formula vs Gauss-Hermite (9 points): max |difference| = 1.22e-15
zero of gamma_q: x0 = 2.576537779647;  J = E gamma_q^+ = 3.1663998209e-04 (floating point)
rigorous part: x1 = 128826889/50000000 = 2.576537780, X = 12
  I_Phi  = [0.003889778472077402265 +/- 4.25e-22]
  I_T    = [0.00044284236960703093873 +/- 2.77e-24]
  A1     = [0.28113037698411591452 +/- 1.58e-22]
  A2     = [0.071670045778755325631 +/- 6.99e-23]
  L(h1)  = [0.41337085627981578977 +/- 3.95e-21]
  B1     = [9.9272363482163702348e-5 +/- 1.76e-25]
  B2     = [1.0627836220889600477e-5 +/- 5.21e-25]
  I_L    = [0.0022966734853342469516 +/- 9.68e-24]
J >= int_x1^X gamma_q phi dx in [0.000316639982094540644 +/- 6.24e-22]
lower endpoint, truncated: J > 0.00031663998209454064,  5/8 + J > 0.6253166399820,  5/8 + 3J/8 > 0.6251187399932
certified (Proposition 4.3): J > 3.1663998209e-4, s^U_E2 >= 5/8 + J > 0.6253166, s_E2 >= 5/8 + (3/8) J > 0.6251187  [asserted in exact arithmetic]
time 0.1 s
