{
 "gates": [
  [
   "loglog x1(X2) >= Y0: w - e^7.9",
   "[0.004838947305, 0.004838947305]"
  ],
  [
   "sqrt(x1)/log^7 x1 >= log^7 N: w/2 - 7 log w - 7 log L",
   "[1237.941605, 1237.941605]"
  ],
  [
   "  ... its L-derivative",
   "[0.4939384099, 0.4939384099]"
  ],
  [
   "log^7 N >= 1e9: 7 log L - log 1e9",
   "[34.67870006, 34.67870006]"
  ],
  [
   "1 - xi/log^2 N >= 0 (xi <= 801)",
   "[0.9998930632, 0.9998930632]"
  ],
  [
   "X2 = N >= 4e18: L - log(4e18)",
   "[2694.027174, 2694.027174]"
  ],
  [
   "eps <= 1/74",
   "[0.01295921351, 0.01295921351]"
  ],
  [
   "N^a/(log^7 x1 log^2.5 N) >= exp(u0(1 + 9e-7/log u0)): L/4 - 7 log w - 2.5 log L - 400(1 + 9e-7/log 400)",
   "[209.128511, 209.128511]"
  ],
  [
   "  ... its L-derivative",
   "[0.2464960855, 0.2464960855]"
  ],
  [
   "N^{1/2-a}/log^14 N >= z^2: 0.2 L - 14 log L",
   "[436.5680682, 436.5680682]"
  ],
  [
   "K_delta(x1) >= 3022: w^1.3 - 3022",
   "[25831.95446, 25831.95446]"
  ],
  [
   "eps1 <= 1/11: K_delta(x1) - 15015 (= 3*5*7*11*13)",
   "[13838.95446, 13838.95446]"
  ],
  [
   "z0 = N^{1/40} >= 1e12 (eps(400,1e12), xi(1e12,40) apply): L/40 - 12 log 10",
   "[40.79047888, 40.79047888]"
  ],
  [
   "c >= 7 (mbar <= max(1-f(6), F(7)-1)): c(L) - 7",
   "[1.380568508, 1.380568508]"
  ],
  [
   "xi <= 801 from BJV22 Lemma 38 (both sides): 801 - L^2((1+a1)(1+a2)(1+a3) - 1)",
   "[1.0, 1.0]"
  ]
 ],
 "monotonicity": [
  [
   "M3 dE_P/dlog w at w0 (increasing: E_P and 1-1/log w increase)",
   "[10.414974, 10.414974]"
  ],
  [
   "M3 dE_S/dlog w at w0 (increasing: E_S and 0.35-2/log w increase for log w > 2/0.35)",
   "[1.4578674, 1.4578674]"
  ],
  [
   "M2a nu*w > 2 (t^2 e^{-nu t} decreasing in t >= w): min(E_P, E_S)(w0) - 2",
   "[9.9243901, 9.9243901]"
  ],
  [
   "M2b t^6.5/v^7: 6.5 - 7 (w-5)/(w-5 log w)",
   "[-0.59086509, -0.59086509]"
  ],
  [
   "M2b 18 t^3 e^{-t/12}: 3 - w/12",
   "[-221.77393, -221.77393]"
  ],
  [
   "M2b 2.5 t^7.5 e^{-t/6}: 7.5 - w/6",
   "[-442.04786, -442.04786]"
  ],
  [
   "M2d c1: t^2 e^{-E_P(t)}: 2 - dE_P/dlog t",
   "[-8.414974, -8.414974]"
  ],
  [
   "M2d c1: t^9 e^{-t/2}: 9 - w/2",
   "[-1339.6436, -1339.6436]"
  ],
  [
   "M2d c1: t^3.515 e^{-0.8274 sqrt t}: 3.515 - 0.4137 sqrt w",
   "[-17.970681, -17.970681]"
  ],
  [
   "M5 w log w e^{-E_P}: 1 + 1/log w0 - dE/dlog w",
   "[-9.2883918, -9.2883918]"
  ],
  [
   "M5 (x j) w log^2 w e^{-E_P}/log(7log w): 1 + 2/log w0 - dE/dlog w",
   "[-9.1618095, -9.1618095]"
  ],
  [
   "M5 w log w e^{-E_S}: 1 + 1/log w0 - dE/dlog w",
   "[-0.33128518, -0.33128518]"
  ],
  [
   "M5 (x j) w log^2 w e^{-E_S}/log(7log w): 1 + 2/log w0 - dE/dlog w",
   "[-0.20470293, -0.20470293]"
  ],
  [
   "M5 C-term log w/w (x j: log^2 w/(w log(7 log w))): -1 + 2/log w0",
   "[-0.7468355, -0.7468355]"
  ],
  [
   "M5 4w^5.5/v^7 (x j): 5.5 - 7(w-5)/(w-5log w) + 2/log w0",
   "[-1.3377006, -1.3377006]"
  ],
  [
   "M5 4w^-1.5 (x j): -1.5 + 2/log w0",
   "[-1.2468355, -1.2468355]"
  ],
  [
   "M5 18w^2 e^{-w/12} (x j): 2 + 2/log w0 - w/12",
   "[-222.52077, -222.52077]"
  ],
  [
   "M5 2.5 w^6.5 e^{-w/6} (x j): 6.5 + 2/log w0 - w/6",
   "[-442.7947, -442.7947]"
  ],
  [
   "M5 w^-4 e^{-w/2}, 0.4 w^4 e^{-w}, w^-6 (x j): 4 + 2/log w0 - w",
   "[-2693.034, -2693.034]"
  ],
  [
   "M5/M8 mult(L) decreasing: (1-4/w)L and L^2 w^3 increasing [w(L) increasing: 1 - 5/L]",
   "[0.99817309, 0.99817309]"
  ],
  [
   "M5 del/L x j: e^{-L/2} L^0.5 j/(w^7 log L): -1/2 + 0.5/L + 1/(w log w)",
   "[-0.49977038, -0.49977038]"
  ],
  [
   "M7 c(L) increasing: d/dL(-14 log L/L) = 14(log L - 1)/L^2",
   "[6.9145666, 6.9145666]"
  ],
  [
   "M9 (L+7log L)/(L-7log L) decreasing: 1 - log L",
   "[-6.9145666, -6.9145666]"
  ],
  [
   "M9 L/w decreasing (log L/L decreasing): 1 - log L",
   "[-6.9145666, -6.9145666]"
  ],
  [
   "M9/M11 lll(L) > 0 (so 1 + log 1.3/lll and 2.5/(log(1.3 log w) lll) decrease)",
   "[2.0687049, 2.0687049]"
  ],
  [
   "M9 log(1.3 log w) > 0",
   "[2.3292273, 2.3292273]"
  ],
  [
   "M10 log L/L^0.7 decreasing: 1 - 0.7 log L",
   "[-4.5401966, -4.5401966]"
  ],
  [
   "M11 lll (log7 + lll)/L^1.3 decreasing: (1/log L)(1/lll + 1/(log 7 + lll)) - 1.3",
   "[-1.2074511, -1.2074511]"
  ],
  [
   "M11 lll/L^1.3 decreasing: 1/(log L lll) - 1.3",
   "[-1.2389235, -1.2389235]"
  ],
  [
   "M8 c2 tail L^4 e^{-L}: 4 - L",
   "[-2732.86, -2732.86]"
  ]
 ],
 "routeA_JSprint": {
  "L": "[2736.86, 2736.86]",
  "w": "[2697.287167215814, 2697.287167215814]",
  "c": "[8.3805685084992, 8.3805685084992]",
  "h_c": "[8.207542034350654e-5, 8.207542034350654e-5]",
  "c4_over_L_uniform": "[1.183942352501671, 1.183942352501671]",
  "c4star_j_over_L_uniform": "[22.58284469481986, 22.58284469481986]",
  "c1": "[52.4063548330039, 52.4063548330039]",
  "c2": "[52.42553175574361, 52.42553175574361]",
  "c3_majorant": "[2.681849747896153, 2.681849747896153]",
  "a1": "[4.582995984627, 4.582995984627]",
  "a": "[1.38715142730626e-6, 1.38715142730626e-6]",
  "brace_b": "[0.9995893911187144, 0.9995893911187144]",
  "case_a": "[38.39416984299427, 38.39416984299427]",
  "case_b": "[9.520070617143857, 9.520070617143857]"
 },
 "routeA_BJV22": {
  "L": "[2736.86, 2736.86]",
  "w": "[2697.287167215814, 2697.287167215814]",
  "c": "[8.3805685084992, 8.3805685084992]",
  "h_c": "[8.207542034350654e-5, 8.207542034350654e-5]",
  "c4_over_L_uniform": "[1.183942352501671, 1.183942352501671]",
  "c4star_j_over_L_uniform": "[22.58284469481986, 22.58284469481986]",
  "c1": "[52.4063548330039, 52.4063548330039]",
  "c2": "[52.42553175574361, 52.42553175574361]",
  "c3_majorant": "[2.681849747896153, 2.681849747896153]",
  "a1": "[4.582995984627, 4.582995984627]",
  "a": "[0.003796439255337411, 0.003796439255337411]",
  "brace_b": "[0.9957937963748742, 0.9957937963748742]",
  "case_a": "[38.39416984299427, 38.39416984299427]",
  "case_b": "[9.368246827390248, 9.368246827390248]"
 },
 "routeB_JSprint": {
  "L1": "3000.0",
  "boxes": 11,
  "min_lower_case_b": "9.95048601887809",
  "min_lower_case_a": "38.4167540687468",
  "tail_case_b": "26.3227199950863",
  "tail_case_a": "39.2819676579897",
  "target_b": "9.95"
 },
 "routeB_BJV22": {
  "L1": "3000.0",
  "boxes": 12,
  "min_lower_case_b": "9.80368416107224",
  "min_lower_case_a": "38.4170083644111",
  "tail_case_b": "26.2182938621985",
  "tail_case_a": "39.2819676579897",
  "target_b": "9.8"
 },
 "point_L0_JSprint": {
  "case_a": "[38.4172626292985, 38.4172626292985]",
  "case_b": "[9.96054882588247, 9.96054882588247]",
  "a": "1.38715142731e-6"
 },
 "point_L0_BJV22": {
  "case_a": "[38.4172626292985, 38.4172626292985]",
  "case_b": "[9.80872503612886, 9.80872503612886]",
  "a": "0.00379643925534"
 }
}