On Corrected Quadrature Rules and Optimal Error Bounds

Table 7

Results for the second Simpson rule.

Second Simpson rule
	Standard rule ()
	Computed	Absolute error	Relative error	Estimated order
	integral	ABS()	REL()
5	1.4464545347401641	0.0000132024920290
10	1.4464421478702252	0.0000008156220901		4.0
15	1.4464414928269707	0.0000001605788356		4.0
20	1.4464413829943144	0.0000000507461793		4.0
25	1.4464413530218192	0.0000000207736841		4.0
	Corrected rule ()
	Computed	Absolute error	Relative error	Estimated order
	integral	ABS()	REL()
5	1.4464413521758457	0.0000000199277106
10	1.4464413326945604	0.0000000004464253		5.5
15	1.4464413322889214	0.0000000000407863		5.9
20	1.4464413322554857	0.0000000000073506		6.0
25	1.4464413322500729	0.0000000000019378		6.0