e2_upper_sanity.py:153: IntegrationWarning: The occurrence of roundoff error is detected, which prevents 
  the requested tolerance from being achieved.  The error may be 
  underestimated.
  ES = quad(lambda x: (2 * psi(fs(x)) + psi(-fs(x))) * phi(x), -12, 12, limit=400, points=[0, 2, 4])[0]
phi=0.30 aligned   gamma=-0.09317 Gamma=-0.07978 gap=0.01338
phi=0.30 (s,s,-s)  gamma=-0.17025 Gamma=-0.07978 gap=0.09047
phi=0.45 aligned   gamma=0.01732 Gamma=0.02866 gap=0.01134
phi=0.45 (s,s,-s)  gamma=-0.06031 Gamma=0.02866 gap=0.08897
phi=0.60 aligned   gamma=0.18039 Gamma=0.18889 gap=0.00850
phi=0.60 (s,s,-s)  gamma=0.11537 Gamma=0.18889 gap=0.07352
phi=0.75 aligned   gamma=0.41187 Gamma=0.41697 gap=0.00511
phi=0.75 (s,s,-s)  gamma=0.37131 Gamma=0.41697 gap=0.04566
phi=0.90 aligned   gamma=0.72932 Gamma=0.73120 gap=0.00188
phi=0.90 (s,s,-s)  gamma=0.71785 Gamma=0.73120 gap=0.01335
halfspaces (random dims/directions/thresholds): min gap (0.0005987004956538033, (array([-1.   ,  0.977, -0.779]), -0.7805, array([[ 1.,  1., -1.],
       [ 1.,  1., -1.],
       [-1., -1.,  1.]])))
1-D unions of intervals: min gap (0.00504843550625933, (array([ 0.891,  0.929, -0.704]), 0.5885))
along (sgn,sgn,-sgn): E gamma^+ = 3.1665e-04, E Gamma(m(x))^+ = 1.2112e-03, E sum psi(m_j(x)) = 1.9503e-03
along (sgn,sgn,-sgn): E gamma_aligned(m(x))^+ = 1.0142e-03 (floor for bounds depending on m(x) only)
