Bugs found during review of the Ganak + synthesis Arjun + MPFI PR.

• comp_cache.hpp: Debug log called num_direct_children(id) after set_first_descendant(0), always printing 0. Reordered to log before clearing.
• main.cpp help text: Mode 8 missing (see --mpfrprec) that modes 6 and 7 have.
• main.cpp mode 8 output: Missing null assertion after dynamic_cast<const FMpfi*>.
• main.cpp compute_collision_prob: Called mpfr_init2(result, 256) on output param internally instead of caller — non-standard MPFR convention that risks double-init leaks. Moved init to caller, changed param from mpfr_t& to mpfr_t.

// Before: function both allocates and computes — caller can't safely pre-init
void compute_collision_prob(mpfr_t& result, ...) {
    mpfr_init2(result, 256);  // hidden allocation
    ...
}

// After: standard MPFR convention — caller owns lifecycle
void compute_collision_prob(mpfr_t result, ...) { ... }
// caller:
mpfr_t collision_prob;
mpfr_init2(collision_prob, 256);
compute_collision_prob(collision_prob, ...);
mpfr_clear(collision_prob);

✨ Let Copilot coding agent set things up for you — coding agent works faster and does higher quality work when set up for your repo.