$ontext How is relative accuracy defined? Given: 1. a point x, 2. the computed value f(x), and 3. the known value fbar, we can compute the relative accuracy of f vis-a-vis fbar in two ways: 1. |f-fbar| <= reps * |fbar| 2. |f-fbar| <= reps * max(1,|x|) The first case is the most common, but for some functions the second is more appropriate (e.g. sin(x)). We can also pass a test if the absolute accuracy is within some tolerance aeps: 1. |f-fbar| <= aeps Contributor: Steven Dirkse, October 2004 $offtext set V / x, y, z f, f_, f_a, f_r fx, fx_, fx_a, fx_r fy, fy_, fy_a, fy_r fz, fz_, fz_a, fz_r fxx, fxx_, fxx_a, fxx_r fxy, fxy_, fxy_a, fxy_r fxz, fxz_, fxz_a, fxz_r fyx, fyx_, fyx_a, fyx_r fyy, fyy_, fyy_a, fyy_r fyz, fyz_, fyz_a, fyz_r fzx, fzx_, fzx_a, fzx_r fzy, fzy_, fzy_a, fzy_r fzz, fzz_, fzz_a, fzz_r rc, rc_, rc_e ec, ec_, ec_e /; scalar aeps 'absolute error tolerance'; scalar aeps0 'absolute error tolerance, function'; scalar aeps1 'absolute error tolerance, first derivative'; scalar aeps2 'absolute error tolerance, second derivative'; scalar reps 'relative error tolerance'; scalar reps0 'relative error tolerance, function'; scalar reps1 'relative error tolerance, first derivative'; scalar reps2 'relative error tolerance, second derivative'; scalar relToInput 'reps is relative to input (not output) magnitude'; set T; parameter data(T,V), tmp(T);