Is a semicolon or comma more appropriate in this case?

I’m wondering whether a semicolon or comma is more appropriate for the following phrase:

Whether or not it succeeds depends on the third option; namely, how well the program computes the values.

Whether or not it succeeds depends on the third option, namely, how well the program computes the values.

It seems intuitive to me that the semicolon seems more appropriate. However, "namely, how well the program computes the values" does not seem like an independent clause (it seems dependent on "Whether or not it succeeds depends on the third option", which is an independent clause), so I’m unsure if it is technically correct. On the other hand, the use of the/a comma in the second option just seems intuitively wrong, given the resulting structure.

So which one of these is the correct (or "best") way to structure this phrase?