My program has found 1622 intersections in 21 sec.
However I am not 100% sure in correctness of my program now. Since it's difficult to manually compare output of one program with output of another program, I propose following method for quick verification/comparison of results.
The idea is to compute some "hash" of results. Hash must be stable to following reorderings:
A B
C D
must yield the same hash as:
D C
B A

But not stable to following reorderings:
A B
C D
must not yield the same hash as:
A C
B D

Here is algorithm I currently use:
char hash [4] = {};
for (size_t i = 0; i != results.size(); i += 1)
{
line_t const* line1 = results[i].line1;
line_t const* line2 = results[i].line2;
for (int t = 0; t != 4; t += 1)
hash[t] ^= (line1->name[t] + line2->name[t]);
}
}
printf("count=%u (%u)\n", results.size(), *(unsigned*)sample);

My output is:
count=1622 (1711155)