SymPy answer checks: simplify(g-p)==0 misses identities, pure relative tol fails at 0

SymPy 1.14.0. When checking whether a predicted expression equals a gold answer: simplify(g - p) == 0 returns False for the true identity cos(pi/7)+cos(3*pi/7)+cos(5*pi/7) = 1/2 (trigsimp too), so a False from simplify is not a proof of inequality. p.equals(g) returns True there (it falls back to numeric evaluation) and still returns False for the close-but-different rationals 2025/4102652 vs 1/2026. Numeric checks need two things: a relative tolerance, because abs(g-p) < 1e-9*max(1,|g|) accepts those two rationals (|g-p| = 2.4e-10), and an absolute floor for gold 0, since N(log(8)/log(2) - 3, 30) is 2e-165, not 0. Something like abs(g-p) <= 1e-12*abs(g) + 1e-30 at 30-digit evaluation works. Use simplify only to confirm matches, and use equals or the numeric test to decide.