S(t) coefficients (lowest first): [0.0, 0.0, 0.0, 0.0, 35.0, -84.0, 70.0, -20.0]
1 - S(t): [1.0, -0.0, -0.0, -0.0, -35.0, 84.0, -70.0, 20.0]
eps   79.8 band [   1000,    1500]: max |F - dphi/dr| / max F = 1.6e-09; phi(b) = 0.0e+00
eps   79.8 band [      0,    1525]: max |F - dphi/dr| / max F = 1.6e-09; phi(b) = 0.0e+00
eps   17.0 band [     40,      60]: max |F - dphi/dr| / max F = 3.7e-09; phi(b) = 0.0e+00
eps   32.7 band [    400,     800]: max |F - dphi/dr| / max F = 2.6e-09; phi(b) = 0.0e+00
eps   79.8 band [  12000,   25000]: max |F - dphi/dr| / max F = 4.3e-07; phi(b) = 0.0e+00
global term: max |F - dphi/dr| / max F = 1.7e-06
edge r = 1000: jumps of phi^(0..6) x r^n = ['0.0', '6.264e-50', '-4.078e-50', '1.792e-49', '-8.654e-49', '-5470.0', '7.733e+4']
edge r = 1500: jumps of phi^(0..6) x r^n = ['0.0', '2.518e-49', '5.419e-48', '7.407e-47', '8.42e-46', '-1.407e+5', '-6.785e+6']
odd derivatives at r = 0 (inside branch, must be 0): ['0.0', '0.0', '5.66e-73']
median sun: c = 304.9, sqrt(c) = 17.46 u/s, eps = Roche = 79.8
  v/sqrt(c) at eps, 1.5 eps, 2 eps, 3 eps, 610 u: [0.707, 0.832, 0.894, 0.949, 0.992]
  peak pull: 0.500 c/eps at r = 1.000 eps (today: 1.0 c/R at R)
float32 eps 79.8 band [1000.0, 1500.0]: max abs err 7.28e-06 (unit strength; depth 2.77)
float32 eps 17.0 band [40.0, 60.0]: max abs err 1.45e-05 (unit strength; depth 1.15)
float32 eps 79.8 band [12000.0, 25000.0]: max abs err 9.06e-07 (unit strength; depth 5.49)
tau   3.00: closed form float32 err 6.9e-03; series float32 err 3.1e-07; F = dphi/dr 3.5e-08
tau  10.00: closed form float32 err 1.2e+01; series float32 err 1.1e-07; F = dphi/dr 3.8e-08
tau   9.92: closed form float32 err 1.2e+01; series float32 err 1.1e-07; F = dphi/dr 2.1e-08
