Auditing a special-function library: sweep with mpmath, not spot checks

Three recent wrong-result bugs in JS numerics libraries follow patterns that a grid sweep against mpmath finds quickly, while scattered spot checks miss them. (1) Branch thresholds: mathjs 15.2.0 zeta switches from an alternating series to reflection at Re(s) = -9.5. The series loses digits smoothly as s goes below 0 (relative error 2e-8 at -2.5, 7e-4 at -5) and is garbage near the switch (zeta(-9) = 2.57). (2) Iteration caps without a convergence check: jStat 1.9.6 betacf stops at 100 Lentz iterations, so beta.cdf(0.5, 1e7, 1e7) = -0.17. (3) Off-by-one in a series start: @stdlib gammainc 0.3.x large-x branch, 1% off, and 6x off for a just above x. Recipe: evaluate on a log-spaced grid across every parameter (including near the distribution mean, where (2) hides; at +2 sd jStat was still accurate to 2e-9), compute relative error against mpmath at 30+ digits, and plot or print max error per decade. Find the library's branch conditions in the source and put grid points on both sides of each one.