2. Filtered databases:

If we only consider execution times, the filtered databases have similar results, though not presented here, as the sampled databases. But since the constraint systems are of larger sizes, we expect to have a different picture concerning the exceptions.

In fact, 6_tab:PerfectClub_satisfiability_64_32_exception_filter shows that $C^3$ Simplex 64-bit has reduced from $92$ exceptions to $2$ exceptions compared to its version 32-bit. The Double Description method 32-bit raises $50$ overflow exceptions among which $36$ timeout exceptions, i.e. $407 - 371$, are expected using its 64-bit version.

Table 14: PerfectClub: Numbers of exceptions in filtered database

	PerfectClub
timeout = 2 minutes	#overflows	#timeouts	#operations
$C^3$ JANUS 64-bit	0	0	1310
$C^3$ JANUS 32-bit	0	0	1310
$C^3$ Simplex 64-bit	2	0	1310
$C^3$ Simplex 32-bit	92	0	1310
$C^3$ Fourier-Motzkin 64-bit	0	0	1310
$C^3$ Fourier-Motzkin 32-bit	0	0	1310
$C^3$ Double Description 64-bit	0	407	1310
$C^3$ Double Description 32-bit	50	371	1310

6_tab:SPEC95_satisfiability_64_32_exception_filter shows that using 32-bit instead of 64-bit results in many more overflow exceptions. The Double Description method has the biggest difference: $939$ to $22$.

Table 15: SPEC95: Numbers of exceptions in filtered database

	SPEC95
timeout = 2 minutes	#overflows	#timeouts	#operations
$C^3$ JANUS 64-bit	3050	0	4676
$C^3$ JANUS 32-bit	3109	0	4676
$C^3$ Simplex 64-bit	3174	0	4676
$C^3$ Simplex 32-bit	3972	0	4676
$C^3$ Fourier-Motzkin 64-bit	8	625	4676
$C^3$ Fourier-Motzkin 32-bit	181	495	4676
$C^3$ Double Description 64-bit	22	0	4676
$C^3$ Double Description 32-bit	939	0	4676