  Local search has recently been applied to SMT problems over various
arithmetic theories. Among these, nonlinear real arithmetic poses special
challenges due to its uncountable solution space and potential need to solve
higher-degree polynomials. As a consequence, existing work on local search only
considered fragments of the theory. In this work, we analyze the difficulties
and propose ways to address them, resulting in an efficient search algorithm
that covers the full theory of nonlinear real arithmetic. In particular, we
present two algorithmic improvements: incremental computation of variable
scores and temporary relaxation of equality constraints. We also discuss choice
of candidate moves and a look-ahead mechanism in case when no critical moves
are available. The resulting implementation is competitive on satisfiable
problem instances against complete methods such as MCSAT in existing SMT
solvers.
