# python3 -u rep510_boolean.py 8 8   (exact integer arithmetic, C kernel rep510_boolean.c; 8 parallel jobs; time from bash time)
# 106 ranges done in 345 s (8 parallel jobs)
ok: k = 4, all four inequalities, every nu: C results coincide with the direct numpy evaluation of all 2^16 P
ok: 736 sample points coincide with exact Fraction evaluations of the four sides (rep510_exact.columns)
k=4 rep5ex nu=(+4,-0): D = 10000; max (LHS - RHS) = 0 at 11 of 65536 P; LHS = RHS for 11 P; largest negative value -0.0002
   equality cases: 0, z1=1, z1=z2=1, z1=z3=1, z1=z4=1, z2=1, z2=z3=1, z2=z4=1, z3=1, z3=z4=1, z4=1
k=4 rep5ex nu=(+3,-1): D = 22000; max (LHS - RHS) = 0 at 7 of 65536 P; LHS = RHS for 7 P; largest negative value -0.000454545
   equality cases: 0, z1=1, z1=z2=1, z1=z3=1, z2=1, z2=z3=1, z3=1
k=4 rep5ex nu=(+2,-2): D = 48400; max (LHS - RHS) = 0 at 4 of 65536 P; LHS = RHS for 4 P; largest negative value -0.00103306
   equality cases: 0, z1=1, z1=z2=1, z2=1
k=4 rep5ex nu=(+1,-3): D = 106480; max (LHS - RHS) = 0 at 2 of 65536 P; LHS = RHS for 2 P; largest negative value -0.00234786
   equality cases: 0, z1=1
k=4 rep5ex nu=(+0,-4): D = 234256; max (LHS - RHS) = 0 at 1 of 65536 P; LHS = RHS for 1 P; largest negative value -0.00533604
   equality cases: 0
k=4 R5 nu=(+4,-0): D = 10000; max (LHS - RHS) = 0 at 23 of 65536 P; LHS = RHS for 23 P; largest negative value -0.0002
   equality cases: 0, z1=-1,z2=1, z1=-1,z3=1, z1=-1,z4=1, z1=1, z1=1,z2=-1, z1=1,z3=-1, z1=1,z4=-1, z1=z2=1, z1=z3=1, z1=z4=1, z2=-1,z3=1, z2=-1,z4=1, z2=1, z2=1,z3=-1, z2=1,z4=-1, z2=z3=1, z2=z4=1, z3=-1,z4=1, z3=1, z3=1,z4=-1, z3=z4=1, z4=1
k=4 R5 nu=(+3,-1): D = 22000; max (LHS - RHS) = 0 at 13 of 65536 P; LHS = RHS for 13 P; largest negative value -0.000454545
   equality cases: 0, z1=-1,z2=1, z1=-1,z3=1, z1=1, z1=1,z2=-1, z1=1,z3=-1, z1=z2=1, z1=z3=1, z2=-1,z3=1, z2=1, z2=1,z3=-1, z2=z3=1, z3=1
k=4 R5 nu=(+2,-2): D = 48400; max (LHS - RHS) = 0 at 6 of 65536 P; LHS = RHS for 6 P; largest negative value -0.00103306
   equality cases: 0, z1=-1,z2=1, z1=1, z1=1,z2=-1, z1=z2=1, z2=1
k=4 R5 nu=(+1,-3): D = 106480; max (LHS - RHS) = 0 at 2 of 65536 P; LHS = RHS for 2 P; largest negative value -0.00234786
   equality cases: 0, z1=1
k=4 R5 nu=(+0,-4): D = 234256; max (LHS - RHS) = 0 at 1 of 65536 P; LHS = RHS for 1 P; largest negative value -0.00533604
   equality cases: 0
k=4 rep10ex nu=(+4,-0): D = 20736; max (LHS - RHS) = 0 at 9 of 65536 P; LHS = RHS for 9 P; largest negative value -0.0185185
   equality cases: 0, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1, z4=-1, z4=1
k=4 rep10ex nu=(+3,-1): D = 34560; max (LHS - RHS) = 0 at 7 of 65536 P; LHS = RHS for 7 P; largest negative value -0.0208333
   equality cases: 0, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1
k=4 rep10ex nu=(+2,-2): D = 57600; max (LHS - RHS) = 0 at 5 of 65536 P; LHS = RHS for 5 P; largest negative value -0.025
   equality cases: 0, z1=-1, z1=1, z2=-1, z2=1
k=4 rep10ex nu=(+1,-3): D = 96000; max (LHS - RHS) = 0 at 3 of 65536 P; LHS = RHS for 3 P; largest negative value -0.0342812
   equality cases: 0, z1=-1, z1=1
k=4 rep10ex nu=(+0,-4): D = 160000; max (LHS - RHS) = 0 at 1 of 65536 P; LHS = RHS for 1 P; largest negative value -0.0449125
   equality cases: 0
k=4 rep10maj nu=(+4,-0): D = 20736; max (LHS - RHS) = 0 at 10 of 65536 P; LHS = RHS for 10 P; largest negative value -0.0183256
   equality cases: 0, 1, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1, z4=-1, z4=1
k=4 rep10maj nu=(+3,-1): D = 34560; max (LHS - RHS) = 0 at 8 of 65536 P; LHS = RHS for 8 P; largest negative value -0.0207176
   equality cases: 0, 1, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1
k=4 rep10maj nu=(+2,-2): D = 57600; max (LHS - RHS) = 0 at 6 of 65536 P; LHS = RHS for 6 P; largest negative value -0.025
   equality cases: 0, 1, z1=-1, z1=1, z2=-1, z2=1
k=4 rep10maj nu=(+1,-3): D = 96000; max (LHS - RHS) = 0 at 4 of 65536 P; LHS = RHS for 4 P; largest negative value -0.0342812
   equality cases: 0, 1, z1=-1, z1=1
k=4 rep10maj nu=(+0,-4): D = 160000; max (LHS - RHS) = 0 at 2 of 65536 P; LHS = RHS for 2 P; largest negative value -0.0371
   equality cases: 0, 1
k=5 rep5ex nu=(+5,-0): D = 100000; max (LHS - RHS) = 0 at 16 of 4294967296 P; LHS = RHS for 16 P; largest negative value -2e-05
   equality cases: 0, z1=1, z1=z2=1, z1=z3=1, z1=z4=1, z1=z5=1, z2=1, z2=z3=1, z2=z4=1, z2=z5=1, z3=1, z3=z4=1, z3=z5=1, z4=1, z4=z5=1, z5=1
k=5 rep5ex nu=(+4,-1): D = 220000; max (LHS - RHS) = 0 at 11 of 4294967296 P; LHS = RHS for 11 P; largest negative value -4.54545e-05
   equality cases: 0, z1=1, z1=z2=1, z1=z3=1, z1=z4=1, z2=1, z2=z3=1, z2=z4=1, z3=1, z3=z4=1, z4=1
k=5 rep5ex nu=(+3,-2): D = 484000; max (LHS - RHS) = 0 at 7 of 4294967296 P; LHS = RHS for 7 P; largest negative value -0.000103306
   equality cases: 0, z1=1, z1=z2=1, z1=z3=1, z2=1, z2=z3=1, z3=1
k=5 rep5ex nu=(+2,-3): D = 1064800; max (LHS - RHS) = 0 at 4 of 4294967296 P; LHS = RHS for 4 P; largest negative value -0.000234786
   equality cases: 0, z1=1, z1=z2=1, z2=1
k=5 rep5ex nu=(+1,-4): D = 2342560; max (LHS - RHS) = 0 at 2 of 4294967296 P; LHS = RHS for 2 P; largest negative value -0.000533604
   equality cases: 0, z1=1
k=5 rep5ex nu=(+0,-5): D = 5153632; max (LHS - RHS) = 0 at 1 of 4294967296 P; LHS = RHS for 1 P; largest negative value -0.00121274
   equality cases: 0
k=5 R5 nu=(+5,-0): D = 100000; max (LHS - RHS) = 0 at 36 of 4294967296 P; LHS = RHS for 36 P; largest negative value -2e-05
   equality cases: 0, z1=-1,z2=1, z1=-1,z3=1, z1=-1,z4=1, z1=-1,z5=1, z1=1, z1=1,z2=-1, z1=1,z3=-1, z1=1,z4=-1, z1=1,z5=-1, z1=z2=1, z1=z3=1, z1=z4=1, z1=z5=1, z2=-1,z3=1, z2=-1,z4=1, z2=-1,z5=1, z2=1, z2=1,z3=-1, z2=1,z4=-1, z2=1,z5=-1, z2=z3=1, z2=z4=1, z2=z5=1, z3=-1,z4=1, z3=-1,z5=1, z3=1, z3=1,z4=-1, z3=1,z5=-1, z3=z4=1, z3=z5=1, z4=-1,z5=1, z4=1, z4=1,z5=-1, z4=z5=1, z5=1
k=5 R5 nu=(+4,-1): D = 220000; max (LHS - RHS) = 0 at 23 of 4294967296 P; LHS = RHS for 23 P; largest negative value -4.54545e-05
   equality cases: 0, z1=-1,z2=1, z1=-1,z3=1, z1=-1,z4=1, z1=1, z1=1,z2=-1, z1=1,z3=-1, z1=1,z4=-1, z1=z2=1, z1=z3=1, z1=z4=1, z2=-1,z3=1, z2=-1,z4=1, z2=1, z2=1,z3=-1, z2=1,z4=-1, z2=z3=1, z2=z4=1, z3=-1,z4=1, z3=1, z3=1,z4=-1, z3=z4=1, z4=1
k=5 R5 nu=(+3,-2): D = 484000; max (LHS - RHS) = 0 at 13 of 4294967296 P; LHS = RHS for 13 P; largest negative value -0.000103306
   equality cases: 0, z1=-1,z2=1, z1=-1,z3=1, z1=1, z1=1,z2=-1, z1=1,z3=-1, z1=z2=1, z1=z3=1, z2=-1,z3=1, z2=1, z2=1,z3=-1, z2=z3=1, z3=1
k=5 R5 nu=(+2,-3): D = 1064800; max (LHS - RHS) = 0 at 6 of 4294967296 P; LHS = RHS for 6 P; largest negative value -0.000234786
   equality cases: 0, z1=-1,z2=1, z1=1, z1=1,z2=-1, z1=z2=1, z2=1
k=5 R5 nu=(+1,-4): D = 2342560; max (LHS - RHS) = 0 at 2 of 4294967296 P; LHS = RHS for 2 P; largest negative value -0.000533604
   equality cases: 0, z1=1
k=5 R5 nu=(+0,-5): D = 5153632; max (LHS - RHS) = 0 at 1 of 4294967296 P; LHS = RHS for 1 P; largest negative value -0.00121274
   equality cases: 0
k=5 rep10ex nu=(+5,-0): D = 248832; max (LHS - RHS) = 0 at 11 of 4294967296 P; LHS = RHS for 11 P; largest negative value -0.00757137
   equality cases: 0, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1, z4=-1, z4=1, z5=-1, z5=1
k=5 rep10ex nu=(+4,-1): D = 414720; max (LHS - RHS) = 0 at 9 of 4294967296 P; LHS = RHS for 9 P; largest negative value -0.00824653
   equality cases: 0, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1, z4=-1, z4=1
k=5 rep10ex nu=(+3,-2): D = 691200; max (LHS - RHS) = 0 at 7 of 4294967296 P; LHS = RHS for 7 P; largest negative value -0.00911458
   equality cases: 0, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1
k=5 rep10ex nu=(+2,-3): D = 1152000; max (LHS - RHS) = 0 at 5 of 4294967296 P; LHS = RHS for 5 P; largest negative value -0.0104688
   equality cases: 0, z1=-1, z1=1, z2=-1, z2=1
k=5 rep10ex nu=(+1,-4): D = 1920000; max (LHS - RHS) = 0 at 3 of 4294967296 P; LHS = RHS for 3 P; largest negative value -0.0131813
   equality cases: 0, z1=-1, z1=1
k=5 rep10ex nu=(+0,-5): D = 3200000; max (LHS - RHS) = 0 at 1 of 4294967296 P; LHS = RHS for 1 P; largest negative value -0.0194294
   equality cases: 0
k=5 rep10maj nu=(+5,-0): D = 248832; max (LHS - RHS) = 0 at 12 of 4294967296 P; LHS = RHS for 12 P; largest negative value -0.00739455
   equality cases: 0, 1, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1, z4=-1, z4=1, z5=-1, z5=1
k=5 rep10maj nu=(+4,-1): D = 414720; max (LHS - RHS) = 0 at 10 of 4294967296 P; LHS = RHS for 10 P; largest negative value -0.00815972
   equality cases: 0, 1, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1, z4=-1, z4=1
k=5 rep10maj nu=(+3,-2): D = 691200; max (LHS - RHS) = 0 at 8 of 4294967296 P; LHS = RHS for 8 P; largest negative value -0.0090625
   equality cases: 0, 1, z1=-1, z1=1, z2=-1, z2=1, z3=-1, z3=1
k=5 rep10maj nu=(+2,-3): D = 1152000; max (LHS - RHS) = 0 at 6 of 4294967296 P; LHS = RHS for 6 P; largest negative value -0.0104688
   equality cases: 0, 1, z1=-1, z1=1, z2=-1, z2=1
k=5 rep10maj nu=(+1,-4): D = 1920000; max (LHS - RHS) = 0 at 4 of 4294967296 P; LHS = RHS for 4 P; largest negative value -0.0131813
   equality cases: 0, 1, z1=-1, z1=1
k=5 rep10maj nu=(+0,-5): D = 3200000; max (LHS - RHS) = 0 at 2 of 4294967296 P; LHS = RHS for 2 P; largest negative value -0.0174762
   equality cases: 0, 1
ok: k=4 rep5ex: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: k=4 R5: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: k=4 rep10ex: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: k=4 rep10maj: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: k=5 rep5ex: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: k=5 R5: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: k=5 rep10ex: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: k=5 rep10maj: LHS <= RHS for every {0,1}-valued P and every nu (max LHS - RHS = 0)
ok: the equality cases are exactly the claimed families (want_eq) for every k, inequality and nu
# total 462 s

real	7m42.028s
user	47m44.025s
sys	0m0.580s
