Calculating the time of motzei Shabbos

Calculating when Shabbos comes in is easy; it's fifteen minutes before sunset (in the UK; generally eighteen minutes elsewhere). Figuring out when Shabbos goes out is a whole different kettle of fish. There are different criteria used, with in the summer ten minute discrepancies. I only figured out recently why twice recently aviva_m said "it's not dark enough!" when I said Shabbos was out: I'd been going by the earlier time, as used by the London Beth Din; she'd been used to the longer time printed by more machmir luachs.

Anyhow, if I move to Berlin (and it's still an "if" at this stage), I wish to continue using the criterion I'm used to, but there doesn't seem to be anything printing times using this criterion for Berlin. So I figured I'd write my own calculator: feed in latitude, longitude and time of year, and it would spit out the time Shabbos goes out. So I went off to sites such as this, this and this; also to Wikipedia on the position of the sun and conversion of coordinate systems, and wrote a little Perl script, and lo and behold it generates gibberish. (The idea was to confirm it produces the known times for London before trying it out elsewhere.)

Any maths/calendar geeks who are familiar with doing such calculations who would like to tell me what I've done wrong, or do I have to painstakingly debug the equations myself?