C.29.2:11.2 - Choose numerical methods by their guarantees and costs
The SciPy bisection documentation states the bracketing premises and its absolute-plus-relative termination criterion. Adopt explicit tolerance selection in :4.5; library defaults need not match the receiver’s requirement.
The documented Brent routine is a serious alternative combining bracketing, bisection and interpolation. Adapt the choice in :5.2: retain bisection for its simple bound and small exact case, while considering Brent’s method when function evaluations are costly. The deliberate trade-off is a simpler argument for potentially more evaluations. Reopen for a changed function class, tolerance, evaluation cost or finite precision failure.