Details

sample123.0ms

Algorithm

intervals

Results

44.0ms	191×	body	80	valid
26.0ms	21×	body	1280	valid
17.0ms	20×	body	640	valid
10.0ms	15×	body	320	valid
4.0ms	9×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	29
1	52	29
2	115	29
3	267	29
4	751	29
5	3196	29
done	5000	29

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.3b	(pow (sin ky) 2.0)
2.1b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`times-frac`
19×	`add-exp-log`
15×	`sqrt-prod`
13×	`unpow-prod-down`
11×	`associate-l`
8×	`add-cbrt-cube`
6×	`pow1` `prod-exp` `associate-/r*`
5×	`associate-r`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `flip3-+` `div-exp` `flip-+` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `associate-/r/` `div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms	(pow (sin ky) 2.0)
17.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
21.0ms	(pow (sin ky) 2.0)
126.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
158.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify7.1min

Counts

122 → 122

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	19	43
1	39	43
2	87	43
3	219	43
4	697	43
5	3115	43
done	5000	43
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	19	62
1	40	40
2	99	22
3	271	22
4	888	22
5	4508	22
done	5000	22
0	19	42
1	40	21
2	88	21
3	219	21
4	682	21
5	3109	21
done	5001	21
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	2	2
1	4	1
done	4	1
0	17	20
1	37	20
2	85	20
3	219	20
4	692	20
5	3101	20
done	5000	20
0	20	24
1	55	24
2	151	24
3	677	24
4	4659	24
done	5000	24
0	21	60
1	57	42
2	199	42
3	846	42
4	4700	42
done	5000	42
0	19	40
1	50	40
2	166	34
3	709	34
4	4367	34
done	5001	34
0	17	20
1	38	20
2	94	20
3	293	20
4	1156	20
done	5000	20
0	3	3
1	6	1
done	6	1
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	18	21
1	32	21
2	59	21
3	118	21
4	215	21
5	417	21
6	1045	21
7	3447	21
done	5000	21
0	17	20
1	32	20
2	52	20
3	109	20
4	208	20
5	406	20
6	1018	20
7	3401	20
done	5001	20
0	16	19
1	31	19
2	51	19
3	103	19
4	215	19
5	443	19
6	1078	19
7	3460	19
done	5000	19
0	16	19
1	31	19
2	51	19
3	103	19
4	215	19
5	443	19
6	1078	19
7	3460	19
done	5000	19
0	16	19
1	31	19
2	55	19
3	115	19
4	309	19
5	1053	19
6	4652	19
done	5000	19
0	15	18
1	37	18
2	86	18
3	239	18
4	780	18
5	3621	18
done	5000	18
0	15	18
1	36	18
2	90	18
3	262	18
4	919	18
5	4506	18
done	5000	18
0	18	53
1	51	47
2	183	21
3	854	21
done	5000	21
0	16	37
1	35	37
2	79	37
3	215	37
4	697	37
5	3222	37
done	5000	37
0	15	18
1	34	18
2	78	18
3	210	18
4	688	18
5	3239	18
done	5000	18
0	16	53
1	45	53
2	173	19
3	867	19
done	5000	19
0	15	18
1	34	18
2	78	18
3	210	18
4	688	18
5	3239	18
done	5000	18
0	15	18
1	34	18
2	78	18
3	210	18
4	688	18
5	3239	18
done	5000	18
0	16	19
1	29	19
2	48	19
3	95	19
4	208	19
5	515	19
6	1617	19
done	5000	19
0	16	19
1	29	19
2	48	19
3	95	19
4	208	19
5	515	19
6	1617	19
done	5000	19
0	16	19
1	29	19
2	45	19
3	84	19
4	169	19
5	401	19
6	1176	19
7	4434	19
done	5001	19
0	16	19
1	29	19
2	45	19
3	84	19
4	169	19
5	401	19
6	1176	19
7	4434	19
done	5001	19
0	17	20
1	29	20
2	52	20
3	99	20
4	218	20
5	552	20
6	1806	20
done	5001	20
0	17	20
1	29	20
2	52	20
3	99	20
4	218	20
5	552	20
6	1806	20
done	5001	20
0	10	12
1	20	12
2	44	12
3	115	12
4	360	12
5	1664	12
done	5000	12
0	10	12
1	20	12
2	44	12
3	115	12
4	360	12
5	1664	12
done	5000	12
0	10	12
1	20	12
2	44	12
3	115	12
4	360	12
5	1663	12
done	5000	12
0	10	12
1	20	12
2	44	12
3	115	12
4	360	12
5	1663	12
done	5000	12
0	16	29
1	31	29
2	57	29
3	120	29
4	271	29
5	726	29
6	2378	29
done	5000	29
0	15	18
1	28	18
2	47	18
3	94	18
4	207	18
5	515	18
6	1600	18
done	5000	18
0	8	9
1	18	7
2	34	7
3	68	7
4	133	7
5	283	7
6	735	7
7	2371	7
done	5001	7
0	9	11
1	21	9
2	36	7
3	72	7
4	137	7
5	288	7
6	737	7
7	2374	7
done	5001	7
0	8	9
1	18	7
2	34	7
3	68	7
4	133	7
5	283	7
6	735	7
7	2371	7
done	5001	7
0	15	18
1	34	18
2	78	18
3	209	18
4	681	18
5	3224	18
done	5000	18
0	15	18
1	34	18
2	78	18
3	209	18
4	681	18
5	3224	18
done	5000	18
0	14	16
1	30	16
2	70	16
3	195	16
4	664	16
5	3194	16
done	5000	16
0	14	16
1	30	16
2	70	16
3	195	16
4	664	16
5	3194	16
done	5000	16
0	13	15
1	29	15
2	69	15
3	202	15
4	672	15
5	3161	15
done	5001	15
0	14	17
1	33	17
2	77	17
3	208	17
4	682	17
5	3171	17
done	5000	17
0	13	15
1	31	15
2	71	15
3	203	15
4	657	15
5	3084	15
done	5001	15
0	15	18
1	34	18
2	58	18
3	113	18
4	251	18
5	643	18
6	2073	18
done	5000	18
0	15	18
1	34	18
2	59	18
3	114	18
4	255	18
5	636	18
6	2061	18
done	5000	18
0	14	17
1	33	17
2	77	17
3	208	17
4	682	17
5	3171	17
done	5000	17
0	16	19
1	34	19
2	82	19
3	216	19
4	700	19
5	3318	19
done	5000	19
0	17	21
1	48	21
2	144	21
3	519	21
4	2411	21
done	5000	21
0	16	27
1	36	21
2	89	21
3	275	21
4	1205	21
done	5000	21
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	3	3
1	6	1
done	6	1
0	6	8
1	10	8
2	17	8
3	41	8
4	98	8
5	256	8
6	883	8
7	3279	8
done	5000	8
0	5	5
1	9	5
2	14	5
3	32	5
4	72	5
5	176	5
6	550	5
7	2167	5
done	5000	5
0	4	4
1	11	2
2	18	2
3	29	2
4	51	2
5	112	2
6	321	2
7	1250	2
done	5000	2
0	6	9
1	10	9
2	15	9
3	33	9
4	75	9
5	182	9
6	565	9
7	1989	9
done	5000	9
0	5	5
1	9	5
2	14	5
3	32	5
4	72	5
5	176	5
6	550	5
7	1957	5
done	5000	5
0	5	5
1	9	5
2	14	5
3	32	5
4	72	5
5	176	5
6	550	5
7	1957	5
done	5000	5
0	5	5
1	9	5
2	14	5
3	32	5
4	72	5
5	176	5
6	550	5
7	1957	5
done	5000	5
0	3	3
1	9	1
2	12	1
3	18	1
4	25	1
5	35	1
6	48	1
7	64	1
8	83	1
9	105	1
10	130	1
11	158	1
12	189	1
13	223	1
14	260	1
15	300	1
16	343	1
17	389	1
18	438	1
19	490	1
20	545	1
21	603	1
22	664	1
23	728	1
24	795	1
25	865	1
26	938	1
27	1014	1
28	1093	1
29	1175	1
30	1260	1
31	1348	1
32	1439	1
33	1533	1
34	1630	1
35	1730	1
36	1833	1
37	1939	1
38	2048	1
39	2160	1
40	2275	1
41	2393	1
42	2514	1
43	2638	1
44	2765	1
45	2895	1
46	3028	1
47	3164	1
48	3303	1
49	3445	1
50	3590	1
51	3738	1
52	3889	1
53	4043	1
54	4200	1
55	4360	1
56	4523	1
57	4689	1
58	4858	1
done	5000	1
0	4	4
1	8	4
2	13	4
3	31	4
4	71	4
5	175	4
6	552	4
7	1953	4
done	5000	4
0	5	5
1	11	5
2	19	5
3	42	5
4	108	5
5	309	5
6	1093	5
7	4992	5
done	5000	5
0	5	5
1	9	5
2	16	5
3	39	5
4	94	5
5	254	5
6	878	5
7	3724	5
done	5000	5
0	6	11
1	10	11
2	15	11
3	33	11
4	73	11
5	177	11
6	560	11
7	1981	11
done	5000	11
0	5	5
1	9	5
2	14	5
3	32	5
4	72	5
5	176	5
6	556	5
7	1964	5
done	5000	5
0	6	14
1	13	11
2	34	6
3	89	6
4	231	6
5	795	6
6	3683	6
done	5001	6
0	5	5
1	9	5
2	15	5
3	33	5
4	73	5
5	175	5
6	555	5
7	1976	5
done	5001	5
0	5	5
1	9	5
2	15	5
3	33	5
4	73	5
5	175	5
6	555	5
7	1976	5
done	5001	5
0	6	6
1	9	6
2	17	6
3	38	6
4	88	6
5	218	6
6	723	6
7	2520	6
done	5000	6
0	6	6
1	9	6
2	17	6
3	38	6
4	88	6
5	218	6
6	723	6
7	2520	6
done	5000	6
0	20	24
1	42	24
2	91	24
3	229	24
4	685	24
5	3133	24
done	5001	24
0	19	23
1	42	23
2	92	23
3	222	23
4	681	23
5	3085	23
done	5000	23
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	22	68
1	51	46
2	140	26
3	370	24
4	1081	24
done	5000	24
0	20	47
1	40	47
2	88	47
3	224	47
4	685	47
5	3179	47
done	5000	47
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	20	68
1	47	68
2	111	24
3	280	24
4	799	24
5	3383	24
done	5001	24
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	2	2
done	2	2
0	18	21
1	38	21
2	86	21
3	222	21
4	683	21
5	3159	21
done	5000	21
0	22	49
1	48	49
2	105	49
3	251	49
4	716	49
5	3152	49
done	5001	49
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	22	48
1	45	27
2	95	27
3	235	27
4	705	27
5	3196	27
done	5001	27
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	21	27
1	43	27
2	93	27
3	233	27
4	691	27
5	3129	27
done	5001	27
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	6	8
1	10	7
2	12	7
3	13	5
4	20	5
done	20	5
0	19	23
1	39	23
2	87	23
3	219	23
4	687	23
5	3121	23
done	5000	23
0	21	27
1	43	27
2	93	27
3	233	27
4	691	27
5	3129	27
done	5001	27
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	5	7
1	9	5
2	15	5
3	20	5
done	20	5
0	19	23
1	39	23
2	87	23
3	219	23
4	687	23
5	3121	23
done	5000	23
0	21	46
1	43	46
2	91	46
3	236	46
4	701	46
5	3147	46
done	5001	46
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	21	45
1	42	24
2	90	24
3	224	24
4	684	24
5	3107	24
done	5000	24
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	5	5
1	7	4
done	7	4
0	19	23
1	39	23
2	87	23
3	219	23
4	687	23
5	3121	23
done	5000	23
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	20	24
1	40	24
2	88	24
3	220	24
4	691	24
5	3100	24
done	5001	24
0	4	4
1	6	2
2	8	2
done	8	2
0	19	23
1	39	23
2	87	23
3	219	23
4	687	23
5	3121	23
done	5000	23
0	21	45
1	45	45
2	93	45
3	232	45
4	693	45
5	3114	45
done	5000	45
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	21	44
1	44	23
2	92	23
3	229	23
4	687	23
5	3123	23
done	5001	23
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	20	23
1	42	23
2	90	23
3	223	23
4	675	23
5	3091	23
done	5001	23
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	3	4
1	5	3
done	5	3
0	18	22
1	38	22
2	86	22
3	222	22
4	683	22
5	3159	22
done	5000	22
0	20	23
1	42	23
2	90	23
3	223	23
4	675	23
5	3091	23
done	5001	23
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	2	3
1	4	1
done	4	1
0	18	22
1	38	22
2	86	22
3	222	22
4	683	22
5	3159	22
done	5000	22
0	19	22
1	41	22
2	89	22
3	224	22
4	688	22
5	3122	22
done	5001	22
0	18	22
1	38	22
2	86	22
3	222	22
4	683	22
5	3159	22
done	5000	22
0	20	45
1	42	45
2	90	45
3	228	45
4	694	45
5	3128	45
done	5001	45
0	20	44
1	41	23
2	89	23
3	222	23
4	687	23
5	3115	23
done	5001	23
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	4	4
1	6	3
done	6	3
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	3	3
1	5	1
done	5	1
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	19	23
1	39	23
2	87	23
3	219	23
4	697	23
5	3115	23
done	5000	23
0	18	22
1	38	22
2	86	22
3	222	22
4	683	22
5	3159	22
done	5000	22
0	21	26
1	56	26
2	152	26
3	682	26
4	4667	26
done	5000	26
0	20	42
1	51	42
2	167	36
3	711	36
4	4276	36
done	5001	36
0	2	2
done	2	2
0	2	2
done	2	2
0	2	2
done	2	2
0	1	1
done	1	1
0	31	41
1	84	37
2	212	33
3	618	31
4	2674	29
done	5000	29
0	32	41
1	84	39
2	208	35
3	628	31
4	2740	31
done	5000	31
0	20	38
1	52	35
2	124	29
3	467	19
4	2432	17
done	5000	17
0	4	4
1	8	4
2	13	4
3	31	4
4	71	4
5	175	4
6	552	4
7	1953	4
done	5000	4
0	4	4
1	8	4
2	13	4
3	31	4
4	71	4
5	175	4
6	552	4
7	1953	4
done	5000	4
0	3	4
1	4	4
done	4	4
0	3	4
1	4	4
done	4	4
0	3	4
1	4	4
done	4	4

prune439.0ms

Filtered

95 candidates to 122 candidates (-28.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	1	123

Merged error: 0.0b

Counts

123 → 1

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	29
1	28	29
done	28	29

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	6256×	body	80	valid
684.0ms	522×	body	1280	valid
627.0ms	658×	body	640	valid
230.0ms	357×	body	320	valid
87.0ms	207×	body	160	valid

Details

sample123.0ms

simplify2.7s

prune6.0ms

localize25.0ms

rewrite34.0ms

series497.0ms

simplify7.1min

prune439.0ms

simplify2.0ms

end0.0ms

sample3.4s

Profiling