Record of Testing of Omnisode

ode.over(Overrides .ode files)

Time	Language	Ode File	Equation	Start	End	Actual End	H	H Reason	Machine Digits	Desired Correct Digits	Estimated Correct Digits	Correct Digits	Terms	Type Sing Given	Given Least Sing	Ratio Least Sing	Three Term Least Sing	Six Term Least Sing	Iterations	Execution Time	Estimated Total Time	Last Save	diffeq program	diffeq results	Comment
2014-09-22T23:48:04-05:00	Ruby	add_c_lin	diff ( y , x , 1 ) = 0.3 + ( 0.1 * x + 0.2 ) ;	0.1	1.0	1.0899999999999999	0.09	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	11	0 Seconds	Done	269	add_c_lin diffeq.rb	add_c_lin Ruby results	OK
2014-09-22T23:48:05-05:00	Ruby	add_c_sin	diff ( y , x , 1 ) = 1.0 + sin ( x ) ;	0.1	1.0	1.0000960000000896	0.000128	Pole Accuracy	16	16	12	14	40	No Pole	NA	NONE	NONE	NONE	7032	1 Seconds	Done	269	add_c_sin diffeq.rb	add_c_sin Ruby results	OK
2014-09-22T23:48:06-05:00	Ruby	add_full_lin	diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ;	1.0	5.0	5.000255999999664	0.000512	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	7813	1 Seconds	Done	269	add_full_lin diffeq.rb	add_full_lin Ruby results	OK
2014-09-22T23:48:07-05:00	Ruby	add_lin_c	diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + 0.3 ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	add_lin_c diffeq.rb	add_lin_c Ruby results	OK
2014-09-22T23:48:07-05:00	Ruby	add_lin_full	diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ;	-5.0	5.0	5.0003839999992605	0.000512	Pole Accuracy	16	16	11	14	40	No Pole	NA	NONE	NONE	NONE	19532	3 Seconds	Done	269	add_lin_full diffeq.rb	add_lin_full Ruby results	OK
2014-09-22T23:48:11-05:00	Ruby	add_lin_lin	diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + ( 0.3 * x + 0.1 ) ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	add_lin_lin diffeq.rb	add_lin_lin Ruby results	OK
2014-09-22T23:48:11-05:00	Ruby	add	diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;	-5.0	5.0	5.000000000004714	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	78125	14 Seconds	Done	269	add diffeq.rb	add Ruby results	OK
2014-09-22T23:48:25-05:00	Ruby	add_sin_c	diff ( y , x , 1 ) = sin ( x ) + 1.0 ;	-5.0	5.0	5.000000000004714	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	78125	13 Seconds	Done	269	add_sin_c diffeq.rb	add_sin_c Ruby results	OK
2014-09-22T23:48:38-05:00	Ruby	add_sub_sin_c_cos_c_tan_c	diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	add_sub_sin_c_cos_c_tan_c diffeq.rb	add_sub_sin_c_cos_c_tan_c Ruby results	OK
2014-09-22T23:48:38-05:00	Ruby	arccos_sqrt	diff ( y , x , 1 ) = arccos ( sqrt ( 0.1 * x + 0.2 ) ) ;	0.0	0.5	0.5000000000000003	0.001	Max H	16	16	12	10	30	Real Sing	2.0	NONE	2.0002204141583833	NONE	500	0 Seconds	Done	269	arccos_sqrt diffeq.rb	arccos_sqrt Ruby results	Poor Accuracy
2014-09-22T23:48:38-05:00	Ruby	arcsin_c_arccos_c_arctan_c	diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	arcsin_c_arccos_c_arctan_c diffeq.rb	arcsin_c_arccos_c_arctan_c Ruby results	OK
2014-09-22T23:48:38-05:00	Ruby	arcsin_sqrt	diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ;	0.0	0.5	0.5000000000000002	0.01	Max H	16	16	13	8	30	Real Sing	2.0	NONE	2.0002204141583992	NONE	50	0 Seconds	Done	269	arcsin_sqrt diffeq.rb	arcsin_sqrt Ruby results	Poor Accuracy
2014-09-22T23:48:39-05:00	Ruby	arctan_sqrt	diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ;	-1.0	0.5	0.5000000000008392	1.6e-05	Pole Accuracy	16	16	11	13	40	Real Sing	1.0	NONE	NONE	NONE	93750	2 Minutes 7 Seconds	Done	269	arctan_sqrt diffeq.rb	arctan_sqrt Ruby results	Poor Accuracy
2014-09-22T23:50:46-05:00	Ruby	cosh_sqrt	diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ;	-1.9	-1.8	-1.7965757465635386	0.006083779613909593	Pole	16	16	13	7	30	Real Sing	0.10000000000000009	NONE	0.09967664519429255	NONE	17	0 Seconds	Done	269	cosh_sqrt diffeq.rb	cosh_sqrt Ruby results	OK
2014-09-22T23:50:46-05:00	Ruby	cos	diff ( y , x , 1 ) = cos ( x ) ;	0.0	5.0	5.000015621102507	0.00018315543846663006	Pole	16	16	9	11	40	No Pole	NA	NONE	0.06555198504945058	NONE	18910	3 Seconds	Done	269	cos diffeq.rb	cos Ruby results	OK
2014-09-22T23:50:49-05:00	Ruby	cos_sqrt_lin	diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ;	-1.4	-1.3	-1.299900000000011	0.0001	Max H	16	16	12	6	30	Real Sing	0.10000000000000009	NONE	0.09967108794652436	NONE	1001	1 Seconds	Done	269	cos_sqrt_lin diffeq.rb	cos_sqrt_lin Ruby results	Poor Accuracy
2014-09-22T23:50:50-05:00	Ruby	diff0	diff ( y , x , 1 ) = y ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	diff0 diffeq.rb	diff0 Ruby results	OK
2014-09-22T23:50:50-05:00	Ruby	diff2	diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;	-1.0	1.0	1.0000000000001823	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	15625	8 Seconds	Done	269	diff2 diffeq.rb	diff2 Ruby results	OK
2014-09-22T23:50:58-05:00	Ruby	diff	diff ( y , x , 2 ) = diff ( y , x , 1 ) ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	diff diffeq.rb	diff Ruby results	OK
2014-09-22T23:50:58-05:00	Ruby	div_c_exp	diff ( y , x , 1 ) = 2.0 / exp ( x ) ;	1.0	5.0	5.099999999999999	0.1	Display Interval	16	16	11	14	30	No Pole	NA	NONE	NONE	NONE	41	0 Seconds	Done	269	div_c_exp diffeq.rb	div_c_exp Ruby results	OK
2014-09-22T23:50:58-05:00	Ruby	div_c_lin	diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ;	2.5	3.1	3.1000000000000005	0.06000000000000001	Display Interval	16	16	13	10	30	Real Sing	4.0	NONE	NONE	NONE	10	0 Seconds	Done	269	div_c_lin diffeq.rb	div_c_lin Ruby results	PROBLEM - Missing Singularity
2014-09-22T23:50:59-05:00	Ruby	div_exp_exp	diff ( y , x , 1 ) = exp ( 0.1 * x ) / exp ( 0.2 * x ) ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	12	15	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	div_exp_exp diffeq.rb	div_exp_exp Ruby results	OK
2014-09-22T23:50:59-05:00	Ruby	div_lin_c	diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / 2.0 ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	div_lin_c diffeq.rb	div_lin_c Ruby results	OK
2014-09-22T23:50:59-05:00	Ruby	div_lin_exp	diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ;	1.0	5.0	5.099999999999999	0.1	Display Interval	16	16	11	14	30	No Pole	NA	NONE	NONE	NONE	41	0 Seconds	Done	269	div_lin_exp diffeq.rb	div_lin_exp Ruby results	OK
2014-09-22T23:50:59-05:00	Ruby	div_lin_lin	diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	16	30	Real Sing	1.6	NONE	1.6000000000000028	NONE	50	0 Seconds	Done	269	div_lin_lin diffeq.rb	div_lin_lin Ruby results	OK
2014-09-22T23:50:59-05:00	Ruby	div	diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;	0.0	1.5	1.5013360009236616	0.007717813985692804	Pole	16	16	13	16	30	Real Sing	0.16136031815181728	NONE	0.16136031794671196	NONE	31	0 Seconds	Done	269	div diffeq.rb	div Ruby results	OK
2014-09-22T23:51:00-05:00	Ruby	div_sin_c	diff ( y , x , 1 ) = sin ( x ) / 2.0 ;	-5.0	5.0	5.000000000004714	0.000128	Pole Accuracy	16	16	10	13	40	No Pole	NA	NONE	NONE	NONE	78125	12 Seconds	Done	269	div_sin_c diffeq.rb	div_sin_c Ruby results	OK
2014-09-22T23:51:12-05:00	Ruby	exp_sqrt	diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ;	2.0	3.0	3.000000000001	6.4e-05	Pole Accuracy	16	16	11	7	40	Real Sing	4.0	NONE	NONE	NONE	15625	9 Seconds	Done	269	exp_sqrt diffeq.rb	exp_sqrt Ruby results	Poor Accuracy
2014-09-22T23:51:21-05:00	Ruby	expt_c_c	diff ( y , x , 1 ) = expt ( 2.0 , 3.0 ) ;	-5.0	5.0	5.099999999999997	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	101	0 Seconds	Done	269	expt_c_c diffeq.rb	expt_c_c Ruby results	OK
2014-09-22T23:51:21-05:00	Ruby	expt_c_lin	diff ( y , x , 1 ) = expt ( 2.0 , ( 0.2 * x + 0.3 ) ) ;	1.0	5.0	5.099999999999999	0.1	Display Interval	16	16	13	16	30	Not Given	NA	NONE	NONE	NONE	41	0 Seconds	Done	269	expt_c_lin diffeq.rb	expt_c_lin Ruby results	OK
2014-09-22T23:51:21-05:00	Ruby	expt_c_sin	diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	Unknown	30	Not Given	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	expt_c_sin diffeq.rb	expt_c_sin Ruby results	OK
2014-09-22T23:51:21-05:00	Ruby	expt_lin_c	diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	expt_lin_c diffeq.rb	expt_lin_c Ruby results	OK
2014-09-22T23:51:21-05:00	Ruby	expt_lin_lin	diff ( y , x , 1 ) = expt ( ( 0.1 * x + 0.2 ) , ( 0.2 * x + 0.3 ) ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	Unknown	30	Not Given	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	expt_lin_lin diffeq.rb	expt_lin_lin Ruby results	OK
2014-09-22T23:51:22-05:00	Ruby	expt_lin_sin	diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( x ) ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	Unknown	30	Not Given	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	expt_lin_sin diffeq.rb	expt_lin_sin Ruby results	OK
2014-09-22T23:51:22-05:00	Ruby	expt_sin_c	diff ( y , x , 1 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ;	0.1	0.2	0.20000000000001328	3.2e-05	Pole Accuracy	16	16	12	11	40	Not Given	NA	NONE	NONE	NONE	3125	2 Seconds	Done	269	expt_sin_c diffeq.rb	expt_sin_c Ruby results	OK
2014-09-22T23:51:24-05:00	Ruby	expt_sin_lin	diff ( y , x , 1 ) = expt ( sin ( x ) , ( 0.2 * x + 0.3 ) ) ;	0.1	0.2	0.2037979958446165	0.006105764461448019	Pole	16	16	13	Unknown	30	Not Given	NA	NONE	NONE	NONE	17	0 Seconds	Done	269	expt_sin_lin diffeq.rb	expt_sin_lin Ruby results	OK
2014-09-22T23:51:24-05:00	Ruby	expt_sin_sin	diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ;	0.1	5.0	5.0151999999999894	0.032768	Optimal	16	16	12	Unknown	30	Not Given	NA	NONE	NONE	NONE	150	0 Seconds	Done	269	expt_sin_sin diffeq.rb	expt_sin_sin Ruby results	OK
2014-09-22T23:51:24-05:00	Ruby	h2sin	diff ( y , x , 2 ) = sin ( x ) ;	0.1	5.0	5.0000960000023555	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	38282	10 Seconds	Done	269	h2sin diffeq.rb	h2sin Ruby results	OK
2014-09-22T23:51:34-05:00	Ruby	h3sin	diff ( y , x , 3 ) = sin ( x ) ;	0.1	1.5	1.5000639999997223	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	10938	4 Seconds	Done	269	h3sin diffeq.rb	h3sin Ruby results	OK
2014-09-22T23:51:38-05:00	Ruby	h5h3	diff ( y , x , 5 ) = m1 * diff ( y , x , 3 ) ;	0.1	1.5	1.5000639999997223	0.000128	Pole Accuracy	16	16	11	12	40	No Pole	NA	NONE	NONE	NONE	10938	8 Seconds	Done	269	h5h3 diffeq.rb	h5h3 Ruby results	OK
2014-09-22T23:51:46-05:00	Ruby	lin_arccos	diff ( y , x , 1 ) = arccos ( 0.1 * x + 0.2 ) ;	-0.8	0.8	0.8999999999999998	0.1	Display Interval	16	16	13	7	30	Not Given	NA	NONE	NONE	NONE	17	0 Seconds	Done	269	lin_arccos diffeq.rb	lin_arccos Ruby results	Poor Accuracy
2014-09-22T23:51:47-05:00	Ruby	lin_arcsin	diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ;	-0.8	0.8	0.8999999999999998	0.1	Display Interval	16	16	13	7	30	Not Given	NA	NONE	NONE	NONE	17	0 Seconds	Done	269	lin_arcsin diffeq.rb	lin_arcsin Ruby results	Poor Accuracy
2014-09-22T23:51:47-05:00	Ruby	lin_arctan	diff ( y , x , 1 ) = arctan ( 0.1 * x + 0.2 ) ;	-1.0	-0.6	-0.5999999999999996	0.04	Display Interval	16	16	13	6	30	Not Given	NA	NONE	NONE	NONE	10	0 Seconds	Done	269	lin_arctan diffeq.rb	lin_arctan Ruby results	Poor Accuracy
2014-09-22T23:51:47-05:00	Ruby	lin_cosh	diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ;	0.1	2.0	0.46082764798282333	2.56e-07	Pole Accuracy	16	16	11	11	30	No Pole	NA	NONE	NONE	NONE	1409483	3 Minutes 0 Seconds	15 Minutes 47.82026618506882 Seconds	269	lin_cosh diffeq.rb	lin_cosh Ruby results	OK
2014-09-22T23:54:47-05:00	Ruby	lin_exp	diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ;	1.0	10.0	10.099999999999982	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	91	0 Seconds	Done	269	lin_exp diffeq.rb	lin_exp Ruby results	OK
2014-09-22T23:54:47-05:00	Ruby	lin_ln	diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ;	20.0	30.0	30.000000000000142	0.1	Display Interval	16	16	13	14	30	Real Sing	22.0	NONE	21.99999999999995	NONE	100	0 Seconds	Done	269	lin_ln diffeq.rb	lin_ln Ruby results	OK
2014-09-22T23:54:47-05:00	Ruby	lin_sin_cos	diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	lin_sin_cos diffeq.rb	lin_sin_cos Ruby results	OK
2014-09-22T23:54:47-05:00	Ruby	lin_sinh	diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ;	0.1	2.0	2.000019711998978	6.5536e-05	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	28992	5 Seconds	Done	269	lin_sinh diffeq.rb	lin_sinh Ruby results	OK
2014-09-22T23:54:52-05:00	Ruby	lin_tanh	diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ;	1.1	2.0	2.000000000000001	0.09	Display Interval	16	16	13	16	40	No Pole	NA	NONE	NONE	NONE	10	0 Seconds	Done	269	lin_tanh diffeq.rb	lin_tanh Ruby results	OK
2014-09-22T23:54:52-05:00	Ruby	lin_tan	diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ;	-1.0	-0.9	-0.8999999999999999	0.009999999999999998	Display Interval	16	16	13	16	30	Real Sing	0.1953981629999999	NONE	0.19539816339744423	NONE	10	0 Seconds	Done	269	lin_tan diffeq.rb	lin_tan Ruby results	OK
2014-09-22T23:54:53-05:00	Ruby	ln_c_exp_c_sqrt_c	diff ( y , x , 1 ) = ln ( 0.1 ) + exp ( 0.1 ) + sqrt ( 0.1 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	ln_c_exp_c_sqrt_c diffeq.rb	ln_c_exp_c_sqrt_c Ruby results	OK
2014-09-22T23:54:53-05:00	Ruby	ln_sqrt	diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ;	10.0	11.0	11.099999999999996	0.1	Display Interval	16	16	13	7	40	Real Sing	12.0	NONE	12.012315919329723	NONE	11	0 Seconds	Done	269	ln_sqrt diffeq.rb	ln_sqrt Ruby results	Poor Accuracy
2014-09-22T23:54:53-05:00	Ruby	mtest1	diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ;	0.1	10.0	2.5483839999999036	0.000128	Pole Accuracy	16	16	10	13	40	No Pole	NA	NONE	NONE	NONE	19128	3 Minutes 0 Seconds	12 Minutes 7.788959171966553 Seconds	269	mtest1 diffeq.rb	mtest1 Ruby results	OK
ditto	ditto	ditto	diff ( y2 , x , 1 ) = y1 - 1.0 ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	11	14	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-22T23:57:53-05:00	Ruby	mtest2	diff ( y1 , x , 1 ) = m1 * y2 ;	0.2	0.8	0.5090300000002589	1.0e-05	Max H	16	16	11	3	40	No Pole	NA	NONE	NONE	NONE	30903	3 Minutes 0 Seconds	5 Minutes 49.469324359013626 Seconds	269	mtest2 diffeq.rb	mtest2 Ruby results	Poor Accuracy -- BAD TEST??
ditto	ditto	ditto	diff ( y2 , x , 1 ) = y1 ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	11	2	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-23T00:00:53-05:00	Ruby	mtest3	diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ;	0.1	0.5	0.5072721281298758	0.009933466539753057	Pole	16	16	12	16	40	No Pole	NA	NONE	0.09933466539753057	NONE	41	0 Seconds	Done	269	mtest3 diffeq.rb	mtest3 Ruby results	OK
ditto	ditto	ditto	diff ( y1 , x , 1 ) = y2 - 1.0 ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	13	16	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-23T00:00:53-05:00	Ruby	mtest4	diff ( y2 , x , 3 ) = m1 * cos ( x ) ;	0.1	5.0	1.3097279999998621	0.000128	Pole Accuracy	16	16	11	14	40	No Pole	NA	NONE	NONE	NONE	9451	2 Minutes 59 Seconds	12 Minutes 5.962309564196175 Seconds	269	mtest4 diffeq.rb	mtest4 Ruby results	OK
ditto	ditto	ditto	diff ( y1 , x , 1 ) = m1 * y2 ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	11	13	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-23T00:03:53-05:00	Ruby	mtest5	diff ( y1 , x , 1 ) = m1 * y2 ;	0.5	5.0	5.099999999999998	0.1	Display Interval	16	16	12	8	30	No Pole	NA	NONE	NONE	NONE	46	0 Seconds	Done	269	mtest5 diffeq.rb	mtest5 Ruby results	OK
ditto	ditto	ditto	diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	13	8	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-23T00:03:53-05:00	Ruby	mtest6	diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ;	1.5	8.0	4.517600000002959	0.0001	Max H	16	16	11	3	40	Not Given	NA	NONE	NONE	NONE	30176	3 Minutes 0 Seconds	6 Minutes 27.712496271615123 Seconds	269	mtest6 diffeq.rb	mtest6 Ruby results	???
ditto	ditto	ditto	diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	11	3	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-23T00:06:53-05:00	Ruby	mtest7	diff ( y2 , x , 5 ) = y1 ;	0.1	0.7	0.7000640000000499	0.000128	Pole Accuracy	16	16	12	14	40	No Pole	NA	NONE	NONE	NONE	4688	56 Seconds	Done	269	mtest7 diffeq.rb	mtest7 Ruby results	OK
ditto	ditto	ditto	diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	11	14	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-23T00:07:50-05:00	Ruby	mtest8	diff ( y2 , x , 4 ) = y1 - 1.0 ;	0.1	1.4	1.4000959999997957	0.000128	Pole Accuracy	16	16	11	15	40	No Pole	NA	NONE	NONE	NONE	10157	1 Minutes 59 Seconds	Done	269	mtest8 diffeq.rb	mtest8 Ruby results	OK
ditto	ditto	ditto	diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;	ditto	ditto	ditto	ditto	ditto	ditto	ditto	11	14	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto	ditto
2014-09-23T00:09:49-05:00	Ruby	mult2	diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ;	0.1	1.0	0.3496403865647582	3.2768e-07	Pole Accuracy	16	16	11	13	30	No Pole	NA	NONE	NONE	NONE	761842	3 Minutes 0 Seconds	10 Minutes 48.93260897005928 Seconds	269	mult2 diffeq.rb	mult2 Ruby results	OK
2014-09-23T00:12:49-05:00	Ruby	mult_c_lin	diff ( y , x , 1 ) = 2.0 * ( 0.2 * x + 0.3 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	mult_c_lin diffeq.rb	mult_c_lin Ruby results	OK
2014-09-23T00:12:49-05:00	Ruby	mult_c_sin	diff ( y , x , 1 ) = 2.0 * sin ( x ) ;	0.1	5.0	5.0000960000023555	0.000128	Pole Accuracy	16	16	11	12	40	No Pole	NA	NONE	NONE	NONE	38282	6 Seconds	Done	269	mult_c_sin diffeq.rb	mult_c_sin Ruby results	OK
2014-09-23T00:12:55-05:00	Ruby	mult_div_sinh_cosh_tanh	diff ( y , x , 1 ) = sinh ( 0.1 ) * cosh ( 0.05 ) / tanh ( 0.02 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	mult_div_sinh_cosh_tanh diffeq.rb	mult_div_sinh_cosh_tanh Ruby results	OK
2014-09-23T00:12:56-05:00	Ruby	mult_lin_c	diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * 2.0 ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	mult_lin_c diffeq.rb	mult_lin_c Ruby results	OK
2014-09-23T00:12:56-05:00	Ruby	mult_lin_lin	diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) * ( 0.2 * x + 0.3 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	mult_lin_lin diffeq.rb	mult_lin_lin Ruby results	OK
2014-09-23T00:12:56-05:00	Ruby	mult_lin_sin	diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	mult_lin_sin diffeq.rb	mult_lin_sin Ruby results	OK
2014-09-23T00:12:56-05:00	Ruby	mult	diff ( y , x , 1 ) = x * x ;	0.1	10.0	10.09999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	100	0 Seconds	Done	269	mult diffeq.rb	mult Ruby results	OK
2014-09-23T00:12:56-05:00	Ruby	mult_sin_c	diff ( y , x , 1 ) = sin ( x ) * 2.0 ;	0.1	5.0	5.0000960000023555	0.000128	Pole Accuracy	16	16	11	12	40	No Pole	NA	NONE	NONE	NONE	38282	7 Seconds	Done	269	mult_sin_c diffeq.rb	mult_sin_c Ruby results	OK
2014-09-23T00:13:03-05:00	Ruby	mult_sin_lin	diff ( y , x , 1 ) = sin ( x ) * ( 0.2 * x + 0.3 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	mult_sin_lin diffeq.rb	mult_sin_lin Ruby results	OK
2014-09-23T00:13:03-05:00	Ruby	mult_sin_sin	diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ;	0.1	0.2	0.20101488982005403	0.005942052342356119	Pole	16	16	13	16	30	No Pole	NA	NONE	0.09735458557716259	NONE	17	0 Seconds	Done	269	mult_sin_sin diffeq.rb	mult_sin_sin Ruby results	PROBLEM - False Singularity
2014-09-23T00:13:03-05:00	Ruby	nonlinear1	diff ( y , x , 1 ) = y * y ;	0.0	0.5	0.5499999999999999	0.05	Display Interval	16	16	13	16	20	Real Sing	0.5	0.5000000000000001	0.500000000000001	NONE	11	0 Seconds	Done	269	nonlinear1 diffeq.rb	nonlinear1 Ruby results	OK
2014-09-23T00:13:03-05:00	Ruby	nonlinear2	diff ( y , x , 1 ) = y * y ;	0.0	0.2	0.21999999999999997	0.02	Display Interval	16	16	13	16	20	Real Sing	0.30000000000000004	0.29999999999999977	0.3	NONE	11	0 Seconds	Done	269	nonlinear2 diffeq.rb	nonlinear2 Ruby results	OK
2014-09-23T00:13:04-05:00	Ruby	sing1	diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ;	-2.0	-1.5	-1.4999999999999996	0.05	Display Interval	16	16	13	16	20	Complex Sing	1.5500003225806114	NONE	1.5500064516950824	1.5500003509810494	10	0 Seconds	Done	269	sing1 diffeq.rb	sing1 Ruby results	OK
2014-09-23T00:13:04-05:00	Ruby	sing2	diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ;	-2.0	-1.5	-1.4999999999999996	0.05	Display Interval	16	16	13	16	20	Complex Sing	1.8445866745696715	NONE	NONE	1.844586674569669	10	0 Seconds	Done	269	sing2 diffeq.rb	sing2 Ruby results	OK
2014-09-23T00:13:04-05:00	Ruby	sing3	diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;	-2.0	-0.7	-0.6560999999999988	0.07290000000000006	Pole	16	16	12	6	20	Real Sing	0.7289999999999989	NONE	0.7290000000000006	NONE	14	0 Seconds	Done	269	sing3 diffeq.rb	sing3 Ruby results	OK
2014-09-23T00:13:04-05:00	Ruby	sing4	diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ;	-2.0	-1.0	-0.9999999999999992	0.1	Display Interval	16	16	13	16	40	Complex Sing	1.48660687473185	NONE	NONE	1.4866068747318468	10	0 Seconds	Done	269	sing4 diffeq.rb	sing4 Ruby results	OK
2014-09-23T00:13:04-05:00	Ruby	sing5	diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;	-1.0	-0.7	-0.6999999999999997	0.030000000000000006	Display Interval	16	16	13	7	20	Real Sing	0.7299999999999998	NONE	0.7300000000000008	NONE	10	0 Seconds	Done	269	sing5 diffeq.rb	sing5 Ruby results	OK
2014-09-23T00:13:05-05:00	Ruby	sing6	diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;	2.0	3.0	3.000000000000001	0.1	Display Interval	16	16	13	9	20	Real Sing	3.099999999999999	NONE	3.0999999999999983	NONE	10	0 Seconds	Done	269	sing6 diffeq.rb	sing6 Ruby results	OK
2014-09-23T00:13:05-05:00	Ruby	sing7	diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;	2.0	3.0	3.000000000000001	0.1	Display Interval	16	16	13	7	30	Real Sing	3.099999999999999	NONE	3.1000000000000005	NONE	10	0 Seconds	Done	269	sing7 diffeq.rb	sing7 Ruby results	OK
2014-09-23T00:13:05-05:00	Ruby	sinh_sqrt	diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ;	2.0	3.0	3.000000000001	6.4e-05	Pole Accuracy	16	16	11	6	40	Real Sing	4.0	NONE	NONE	NONE	15625	12 Seconds	Done	269	sinh_sqrt diffeq.rb	sinh_sqrt Ruby results	Poor Accuracy
2014-09-23T00:13:17-05:00	Ruby	sin	diff ( y , x , 1 ) = sin ( x ) ;	0.0	1.0	1.0039454551175273	0.009933466539753067	Pole	16	16	13	16	40	No Pole	NA	NONE	0.09933466539753066	NONE	92	0 Seconds	Done	269	sin diffeq.rb	sin Ruby results	OK
2014-09-23T00:13:17-05:00	Ruby	sin_lg_h	diff ( y , x , 1 ) = sin ( x ) ;	0.0	5.0	5.5	1.0	Min H (Pole)	16	16	13	16	40	No Pole	NA	NONE	0.07056000402993359	NONE	6	0 Seconds	Done	269	sin_lg_h diffeq.rb	sin_lg_h Ruby results	OK
2014-09-23T00:13:17-05:00	Ruby	sin_sqrt_lin	diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ;	2.0	3.0	3.0000000000021103	0.0001	Max H	16	16	12	6	40	Real Sing	3.5	NONE	NONE	3.9997343936297693	10000	8 Seconds	Done	269	sin_sqrt_lin diffeq.rb	sin_sqrt_lin Ruby results	Poor Accuracy & PROBLEM - found complex singularity instead of real - COULD BE RIGHT!!!
2014-09-23T00:13:25-05:00	Ruby	sqrt	diff ( y , x , 1 ) = sqrt ( x ) ;	0.1	0.2	0.2000000000000006	0.006250000000000044	Pole	16	16	13	16	40	Real Sing	0.1	NONE	0.09999999999999959	NONE	16	0 Seconds	Done	269	sqrt diffeq.rb	sqrt Ruby results	OK
2014-09-23T00:13:25-05:00	Ruby	sqrt_tone	diff ( y , x , 1 ) = sqrt ( x ) ;	0.5	0.6	0.6000000000000001	0.009999999999999998	Display Interval	16	16	13	16	40	Real Sing	0.5	NONE	0.5000000000000004	NONE	10	0 Seconds	Done	269	sqrt_tone diffeq.rb	sqrt_tone Ruby results	OK
2014-09-23T00:13:25-05:00	Ruby	sqrt_sqrt	diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ;	0.1	0.5	0.5399999999999999	0.04	Display Interval	16	16	13	16	40	Real Sing	2.1	NONE	2.0999999999999845	NONE	11	0 Seconds	Done	269	sqrt_sqrt diffeq.rb	sqrt_sqrt Ruby results	OK
2014-09-23T00:13:25-05:00	Ruby	sqrt_sqrt_tone	diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ;	0.5	1.5	1.5000000000000002	0.1	Display Interval	16	16	13	16	40	Real Sing	2.5	NONE	2.5000000000000204	NONE	10	0 Seconds	Done	269	sqrt_sqrt_tone diffeq.rb	sqrt_sqrt_tone Ruby results	OK
2014-09-23T00:13:26-05:00	Ruby	sqrt_sqrt_tzero	diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ;	0.0	0.5	0.5499999999999999	0.05	Display Interval	16	16	13	16	40	Real Sing	2.0	NONE	2.0000000000000173	NONE	11	0 Seconds	Done	269	sqrt_sqrt_tzero diffeq.rb	sqrt_sqrt_tzero Ruby results	OK
2014-09-23T00:13:26-05:00	Ruby	sub_c_lin	diff ( y , x , 1 ) = 0.3 - ( 0.1 * x + 0.2 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	sub_c_lin diffeq.rb	sub_c_lin Ruby results	OK
2014-09-23T00:13:26-05:00	Ruby	sub_c_sin	diff ( y , x , 1 ) = 1.0 - sin ( x ) ;	0.1	5.0	5.0000960000023555	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	38282	6 Seconds	Done	269	sub_c_sin diffeq.rb	sub_c_sin Ruby results	OK
2014-09-23T00:13:32-05:00	Ruby	sub_full_lin	diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;	0.1	5.0	5.00035199999963	0.000512	Pole Accuracy	16	16	11	14	40	No Pole	NA	NONE	NONE	NONE	9571	2 Seconds	Done	269	sub_full_lin diffeq.rb	sub_full_lin Ruby results	OK
2014-09-23T00:13:34-05:00	Ruby	sub_lin_c	diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - 0.3 ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	15	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	sub_lin_c diffeq.rb	sub_lin_c Ruby results	OK
2014-09-23T00:13:34-05:00	Ruby	sub_lin_lin	diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - ( 0.3 * x + 0.1 ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	16	30	No Pole	NA	NONE	NONE	NONE	50	0 Seconds	Done	269	sub_lin_lin diffeq.rb	sub_lin_lin Ruby results	OK
2014-09-23T00:13:34-05:00	Ruby	sub_lin_sin	diff ( y , x , 1 ) = ( 0.1 * x + 1.0 ) - sin ( x ) ;	0.1	5.0	5.0000960000023555	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	38282	6 Seconds	Done	269	sub_lin_sin diffeq.rb	sub_lin_sin Ruby results	OK
2014-09-23T00:13:41-05:00	Ruby	sub	diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ;	0.0	10.0	10.000000000007356	0.000128	Pole Accuracy	16	16	11	13	40	No Pole	NA	NONE	NONE	NONE	78125	14 Seconds	Done	269	sub diffeq.rb	sub Ruby results	OK
2014-09-23T00:13:55-05:00	Ruby	sub_sin_c	diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ;	0.1	5.0	5.0000960000023555	0.000128	Pole Accuracy	16	16	11	12	40	No Pole	NA	NONE	NONE	NONE	38282	7 Seconds	Done	269	sub_sin_c diffeq.rb	sub_sin_c Ruby results	OK
2014-09-23T00:14:02-05:00	Ruby	sub_sin_cos	diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ;	0.1	5.0	5.0000960000023555	0.000128	Pole Accuracy	16	16	11	12	40	No Pole	NA	NONE	NONE	NONE	38282	13 Seconds	Done	269	sub_sin_cos diffeq.rb	sub_sin_cos Ruby results	OK
2014-09-23T00:14:15-05:00	Ruby	tanh_sqrt	diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	Unknown	30	Real Sing	1.6	NONE	NONE	NONE	50	0 Seconds	Done	269	tanh_sqrt diffeq.rb	tanh_sqrt Ruby results	??
2014-09-23T00:14:15-05:00	Ruby	tan_sqrt	diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;	1.4	2.1	2.100000000000145	0.0001	Max H	16	16	11	5	40	Real Sing	3.4	NONE	NONE	NONE	7000	14 Seconds	Done	269	tan_sqrt diffeq.rb	tan_sqrt Ruby results	PROBLEM - Singularity not accurate
2014-09-23T00:14:30-05:00	Ruby	tan_sqrt_lin	diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ;	0.1	5.0	5.099999999999998	0.1	Display Interval	16	16	13	Unknown	40	Real Sing	1.6	NONE	1.4925096023196347	NONE	50	0 Seconds	Done	269	tan_sqrt_lin diffeq.rb	tan_sqrt_lin Ruby results	PROBLEM - Singularity not accurate
2014-09-23T00:14:31-05:00	Ruby	tan	diff ( y , x , 1 ) = tan ( x ) ;	0.1	1.5	1.5011030538449674	0.007743696994436347	Pole	16	16	13	15	40	Real Sing	0.16190146756641277	NONE	0.16190146736131195	NONE	30	0 Seconds	Done	269	tan diffeq.rb	tan Ruby results	OK
2014-09-23T00:14:31-05:00	Ruby	div_c_lin_back	diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ;	3.1	2.5	2.4999999999999996	-0.1	Display Interval	16	16	13	10	30	Real Sing	4.1	NONE	NONE	NONE	6	0 Seconds	0.0 Seconds	269	div_c_lin_back diffeq.rb	div_c_lin_back Ruby results	PROBLEM - missing singularity
2014-09-23T00:14:31-05:00	Ruby	sin_back	diff ( y , x , 1 ) = sin ( x ) ;	-0.1	-1.0	-1.0000960000000896	-0.000128	Pole Accuracy	16	16	12	14	40	No Pole	NA	NONE	NONE	NONE	7032	1 Seconds	1.0 Seconds	269	sin_back diffeq.rb	sin_back Ruby results	OK
2014-09-23T00:14:32-05:00	Ruby	sing1_back	diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ;	-1.5	-2.0	-2.0000000000000004	-0.1	Display Interval	16	16	13	16	20	Complex Sing	1.6000003124999698	NONE	1.6000062500747076	1.6000002092275922	5	0 Seconds	0.0 Seconds	269	sing1_back diffeq.rb	sing1_back Ruby results	OK
2014-09-23T00:14:33-05:00	Ruby	sing2_back	diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ;	-1.5	-2.0	-2.0000000000000004	-0.1	Display Interval	16	16	14	16	20	Complex Sing	1.886796226411321	NONE	NONE	1.8867962264113212	5	0 Seconds	0.0 Seconds	269	sing2_back diffeq.rb	sing2_back Ruby results	OK
2014-09-23T00:14:33-05:00	Ruby	sing3_back	diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;	-0.7	-2.0	-2.0107199999999974	-0.032768	Optimal	16	16	12	7	20	Real Sing	0.732768	NONE	0.7327679999999994	NONE	40	0 Seconds	0.0 Seconds	269	sing3_back diffeq.rb	sing3_back Ruby results	Poor Accuracy
2014-09-23T00:14:33-05:00	Ruby	sing4_back	diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ;	-1.0	-2.0	-2.000000000000001	-0.1	Display Interval	16	16	13	15	40	Complex Sing	1.4866068747318506	NONE	NONE	1.4866068747318473	10	0 Seconds	0.0 Seconds	269	sing4_back diffeq.rb	sing4_back Ruby results	OK
2014-09-23T00:14:33-05:00	Ruby	sing5_back	diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;	-0.7	-1.0	-1.0276800000000001	-0.032768	Optimal	16	16	13	7	20	Real Sing	0.732768	NONE	0.7327680000000004	NONE	10	0 Seconds	0.0 Seconds	269	sing5_back diffeq.rb	sing5_back Ruby results	Poor Accuracy
2014-09-23T00:14:33-05:00	Ruby	sing6_back	diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;	3.0	2.0	1.9999999999999991	-0.1	Display Interval	16	16	13	8	20	Real Sing	3.1	NONE	3.100000000000007	NONE	10	0 Seconds	0.0 Seconds	269	sing6_back diffeq.rb	sing6_back Ruby results	OK
2014-09-23T00:14:34-05:00	Ruby	sing7_back	diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;	3.0	2.0	1.9999999999999991	-0.1	Display Interval	16	16	12	6	30	Real Sing	3.1	NONE	3.099999999999985	NONE	10	0 Seconds	0.0 Seconds	269	sing7_back diffeq.rb	sing7_back Ruby results	OK