closed form M_k vs geometric M_k, 20000 cases, max relative difference 1.646e-14
random tests: 360000 (polygon,point,radius,k) combinations, violations (slack < -1e-10): 0
   min relative slack  z=boundary k=n+0 : -1.503e-15
   min relative slack  z=boundary k=n+1 : -1.387e-15
   min relative slack  z=boundary k=n+3 : -1.272e-15
   min relative slack  z=inside   k=n+0 : -1.142e-15
   min relative slack  z=inside   k=n+1 : -1.371e-15
   min relative slack  z=inside   k=n+3 : -1.257e-15
   min relative slack  z=outside  k=n+0 : -5.419e-15
   min relative slack  z=outside  k=n+1 : -5.532e-15
   min relative slack  z=outside  k=n+3 : -5.419e-15
adversarial minimisation, k=3: minimum relative slack over 14 starts = -1.017e-15
adversarial minimisation, k=4: minimum relative slack over 14 starts = -6.107e-16
adversarial minimisation, k=5: minimum relative slack over 14 starts = -7.976e-16
adversarial minimisation, k=6: minimum relative slack over 14 starts = -9.185e-16
adversarial minimisation, k=7: minimum relative slack over 14 starts = -7.862e-16
adversarial minimisation, k=8: minimum relative slack over 14 starts = -7.934e-16
elapsed 153.8 s
RESULT PASS
