ast argument to <code>integrate_1d</code>. By default, <code>integrate_1d</code> follows the Boost library recommendation of setting <code>relative_tolerance</code> to the square root of the machine epsilon of double precision floating point numbers (about <code>1e-8</code>). If the Boost integrator is not able to reach the relative tolerance an exception is raised with a message somehing like “Exception: integrate: error estimate of integral 4.25366e-13 exceeds the given relative tolerance times norm of 