p=4 n=2 d=1: quadrature E disc_p^p lat 0.020833333333 (exact 0.020833333333, |diff| 3.5e-18) iid 0.020833333333 (exact 0.020833333333, |diff| 0.0e+00)
      E disc_p (root inside): lat 0.3292634308 (+-1.3e-12) iid 0.3292634308 (+-2.8e-11)  lat - iid = +0.0000000000
p=4 n=3 d=1: quadrature E disc_p^p lat 0.011728395062 (exact 0.011728395062, |diff| 0.0e+00) iid 0.009876543210 (exact 0.009876543210, |diff| 0.0e+00)
      E disc_p (root inside): lat 0.2601443144 (+-4.0e-12) iid 0.2681902273 (+-9.2e-11)  lat - iid = -0.0080459129
