This fails for test case 4 even though it is mathematically correct--it gives 0.27343749999999994 instead of 0.2734375, while the test suite asks for 0.273438; it seems as though a fair test generally has to be of the form abs(y-y_correct)<tol*abs(y_correct); rounding to some number of decimal places always allows for possibilities like this. (Not a complaint, just a point of interest.)