, 0.9639924854766465, + 137.00273342910018, 137.50776405003785, 1.0629371141716377, 0.11789435669156006, + 0.11810412379684863, 3.7400122673791, 0.23123127151778447, 0.23127927165774131, + 2.4933415115860664, 0.8815119511311851, 80.35882551624907, 91.18627109394714, + 91.19317640604524, 2.1459962855274672, 41.452740681529484, 878.3359592854905, + 246.21424848618344, 0.6691344393385642, 0.6691344393385642, 0.5620697710606941, + 0.510959324934586, 105.65406566725304, 0.004833955958145068, 206.7116782205399, + 2.8179402607217354, 0.05941751158424663, 4.675086960980594, 93.15600026754218, + 2.161217232981792, 0.022337589348187793, 0.007274546996605354, 2.161217232981792, + 20.00030642362259, 0.8260020396362309, 3.080104284026266e-05, 0.041026800602072894, + 0.04132959128020561, 0.975285931257137, 0.008540532409520962, 0.041200008706771964, + 0.04177142909294953, 0.00366771204218208, 0.9744066745247079, 0.2243312378140147, + 0.2254283131487871, 0.3479963057893335, 0.15899722876124278, 0.5410196624968453, + 2.4525671834599625, 0.9914951255221358, 0.30702298273653966, 0.3065708979324953, + 0.022255922208747985, 0.02224888271583419, 0.5459846639804432, 8.594235253127366, + 5.323118458826043, 67.36022206074955, 2.207242829461467, 0.26068847437456516, + 0.04897213586299087, 2.7257478998559703, 0.9645411470483388, 125.20217569851857, + 125.22624717622841, 1.3770843003168525, 0.16676569894216717, 157.61122010624854, + 130.22762559625576, 1.2944073591503107, 1836.1181087116884, 16.18033988749895, + 80.37698496793203, 80.3770727139288, 91.18756570171567, 91.1876345154696, + 91.18766791343391, 91.18766817532311, 91.18766886674533, 206.75458846109768, + 16.818436562378373, 0.04080289367895239, 0.008600145651389213, 0.0038208686437625292, + 0.22432562429725392, 0.0025002719750601013, 33.475894871979435, 8.568033618193894, + 49.240863048501005, 13.787709203935389, 73.0353111189703, 67.38114423779483, + 0.24971226624765736, 2.7240634716719687, 0.9643960373713371, 0.04930523931917093, + 0.31494433012492973, 0.684610844987134, 0.23757821560211306, 1.0, + 52.9210269319826, 2.828371314671409, 13.603577099437224, 2.0017792895314077, + 0.7820654231236955, 8.796544778895893, 202.5031025391787, 1233.0246008619017, + 135.0, 137.00273342910018, 4.182218395972038, 493.49534156997737, + 0.6666666666666666, 125.22624717622841, 80.35882551624907, 91.05530291183246, + 172.72239911032406, 0.510959324934586, 1838.1612535844174, 105.55853734675071, + 0.2254283131487871, 0.23148857467523093, 0.2230448131128547, 0.2254283131487871, + 0.2254283131487871, 1.2923765585428928, 0.11789435669156006, 6.022209954047078, + 13.596870925274196, 5.391445316241101, 3.5282821973844842, 9.274235236927302, + 5.050890763798015, 25.817237193416698, 1.989035072465441, 816.96055714863, + 2.0, 3.0, 217.2403570922326, 0.007297321578715593, + 0.007297293074164602, 0.007297092144219436, 0.007298073166366016, 136.96019340582046, + 137.12240671485281, 0.1179309748398957, 0.11838828795798698, 0.11840055746782352, + 0.11840065210373174, 0.11840084091653294, 0.0011596656373136225, 0.0011596665642181335, + 0.0011596684135313643, 0.001159545464493085, 0.2358619496797914, 0.2362816141982678, + 1.1663796409698802e-05, 1.1663683241225188e-05, 1.166360838674034e-05, 1.166397511283626e-05, + 80.37699990113505, 80.37699972904143, 80.37699948367316, 80.37700113967301, + 80.37700480136283, 80.37701753476692, 80.37707666549154, 80.37687139996942, + 80.3767570528868, 80.37578096937197, 80.38597909322519, 80.34214769275066, + 80.4123273786457, 80.41284344735635, 80.41362366391091, 80.41485569560433, + 91.18760000606916, 91.18759969545178, 91.18759935971194, 91.18760065563148, + 91.18759932525086, 91.1876009359342, 91.18759897615095, 91.18760142479037, + 91.1875980030083, 91.18760397711748, 91.18759529035462, 91.18756390126582, + 91.18743123707218, 91.18781359174405, 91.18736899963933, 91.18863619265784, + 91.19551704146, 91.19610231432088, 91.19838440247048, 91.25257390364656, + 0.0005110074114553424, 0.0005110156491397806, 0.0005110234785031012, 0.10566148113819, + 0.10565305914218473, 1.7768582671662083, 1.776862262661358, 1.7768565932506566, + 1.7768508592215893, 1.776846475806294, 1.77703500825754, 4.180033887625999, + 4.180101271776082, 4.180165315864807, 4.17960340936459, 1.2700208327413482, + 1.2700331552912778, 1.2700526136992905, 1.2700617847702986, 0.09500008867966682, + 0.09500032304141243, 0.09499940137675045, 0.09500074746376999, 0.09500093273268514, + 172.6893087417148, 172.68666297807258, 172.70541932493677, 172.67351036616026, + 172.72239911032406, 172.5688741147445, 172.56623019627483, 172.56455586519232, + 0.04100243721412261, 0.0409666524251677, 0.04103954358241853, 0.04080291990707137, + 0.04080229476772273, 0.040801898881747296, 0.04079997440631623, 0.04079990226981861, + 0.9752659794265858, 0.9758360080999094, 0.9758454762815508, 0.9758604273868475, + 0.9749780921252159, 0.008679124555557414, 0.008677121473271914, 0.008683701183875755, + 0.00867584971706659, 0.008688643559684104, 0.003699768802990369, 0.003699712119030865, + 0.003699676222418938, 0.0036996524788593757, 0.0037027321697519484, 0.9743841816418124, + 0.9743991103583493, 0.9741271820907669, 0.9749780921252159, 0.9735180963630653, + 0.22430957475768565, 0.22430907036978978, 0.22430885905611983, 0.22431175115185445, + 0.22430813519718676, 0.22433138201423844, 0.22425955029554637, 0.22437780561058082, + 0.2242077927329401, 0.22417493187550397, 0.22653173958643327, 3.4380653400773658, + 3.4396506835656475, 3.439684057244406, 3.439736757266875, 3.436626680306593, + 196.84509741899035, 196.8420815658047, 196.84017169725664, 197.0965002395369, + 197.09951999071708, 0.3069641631561059, 0.30684833833410086, 0.30715919655372464, + 0.3072449402530345, 0.021946208005984933, 0.02195924830348957, 0.5469649409271982, + 0.5469596339769298, 0.5469561237322851, 0.5471850935462309, 0.5474511078539102, + 0.5464787689508329, 0.15028554209919143, 0.15028408407390342, 0.15026776275393522, + 0.5835992221443722, 0.5835921350012617, 0.583634440854237, 0.5836349073450758, + 0.5836381864922902, 0.5836438493212047, 0.8604430340725036, 0.8604451567540112, + 0.8604479334741358, 0.8604506789026307, 0.8604590275424162, 0.8604722107910315, + 0.048971660708789735, 0.048972886173954726, 0.048943804076218816, 0.04900198555208853, + 0.04892860678407225, 0.9649690753757244, 0.9652384471515681, 0.965414037087827, + 0.9658119857105002, 1.3738133000300896, 1.3738221168630496, 1.3738354465590614, + 1.3738564953407801, 1.3726143074251305, 1.3746728321504487, 125.23914485380382, + 156.50120114895043, 156.5027196231482, 156.50511742966285, 156.4290693591337, + 156.412178306061, 156.36361155458218 +]; +/// The measured value the source cites (CODATA 2022 / PDG 2024 / NuFIT / Planck 2018 / lattice QCD), in the unit of the formula. +pub const MEASURED : [358]f64 = [ + 0.23753, 0.2206356001526516, 0.3496991525660598, 137.035999177, + 0.118, 156.5, 1.00137841931, 206.768283, + 0.51099895, 105.6583755, 1776.86, 0.666661, + 4.183, 172.57, 20.0, 0.22651, + 0.041, 0.22431, 0.545, 3.4382986264288293, + 0.307, 122.0, 1.37354, 0.97435, + 0.97548, 0.00868, 0.307, 3.4382986264288293, + 0.88431, 0.02426, 0.04897, 0.9649, + 137.036, 137.036, 1.0631, 0.1179, + 0.118, 3.7387, 0.23122, 0.23121, + 2.4955, 0.8814466001956406, 80.369, 91.1876, + 91.188, 2.1472, 41.48, 878.4, + 246.22, 0.669, 0.66666, 0.562, + 0.511, 105.658, 0.00484, 206.768, + 2.8179403, 0.05946, 4.67, 93.4, + 2.16, 0.02234, 0.00729, 2.162, + 20.0, 0.826, 3.08e-05, 0.0411, + 0.0411, 0.97548, 0.00854, 0.0412, + 0.0418, 0.00369, 0.97435, 0.22431, + 0.22431, 0.348, 0.159, 0.54167, + 2.453, 0.9915, 0.307, 0.307, + 0.02225, 0.02224, 0.546, 8.57, + 5.3237, 67.36, 2.2091, 0.2607, + 0.04897, 2.7255, 0.9649, 125.2, + 125.1, 1.3784, 0.1668, 157.55, + 130.41, 1.2933, 1836.15267343, 16.170247902886, + 80.377, 80.377, 91.1876, 91.1876, + 91.1876, 91.1876, 91.1876, 206.77, + 16.818, 0.0408, 0.0086, 0.00382, + 0.2243, 0.002515, 33.44, 8.57, + 49.2, 13.787, 73.04, 67.4, + 0.25, 2.7255, 0.9649, 0.0493, + 0.315, 0.685, 0.2375, 1.0, + 52.9177, 2.828427, 13.6057, 2.002319, + 0.782, 8.7945, 202.5, 1232.0, + 134.977, 137.036, 4.183, 493.677, + 0.66667, 125.25, 80.377, 91.1876, + 172.76, 0.511, 1836.15, 105.658, + 0.2253, 0.23153, 0.2229, 0.22452, + 0.2243, 1.2934, 0.1179, 6.02214, + 13.598, 5.391247, 3.528, 9.274, + 5.0508, 25.813, 1.989, 817.3, + 2.0, 3.0, 217.0, 0.0072973525693, + 0.0072973525693, 0.0072973525693, 0.0072973525693, 137.036, + 137.036, 0.118034, 0.118034, 0.118034, + 0.118034, 0.118034, 0.00115965218, 0.00115965218, + 0.00115965218, 0.00115965218, 0.23607, 0.23607, + 1.1663788e-05, 1.1663788e-05, 1.1663788e-05, 1.1663788e-05, + 80.377, 80.377, 80.377, 80.377, + 80.377, 80.377, 80.377, 80.377, + 80.377, 80.377, 80.377, 80.377, + 80.377, 80.377, 80.377, 80.377, + 91.1876, 91.1876, 91.1876, 91.1876, + 91.1876, 91.1876, 91.1876, 91.1876, + 91.1876, 91.1876, 91.1876, 91.1876, + 91.1876, 91.1876, 91.1876, 91.1876, + 91.1876, 91.1876, 91.1876, 91.1876, + 0.000511, 0.000511, 0.000511, 0.10566, + 0.10566, 1.77686, 1.77686, 1.77686, + 1.77686, 1.77686, 1.77686, 4.18, + 4.18, 4.18, 4.18, 1.27, + 1.27, 1.27, 1.27, 0.095, + 0.095, 0.095, 0.095, 0.095, + 172.69, 172.69, 172.69, 172.69, + 172.69, 172.69, 172.69, 172.69, + 0.041, 0.041, 0.041, 0.041, + 0.041, 0.041, 0.041, 0.041, + 0.97548, 0.97548, 0.97548, 0.97548, + 0.97548, 0.00868, 0.00868, 0.00868, + 0.00868, 0.00868, 0.0037, 0.0037, + 0.0037, 0.0037, 0.0037, 0.97435, + 0.97435, 0.97435, 0.97435, 0.97435, + 0.22431, 0.22431, 0.22431, 0.22431, + 0.22431, 0.22431, 0.22431, 0.22431, + 0.22431, 0.22431, 0.22651, 3.438299, + 3.438299, 3.438299, 3.438299, 3.438299, + 196.965, 196.965, 196.965, 196.965, + 196.965, 0.307, 0.307, 0.307, + 0.307, 0.02195, 0.02195, 0.547, + 0.547, 0.547, 0.547, 0.547, + 0.547, 0.1503, 0.1503, 0.1503, + 0.5836, 0.5836, 0.5836, 0.5836, + 0.5836, 0.5836, 0.8604, 0.8604, + 0.8604, 0.8604, 0.8604, 0.8604, + 0.04897, 0.04897, 0.04897, 0.04897, + 0.04897, 0.9649, 0.9649, 0.9649, + 0.9649, 1.37354, 1.37354, 1.37354, + 1.37354, 1.37354, 1.37354, 125.2, + 156.5, 156.5, 156.5, 156.5, + 156.5, 156.5 +]; + +pub const PHI : f64 = 1.6180339887498948; +pub const PI : f64 = 3.141592653589793; +pub const LN3 : f64 = 1.0986122886681098; +pub const LNPI : f64 = 1.1447298858494002; +pub const LNPHI : f64 = 0.48121182505960347; pub fn formula_field_start(i : u32, f : u32) -> u32 { return FIELD_START[i * 4 + f]; } pub fn formula_field_len(i : u32, f : u32) -> u32 { return FIELD_LEN[i * 4 + f]; } pub fn err_milli_pct(i : u32) -> i64 { return ERR_MILLI_PCT[i]; } pub fn abs_err(i : u32) -> i64 { if ERR_MILLI_PCT[i] < 0 { return 0 - ERR_MILLI_PCT[i]; } return ERR_MILLI_PCT[i]; } +pub fn repro_milli_pct(i : u32) -> i64 { return REPRO_MILLI_PCT[i]; } +pub fn abs_repro(i : u32) -> i64 { if REPRO_MILLI_PCT[i] < 0 { return 0 - REPRO_MILLI_PCT[i]; } return REPRO_MILLI_PCT[i]; } +pub fn tag_of(i : u32) -> u32 { return TAG_OF[i]; } +/// Is row i within 1 percent of the measured value its source cites, recomputed? +pub fn is_close(i : u32) -> bool { return abs_repro(i) <= CLOSE_MILLI_PCT; } + +pub fn tag_count(t : u32) -> u32 { + var c : u32 = 0; + var i : u32 = 0; + while (i < ROW_COUNT) { if TAG_OF[i] == t { c = c + 1; } i = i + 1; } + return c; +} + +fn pow_int(x : f64, n : u32) -> f64 { + var r : f64 = 1.0; + var i : u32 = 0; + while (i < n) { r = r * x; i = i + 1; } + return r; +} + +/// The closed forms of RECIPE_KIND 1..8. +pub fn closed_form(kind : u32) -> f64 { + if kind == 1 { return @log(2.0) / PI; } + if kind == 2 { return @log(3.0) / PI; } + if kind == 3 { return 360.0 / (PHI * PHI) - 2.0 / pow_int(PHI, 3) + 1.0 / pow_int(3.0 * PHI, 5); } + if kind == 4 { return 1.0 / (pow_int(PHI, 4) + PHI); } + if kind == 5 { return 1.0 + (1.0 / 137.035999084) / pow_int(PHI, 3); } + if kind == 6 { return pow_int(5.0 / PHI, 4); } + const th : f64 = 0.22673; + if kind == 7 { return @cos(th); } + const vud : f64 = 7.0 * @exp(3.0 * LNPI - 5.0 * LNPHI - 3.0); + const ns : f64 = 3.0 * @exp(3.0 * LNPHI - 4.0 * LNPI + 2.0); + return @exp(ns * @log(vud)); +} + +/// The value of row i, recomputed from its recipe. +pub fn recipe_value(i : u32) -> f64 { + if RECIPE_KIND[i] != 0 { return closed_form(RECIPE_KIND[i]); } + const x : f64 = @as(f64, @floatFromInt(RECIPE_K[i])) * LN3 + @as(f64, @floatFromInt(RECIPE_M[i])) * LNPI + @as(f64, @floatFromInt(RECIPE_P[i])) * LNPHI + @as(f64, @floatFromInt(RECIPE_Q[i])); + return RECIPE_N[i] * @exp(x); +} -test every_row_is_verified_and_counted { +/// The signed error of row i against its measured value, in thousandths of a percent, rounded to the nearest. +pub fn recomputed_milli_pct(i : u32) -> i64 { + const r : f64 = (recipe_value(i) - MEASURED[i]) / MEASURED[i] * 100000.0; + if r < 0.0 { return 0 - @as(i64, @intFromFloat(0.5 - r)); } + return @as(i64, @intFromFloat(r + 0.5)); +} + +test every_row_is_counted_and_tagged { assert FORMULA_COUNT == 32; - assert SECTOR_COUNT == 9; + assert ROW_COUNT == 358; + assert tag_count(TAG_VERIFIED) == 32; + assert tag_count(TAG_CANDIDATE) == 71; + assert tag_count(TAG_CONJECTURE) == 255; + assert tag_count(TAG_VERIFIED) + tag_count(TAG_CANDIDATE) + tag_count(TAG_CONJECTURE) == ROW_COUNT; +} + +test verified_rows_come_first_then_candidates_then_conjectures { + var i : u32 = 1; + while (i < ROW_COUNT) { assert TAG_OF[i] >= TAG_OF[i - 1]; i = i + 1; } + assert TAG_OF[0] == TAG_VERIFIED; + assert TAG_OF[31] == TAG_VERIFIED; + assert TAG_OF[32] == TAG_CANDIDATE; + assert TAG_OF[ROW_COUNT - 1] == TAG_CONJECTURE; } test fields_tile_the_text_without_gaps { assert formula_field_start(0, 0) == 0; - assert formula_field_start(31, 3) + formula_field_len(31, 3) == 1949; + assert formula_field_start(ROW_COUNT - 1, 3) + formula_field_len(ROW_COUNT - 1, 3) == 30525; assert formula_field_start(0, 1) == formula_field_start(0, 0) + formula_field_len(0, 0); - assert formula_field_len(0, 0) > 0; + var k : u32 = 1; + while (k < ROW_COUNT * 4) { + assert FIELD_START[k] == FIELD_START[k - 1] + FIELD_LEN[k - 1]; + assert FIELD_LEN[k] > 0; + k = k + 1; + } } -test errors_are_small_and_signed { +test the_first_32_rows_are_the_registrys_and_unchanged { assert err_milli_pct(0) == -620; assert abs_err(0) == 620; assert abs_err(17) < 2000; + assert err_milli_pct(3) == 29; + assert ERR_MILLI_PCT[31] == 94; +} + +test every_value_is_recomputed_from_its_recipe_within_1e_9 { + var i : u32 = 0; + while (i < ROW_COUNT) { + const a : f64 = recipe_value(i); + const b : f64 = VALUE[i]; + assert @abs(a - b) <= 1.0e-9 * @abs(b); + i = i + 1; + } +} + +test every_error_is_recomputed_from_the_measured_value { + var i : u32 = 0; + while (i < ROW_COUNT) { + const d : i64 = recomputed_milli_pct(i) - REPRO_MILLI_PCT[i]; + assert d >= -1 and d <= 1; + i = i + 1; + } +} + +test rows_from_32_on_are_all_within_1_percent_and_carry_their_recomputed_error { + var i : u32 = 32; + while (i < ROW_COUNT) { + assert is_close(i); + assert ERR_MILLI_PCT[i] == REPRO_MILLI_PCT[i]; + i = i + 1; + } +} + +test some_registry_rows_are_not_within_1_percent_when_recomputed { + var far : u32 = 0; + var i : u32 = 0; + while (i < FORMULA_COUNT) { if is_close(i) == false { far = far + 1; } i = i + 1; } + assert far == 12; + assert is_close(0); + assert is_close(8) == false; + assert is_close(17) == false; +} + +test the_close_rows_are_counted_per_tag { + var v : u32 = 0; + var c : u32 = 0; + var j : u32 = 0; + var i : u32 = 0; + while (i < ROW_COUNT) { + if is_close(i) { + if TAG_OF[i] == TAG_VERIFIED { v = v + 1; } + if TAG_OF[i] == TAG_CANDIDATE { c = c + 1; } + if TAG_OF[i] == TAG_CONJECTURE { j = j + 1; } + } + i = i + 1; + } + assert v == 20; + assert c == 71; + assert j == 255; } diff --git a/specs/t27os/orbit_view.t27 b/specs/t27os/orbit_view.t27 index 70a7850ef5..2af919d8f1 100644 --- a/specs/t27os/orbit_view.t27 +++ b/specs/t27os/orbit_view.t27 @@ -34,6 +34,12 @@ use t27f::formula_table::FORMULA_TEXT; use t27f::formula_table::formula_field_start; use t27f::formula_table::formula_field_len; use t27f::formula_table::err_milli_pct; +use t27f::formula_table::ROW_COUNT; +use t27f::formula_table::TAG_VERIFIED; +use t27f::formula_table::TAG_CANDIDATE; +use t27f::formula_table::CLOSE_MILLI_PCT; +use t27f::formula_table::tag_of; +use t27f::formula_table::repro_milli_pct; pub const OV_MAX : usize = 32; /// A frame that took longer than this is clamped (the window was asleep or dragged), so the labels never jump. @@ -78,6 +84,29 @@ pub fn ov_animates(visible: bool, reduce: bool, placed: usize) -> bool { return visible and reduce == false and placed > 0; } +// ---- which rows the orbit may show, and how bright (owner 2026-10-21: VERIFIED and candidate rows, |err| <= 1 percent, candidates a little dimmer) ---- +// formula_table.t27 now holds every close hit (ROW_COUNT rows) with a TAG and the error recomputed against the cited measured value. The rule is here; +// the window still draws the first FORMULA_COUNT = OV_MAX = 32 rows (glass_window.t27 sizes its arrays by 32), so wiring the rule into the draw loop and +// raising that cap is the next step. Conjectures never show; a row whose recomputed error is beyond 1 percent never shows, whatever its tag says. +pub const OV_ALPHA_VERIFIED : i64 = 1000; +pub const OV_ALPHA_CANDIDATE : i64 = 720; + +/// The alpha (permille) of a row from its tag and its recomputed error in thousandths of a percent; 0 = not shown. +pub fn ov_row_alpha_permille(tag: u32, repro_milli: i64) -> i64 { + var m : i64 = repro_milli; + if (m < 0) { m = 0 - m; } + if (m > CLOSE_MILLI_PCT) { return 0; } + if (tag == TAG_VERIFIED) { return OV_ALPHA_VERIFIED; } + if (tag == TAG_CANDIDATE) { return OV_ALPHA_CANDIDATE; } + return 0; +} + +/// The alpha of row i of the table (0 = hidden). +pub fn ov_row_alpha(i: u32) -> i64 { + if (i >= ROW_COUNT) { return 0; } + return ov_row_alpha_permille(tag_of(i), repro_milli_pct(i)); +} + /// Field f (OF_*) of formula i copied into out; the length. pub fn ov_field(i: u32, f: u32, out: []u8) -> usize { if (i >= FORMULA_COUNT) { return 0; } @@ -677,3 +706,33 @@ test phi_pi_and_exponents_are_drawn_as_math_with_utf8_bytes_from_a_table { i = i + 1; } } + +test the_orbit_shows_verified_and_candidate_rows_within_1_percent_candidates_dimmer { + assert ov_row_alpha_permille(0, 620) == 1000; + assert ov_row_alpha_permille(0, 0 - 620) == 1000; + assert ov_row_alpha_permille(1, 999) == 720; + assert ov_row_alpha_permille(1, 1000) == 720; + assert ov_row_alpha_permille(1, 1001) == 0; + assert ov_row_alpha_permille(0, 1360) == 0; + assert ov_row_alpha_permille(2, 0) == 0; + assert OV_ALPHA_CANDIDATE < OV_ALPHA_VERIFIED and OV_ALPHA_CANDIDATE > 0; +} + +test the_rule_on_the_table_hides_far_registry_rows_and_every_conjecture { + assert ov_row_alpha(0) == 1000; + assert ov_row_alpha(8) == 0; + assert ov_row_alpha(32) == 720; + assert ov_row_alpha(ROW_COUNT - 1) == 0; + assert ov_row_alpha(ROW_COUNT) == 0; + var shown : u32 = 0; + var bright : u32 = 0; + var i : u32 = 0; + while (i < ROW_COUNT) { + const a : i64 = ov_row_alpha(i); + if (a > 0) { shown = shown + 1; } + if (a == OV_ALPHA_VERIFIED) { bright = bright + 1; } + i = i + 1; + } + assert bright == 20; + assert shown == 91; +}