Not sure how you implemented it but a likely cause if you converted things to polar co-ordinates is that one of the computed co-ordinates for an item that is directly up or down will be slightly off, meaning it is processed out of order.
Taking the test case and removing my hard coding to fix this:-
I use atan2() to convert to polar in radians, converting to degrees, adding 90 degrees and normalising to range of [0,360) :-
0,-1 -> -1.5707963267949 -> 359.99999989716
This means the items directly vertically "above" the starting point are processed last in the rotation rather than first as it should be 0 degrees.
This was fixed by:-
return( 0 ) if( $x == 0 && $y < 0 );
The first 20 asteroids that get [sic] vaporized in the big test example by my program (which might be equally incorrect!) are:-
Trying: 0,-1 (0) - The 1 asteroid to be vaporized is at 11,12
Trying: 1,-12 (4.76364159332945) - The 2 asteroid to be vaporized is at 12,1
Trying: 1,-11 (5.19442881083029) - The 3 asteroid to be vaporized is at 12,2
Trying: 1,-9 (6.34019165031464) - The 4 asteroid to be vaporized is at 12,4
Trying: 1,-8 (7.12501625420333) - The 5 asteroid to be vaporized is at 12,5
Trying: 1,-7 (8.13010226060595) - The 6 asteroid to be vaporized is at 12,6
Trying: 2,-13 (8.74616216970912) - The 7 asteroid to be vaporized is at 13,0
Trying: 1,-6 (9.46232211599789) - The 8 asteroid to be vaporized is at 12,7
Trying: 2,-11 (10.304846377701) - The 9 asteroid to be vaporized is at 13,2
Trying: 1,-5 (11.3099323841037) - The 10 asteroid to be vaporized is at 12,8
Trying: 3,-13 (12.994616703925) - The 11 asteroid to be vaporized is at 14,0
Trying: 1,-4 (14.0362433811252) - The 12 asteroid to be vaporized is at 13,5
Trying: 3,-11 (15.2551186176493) - The 13 asteroid to be vaporized is at 14,2
Trying: 2,-7 (15.9453958163031) - The 14 asteroid to be vaporized is at 13,6
Trying: 3,-10 (16.6992441502352) - The 15 asteroid to be vaporized is at 14,3
Trying: 4,-13 (17.1027288857551) - The 16 asteroid to be vaporized is at 15,0
Trying: 1,-3 (18.434948741147) - The 17 asteroid to be vaporized is at 14,4
Trying: 4,-11 (19.983106441894) - The 18 asteroid to be vaporized is at 15,2
Trying: 3,-8 (20.5560451402322) - The 19 asteroid to be vaporized is at 14,5
Trying: 5,-13 (21.0375109466207) - The 20 asteroid to be vaporized is at 16,0
and 191-200 are:-
Trying: -4,-9 (336.037510895201) - The 191 asteroid to be vaporized is at 7,4
Trying: -3,-7 (336.801409357004) - The 192 asteroid to be vaporized is at 8,6
Trying: -5,-12 (337.380134923273) - The 193 asteroid to be vaporized is at 6,1
Trying: -2,-5 (338.198590385896) - The 194 asteroid to be vaporized is at 9,8
Trying: -4,-11 (340.016893352426) - The 195 asteroid to be vaporized is at 7,2
Trying: -1,-3 (341.565051053173) - The 196 asteroid to be vaporized is at 10,10
Trying: -4,-13 (342.897270908565) - The 197 asteroid to be vaporized is at 7,0
Trying: -3,-10 (343.300755644085) - The 198 asteroid to be vaporized is at 8,3
Trying: -2,-7 (344.054603978017) - The 199 asteroid to be vaporized is at 9,6
Trying: -3,-11 (344.744881176671) - The 200 asteroid to be vaporized is at 8,2
ANSWER = 802