Details

sample125.0ms

Algorithm

intervals

Results

46.0ms	54×	body	1280	valid
23.0ms	38×	body	640	valid
16.0ms	135×	body	80	valid
8.0ms	18×	body	320	valid
3.0ms	12×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	71	24
3	127	24
4	169	24
5	271	24
6	654	24
7	2069	24
done	5000	24

prune5.0ms

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: 19.4b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

6.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
36.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
48.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
49.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify5.2min

Counts

97 → 97

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	71	24
3	127	24
4	169	24
5	271	24
6	654	24
7	2069	24
done	5000	24
0	17	24
1	34	24
2	71	24
3	127	24
4	169	24
5	271	24
6	654	24
7	2069	24
done	5000	24
0	17	24
1	34	24
2	71	24
3	127	24
4	169	24
5	271	24
6	654	24
7	2069	24
done	5000	24
0	21	28
1	39	28
2	77	28
3	130	28
4	173	28
5	278	28
6	660	28
7	2080	28
done	5000	28
0	20	27
1	39	27
2	70	27
3	124	27
4	179	27
5	285	27
6	664	27
7	2092	27
done	5000	27
0	19	26
1	37	26
2	71	26
3	127	26
4	199	26
5	308	26
6	689	26
7	2111	26
done	5001	26
0	18	25
1	38	25
2	85	25
3	172	25
4	262	25
5	371	25
6	742	25
7	2154	25
done	5001	25
0	18	25
1	37	25
2	86	25
3	178	25
4	333	25
5	732	25
6	1827	25
done	5000	25
0	25	74
1	55	57
2	199	32
3	1104	32
done	5001	32
0	23	74
1	57	57
2	201	30
3	1163	30
done	5000	30
0	21	74
1	51	57
2	195	28
3	1167	28
done	5000	28
0	19	51
1	36	51
2	73	51
3	129	51
4	173	51
5	277	51
6	660	51
7	2077	51
done	5000	51
0	18	25
1	35	25
2	72	25
3	130	25
4	173	25
5	275	25
6	651	25
7	2068	25
done	5001	25
0	19	74
1	46	74
2	160	26
3	954	26
done	5000	26
0	18	25
1	35	25
2	72	25
3	130	25
4	173	25
5	275	25
6	651	25
7	2068	25
done	5001	25
0	18	25
1	35	25
2	72	25
3	130	25
4	173	25
5	275	25
6	651	25
7	2068	25
done	5001	25
0	19	42
1	38	42
2	84	42
3	172	42
4	253	42
5	355	42
6	740	42
7	2172	42
done	5000	42
0	19	41
1	37	25
2	74	25
3	126	25
4	171	25
5	278	25
6	661	25
7	2083	25
done	5000	25
0	18	25
1	35	25
2	72	25
3	128	25
4	171	25
5	275	25
6	653	25
7	2069	25
done	5000	25
0	11	11
1	20	10
2	40	10
3	63	8
4	86	8
done	86	8
0	11	11
1	20	10
2	40	10
3	63	8
4	86	8
done	86	8
0	18	25
1	35	25
2	72	25
3	128	25
4	171	25
5	275	25
6	653	25
7	2069	25
done	5000	25
0	10	10
1	19	8
2	45	8
3	82	8
4	94	8
done	94	8
0	14	20
1	26	20
2	44	20
3	73	20
4	115	20
5	223	20
6	601	20
7	2016	20
done	5000	20
0	20	28
1	49	28
2	109	28
3	217	28
4	464	28
5	1491	28
done	5000	28
0	19	39
1	42	28
2	94	28
3	192	28
4	385	28
5	1159	28
6	4964	28
done	5000	28
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	33
1	26	33
2	44	33
3	73	33
4	115	33
5	223	33
6	601	33
7	2023	33
done	5000	33
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	47
1	27	30
2	56	17
3	95	17
4	156	17
5	321	17
6	962	17
7	3486	17
done	5000	17
0	15	32
1	27	16
2	45	16
3	76	16
4	118	16
5	224	16
6	605	16
7	2012	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	16	19
1	39	19
2	80	19
3	161	19
4	406	19
5	1437	19
done	5000	19
0	17	45
1	37	32
2	84	32
3	175	32
4	399	32
5	1124	32
6	3956	32
done	5000	32
0	15	30
1	32	19
2	65	19
3	140	19
4	330	19
5	1110	19
6	4827	19
done	5000	19
0	13	15
1	25	15
2	47	15
3	83	15
4	149	15
5	331	15
6	1012	15
7	3809	15
done	5000	15
0	3	3
1	6	1
done	6	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	23	16
2	52	16
3	117	16
4	285	16
5	527	16
6	783	16
7	1104	16
8	1349	16
9	1439	16
10	1442	16
done	1442	16
0	13	15
1	23	15
2	45	15
3	97	15
4	240	15
5	467	15
6	704	15
7	1066	15
8	1318	15
9	1424	15
10	1433	15
done	1433	15
0	12	14
1	22	14
2	47	14
3	89	14
4	214	14
5	413	14
6	663	14
7	995	14
8	1278	14
9	1509	14
10	1528	14
done	1528	14
0	11	13
1	21	13
2	45	13
3	93	13
4	185	13
5	363	13
6	608	13
7	865	13
8	1186	13
9	1431	13
10	1519	13
11	1522	13
done	1522	13
0	11	13
1	21	13
2	45	13
3	93	13
4	185	13
5	363	13
6	608	13
7	865	13
8	1186	13
9	1431	13
10	1519	13
11	1522	13
done	1522	13
0	3	3
1	6	1
done	6	1
0	12	16
1	22	16
2	42	16
3	77	16
4	136	16
5	295	16
6	900	16
7	3265	16
done	5000	16
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2211	13
done	5000	13
0	11	12
1	24	10
2	44	10
3	66	10
4	89	10
5	146	10
6	353	10
7	1275	10
done	5000	10
0	12	25
1	22	25
2	40	25
3	71	25
4	112	25
5	218	25
6	595	25
7	2016	25
done	5000	25
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2003	13
done	5000	13
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2003	13
done	5000	13
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2003	13
done	5000	13
0	8	11
1	20	11
2	38	11
3	68	11
4	112	11
5	217	11
6	597	11
7	2009	11
done	5000	11
0	8	9
1	12	9
2	17	9
3	35	9
4	75	9
5	184	9
6	561	9
7	1968	9
done	5000	9
0	7	8
1	14	8
2	21	8
3	39	8
4	79	8
5	184	8
6	556	8
7	1967	8
done	5001	8
0	8	9
1	12	9
2	17	9
3	35	9
4	75	9
5	184	9
6	561	9
7	1968	9
done	5000	9
0	6	7
1	15	7
2	22	7
3	40	7
4	81	7
5	181	7
6	554	7
7	1963	7
done	5000	7
0	7	8
1	11	8
2	16	8
3	34	8
4	74	8
5	181	8
6	552	8
7	1967	8
done	5000	8
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	10	12
1	20	12
2	38	12
3	67	12
4	111	12
5	218	12
6	600	12
7	2028	12
done	5001	12
0	3	3
1	7	3
2	12	3
3	30	3
4	72	3
5	183	3
6	568	3
7	1980	3
done	5001	3
0	10	12
1	22	12
2	40	12
3	71	12
4	112	12
5	221	12
6	599	12
7	2006	12
done	5000	12
0	11	13
1	23	13
2	50	13
3	107	13
4	259	13
5	915	13
done	5000	13
0	11	13
1	21	13
2	41	13
3	75	13
4	134	13
5	303	13
6	926	13
7	3766	13
done	5000	13
0	12	27
1	22	27
2	40	27
3	71	27
4	112	27
5	218	27
6	605	27
7	2013	27
done	5000	27
0	11	13
1	21	13
2	39	13
3	68	13
4	111	13
5	218	13
6	600	13
7	2036	13
done	5000	13
0	12	38
1	25	27
2	59	14
3	123	14
4	268	14
5	827	14
6	3707	14
done	5001	14
0	11	13
1	21	13
2	40	13
3	69	13
4	111	13
5	222	13
6	602	13
7	2000	13
done	5000	13
0	11	13
1	21	13
2	40	13
3	69	13
4	111	13
5	222	13
6	602	13
7	2000	13
done	5000	13
0	12	14
1	21	14
2	42	14
3	74	14
4	124	14
5	249	14
6	752	14
7	2576	14
done	5000	14
0	12	14
1	21	14
2	42	14
3	74	14
4	124	14
5	249	14
6	752	14
7	2576	14
done	5000	14
0	7	8
1	11	8
2	17	8
done	17	8
0	7	8
1	11	8
2	17	8
done	17	8
0	10	11
1	14	11
2	20	11
3	22	11
done	22	11
0	9	10
1	14	10
2	19	10
3	23	10
done	23	10
0	8	9
1	15	9
2	28	9
3	40	9
4	42	9
done	42	9
0	8	9
1	14	9
2	31	9
3	53	9
4	109	9
5	250	9
6	593	9
7	1562	9
done	5001	9
0	13	26
1	26	26
2	91	14
3	327	14
4	1064	12
5	3016	12
done	5000	12
0	11	26
1	28	26
2	95	12
3	369	12
4	1087	10
5	2079	10
6	4979	10
done	5000	10
0	9	19
1	13	19
2	19	19
done	19	19
0	8	9
1	12	9
2	18	9
done	18	9
0	9	26
1	23	26
2	93	10
3	430	10
4	1239	10
5	1699	10
6	3293	10
done	5001	10
0	8	9
1	12	9
2	18	9
done	18	9
0	8	9
1	12	9
2	18	9
done	18	9
0	9	15
1	15	15
2	28	15
3	40	15
done	40	15
0	8	9
1	12	9
2	18	9
3	20	9
done	20	9
0	5	5
1	11	3
2	23	3
3	27	3
done	27	3
0	6	6
1	7	6
done	7	6
0	1	1
done	1	1
0	11	11
1	19	11
2	39	11
3	63	11
4	64	11
done	64	11
0	11	11
1	19	11
2	39	11
3	63	11
4	64	11
done	64	11
0	2	2
done	2	2
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	11	11
1	19	11
2	44	11
3	98	11
4	178	7
5	372	7
6	870	7
7	3099	7
done	5000	7
0	18	20
1	39	18
2	85	16
3	273	16
4	866	14
5	2185	12
6	4996	12
done	5000	12
0	18	20
1	35	20
2	82	20
3	274	20
4	1074	16
5	4396	16
done	5000	16
0	3	3
1	4	3
done	4	3
0	8	8
1	13	8
2	19	8
done	19	8
0	8	8
1	13	8
2	19	8
done	19	8

prune332.0ms

Filtered

75 candidates to 97 candidates (-29.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	88	9	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	9	98

Merged error: 14.7b

Counts

98 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.0b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
23×	`pow1`
21×	`add-cbrt-cube`
14×	`prod-exp`
11×	`*-un-lft-identity` `pow-prod-down` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
7×	`unpow-prod-down`
4×	`sqrt-div` `associate-r/` `associate-r*` `pow-exp` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l` `*-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

6.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
11.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

series136.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
36.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
43.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
48.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify5.0min

Counts

94 → 94

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	35	24
2	71	24
3	122	24
4	166	24
5	270	24
6	655	24
7	2069	24
done	5000	24
0	17	24
1	35	24
2	71	24
3	122	24
4	166	24
5	270	24
6	655	24
7	2069	24
done	5000	24
0	17	24
1	35	24
2	71	24
3	122	24
4	166	24
5	270	24
6	655	24
7	2069	24
done	5000	24
0	17	24
1	35	24
2	71	24
3	122	24
4	166	24
5	270	24
6	655	24
7	2069	24
done	5000	24
0	21	28
1	39	28
2	76	28
3	126	28
4	173	28
5	277	28
6	661	28
7	2071	28
done	5001	28
0	20	27
1	39	27
2	70	27
3	122	27
4	170	27
5	278	27
6	660	27
7	2084	27
done	5001	27
0	20	27
1	39	27
2	70	27
3	123	27
4	175	27
5	281	27
6	665	27
7	2079	27
done	5000	27
0	19	26
1	39	26
2	67	26
3	118	26
4	172	26
5	275	26
6	656	26
7	2079	26
done	5000	26
0	18	25
1	39	25
2	88	25
3	172	25
4	259	25
5	367	25
6	732	25
7	2141	25
done	5001	25
0	18	25
1	38	25
2	86	25
3	180	25
4	343	25
5	770	25
6	1951	25
done	5000	25
0	25	74
1	55	57
2	196	32
3	997	32
done	5000	32
0	23	74
1	57	74
2	183	30
3	908	30
done	5000	30
0	23	74
1	57	57
2	200	30
3	1008	30
done	5000	30
0	21	74
1	59	74
2	187	28
3	910	28
done	5000	28
0	19	51
1	37	51
2	73	51
3	124	51
4	168	51
5	273	51
6	652	51
7	2065	51
done	5001	51
0	18	25
1	36	25
2	72	25
3	121	25
4	165	25
5	271	25
6	650	25
7	2069	25
done	5000	25
0	19	74
1	47	74
2	183	26
3	963	26
done	5000	26
0	18	25
1	36	25
2	72	25
3	121	25
4	165	25
5	271	25
6	650	25
7	2069	25
done	5000	25
0	18	25
1	36	25
2	72	25
3	121	25
4	165	25
5	271	25
6	650	25
7	2069	25
done	5000	25
0	8	8
1	12	8
2	18	8
3	20	8
done	20	8
0	15	22
1	29	22
2	52	22
3	81	22
4	123	22
5	229	22
6	601	22
7	2010	22
done	5001	22
0	20	28
1	50	28
2	109	28
3	210	28
4	458	28
5	1468	28
done	5000	28
0	19	39
1	43	28
2	94	28
3	187	28
4	386	28
5	1217	28
6	4967	28
done	5000	28
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	33
1	26	33
2	44	33
3	73	33
4	115	33
5	223	33
6	601	33
7	2023	33
done	5000	33
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	47
1	27	30
2	56	17
3	95	17
4	156	17
5	321	17
6	962	17
7	3486	17
done	5000	17
0	15	32
1	27	16
2	45	16
3	76	16
4	118	16
5	224	16
6	605	16
7	2012	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	16	19
1	39	19
2	80	19
3	161	19
4	406	19
5	1437	19
done	5000	19
0	17	45
1	37	32
2	84	32
3	175	32
4	399	32
5	1124	32
6	3956	32
done	5000	32
0	15	30
1	32	19
2	65	19
3	140	19
4	330	19
5	1110	19
6	4827	19
done	5000	19
0	13	15
1	25	15
2	47	15
3	83	15
4	149	15
5	331	15
6	1012	15
7	3809	15
done	5000	15
0	3	3
1	6	1
done	6	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	23	16
2	52	16
3	117	16
4	285	16
5	527	16
6	783	16
7	1104	16
8	1349	16
9	1439	16
10	1442	16
done	1442	16
0	13	15
1	23	15
2	45	15
3	97	15
4	240	15
5	467	15
6	704	15
7	1066	15
8	1318	15
9	1424	15
10	1433	15
done	1433	15
0	12	14
1	22	14
2	47	14
3	89	14
4	214	14
5	413	14
6	663	14
7	995	14
8	1278	14
9	1509	14
10	1528	14
done	1528	14
0	11	13
1	21	13
2	45	13
3	93	13
4	185	13
5	363	13
6	608	13
7	865	13
8	1186	13
9	1431	13
10	1519	13
11	1522	13
done	1522	13
0	11	13
1	21	13
2	45	13
3	93	13
4	185	13
5	363	13
6	608	13
7	865	13
8	1186	13
9	1431	13
10	1519	13
11	1522	13
done	1522	13
0	3	3
1	6	1
done	6	1
0	12	16
1	22	16
2	42	16
3	77	16
4	136	16
5	295	16
6	900	16
7	3265	16
done	5000	16
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2211	13
done	5000	13
0	11	12
1	24	10
2	44	10
3	66	10
4	89	10
5	146	10
6	353	10
7	1275	10
done	5000	10
0	12	25
1	22	25
2	40	25
3	71	25
4	112	25
5	218	25
6	595	25
7	2016	25
done	5000	25
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2003	13
done	5000	13
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2003	13
done	5000	13
0	11	13
1	21	13
2	39	13
3	68	13
4	109	13
5	213	13
6	585	13
7	2003	13
done	5000	13
0	8	11
1	20	11
2	38	11
3	68	11
4	112	11
5	217	11
6	597	11
7	2009	11
done	5000	11
0	8	9
1	12	9
2	17	9
3	35	9
4	75	9
5	184	9
6	561	9
7	1968	9
done	5000	9
0	7	8
1	14	8
2	21	8
3	39	8
4	79	8
5	184	8
6	556	8
7	1967	8
done	5001	8
0	8	9
1	12	9
2	17	9
3	35	9
4	75	9
5	184	9
6	561	9
7	1968	9
done	5000	9
0	6	7
1	15	7
2	22	7
3	40	7
4	81	7
5	181	7
6	554	7
7	1963	7
done	5000	7
0	7	8
1	11	8
2	16	8
3	34	8
4	74	8
5	181	8
6	552	8
7	1967	8
done	5000	8
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	10	12
1	20	12
2	38	12
3	67	12
4	111	12
5	218	12
6	600	12
7	2028	12
done	5001	12
0	3	3
1	7	3
2	12	3
3	30	3
4	72	3
5	183	3
6	568	3
7	1980	3
done	5001	3
0	10	12
1	22	12
2	40	12
3	71	12
4	112	12
5	221	12
6	599	12
7	2006	12
done	5000	12
0	11	13
1	23	13
2	50	13
3	107	13
4	259	13
5	915	13
done	5000	13
0	11	13
1	21	13
2	41	13
3	75	13
4	134	13
5	303	13
6	926	13
7	3766	13
done	5000	13
0	12	27
1	22	27
2	40	27
3	71	27
4	112	27
5	218	27
6	605	27
7	2013	27
done	5000	27
0	11	13
1	21	13
2	39	13
3	68	13
4	111	13
5	218	13
6	600	13
7	2036	13
done	5000	13
0	12	38
1	25	27
2	59	14
3	123	14
4	268	14
5	827	14
6	3707	14
done	5001	14
0	11	13
1	21	13
2	40	13
3	69	13
4	111	13
5	222	13
6	602	13
7	2000	13
done	5000	13
0	11	13
1	21	13
2	40	13
3	69	13
4	111	13
5	222	13
6	602	13
7	2000	13
done	5000	13
0	12	14
1	21	14
2	42	14
3	74	14
4	124	14
5	249	14
6	752	14
7	2576	14
done	5000	14
0	12	14
1	21	14
2	42	14
3	74	14
4	124	14
5	249	14
6	752	14
7	2576	14
done	5000	14
0	7	8
1	11	8
2	17	8
done	17	8
0	7	8
1	11	8
2	17	8
done	17	8
0	10	11
1	14	11
2	20	11
3	22	11
done	22	11
0	9	10
1	14	10
2	19	10
3	23	10
done	23	10
0	8	9
1	15	9
2	28	9
3	40	9
4	42	9
done	42	9
0	8	9
1	14	9
2	31	9
3	53	9
4	109	9
5	250	9
6	593	9
7	1562	9
done	5001	9
0	13	26
1	26	26
2	91	14
3	327	14
4	1064	12
5	3016	12
done	5000	12
0	11	26
1	28	26
2	95	12
3	369	12
4	1087	10
5	2079	10
6	4979	10
done	5000	10
0	9	19
1	13	19
2	19	19
done	19	19
0	8	9
1	12	9
2	18	9
done	18	9
0	9	26
1	23	26
2	93	10
3	430	10
4	1239	10
5	1699	10
6	3293	10
done	5001	10
0	8	9
1	12	9
2	18	9
done	18	9
0	8	9
1	12	9
2	18	9
done	18	9
0	9	15
1	15	15
2	28	15
3	40	15
done	40	15
0	8	9
1	12	9
2	18	9
3	20	9
done	20	9
0	5	5
1	11	3
2	23	3
3	27	3
done	27	3
0	6	6
1	7	6
done	7	6
0	1	1
done	1	1
0	11	11
1	19	11
2	39	11
3	63	11
4	64	11
done	64	11
0	11	11
1	19	11
2	39	11
3	63	11
4	64	11
done	64	11
0	2	2
done	2	2
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	11	11
1	19	11
2	44	11
3	98	11
4	178	7
5	372	7
6	870	7
7	3099	7
done	5000	7
0	18	20
1	39	18
2	85	16
3	273	16
4	866	14
5	2185	12
6	4996	12
done	5000	12
0	18	20
1	35	20
2	82	20
3	274	20
4	1074	16
5	4396	16
done	5000	16
0	3	3
1	4	3
done	4	3
0	8	8
1	13	8
2	19	8
done	19	8
0	8	8
1	13	8
2	19	8
done	19	8

prune304.0ms

Filtered

74 candidates to 94 candidates (-27.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 14.7b

Counts

103 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

13.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
38.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
72.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
68.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify4.2min

Counts

88 → 88

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	35
1	27	35
2	45	35
3	76	35
4	118	35
5	224	35
6	605	35
7	2019	35
done	5000	35
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	50
1	28	32
2	49	18
3	82	18
4	129	18
5	243	18
6	632	18
7	2078	18
done	5000	18
0	16	34
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	33
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	2	2
1	4	1
done	4	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	17	20
1	40	20
2	81	20
3	162	20
4	398	20
5	1418	20
done	5000	20
0	18	46
1	38	33
2	85	33
3	176	33
4	401	33
5	1145	33
6	4004	33
done	5000	33
0	16	31
1	33	20
2	66	20
3	141	20
4	330	20
5	1128	20
6	4992	20
done	5000	20
0	14	16
1	26	16
2	48	16
3	86	16
4	152	16
5	336	16
6	1022	16
7	3844	16
done	5000	16
0	3	3
1	4	1
done	4	1
0	3	3
1	6	1
done	6	1
0	4	5
1	10	3
2	11	1
done	11	1
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	35
1	27	35
2	45	35
3	76	35
4	118	35
5	224	35
6	605	35
7	2019	35
done	5000	35
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	50
1	28	32
2	49	18
3	82	18
4	129	18
5	243	18
6	632	18
7	2078	18
done	5000	18
0	16	34
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	33
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	2	2
1	4	1
done	4	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	17	20
1	40	20
2	81	20
3	162	20
4	398	20
5	1418	20
done	5000	20
0	18	46
1	38	33
2	85	33
3	176	33
4	401	33
5	1145	33
6	4004	33
done	5000	33
0	16	31
1	33	20
2	66	20
3	141	20
4	330	20
5	1128	20
6	4992	20
done	5000	20
0	14	16
1	26	16
2	48	16
3	86	16
4	152	16
5	336	16
6	1022	16
7	3844	16
done	5000	16
0	3	3
1	4	1
done	4	1
0	3	3
1	6	1
done	6	1
0	4	5
1	10	3
2	11	1
done	11	1
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	33
1	26	33
2	44	33
3	73	33
4	115	33
5	223	33
6	601	33
7	2023	33
done	5000	33
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	47
1	27	30
2	56	17
3	95	17
4	156	17
5	321	17
6	962	17
7	3486	17
done	5000	17
0	15	32
1	27	16
2	45	16
3	76	16
4	118	16
5	224	16
6	605	16
7	2012	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	16	19
1	39	19
2	80	19
3	161	19
4	406	19
5	1437	19
done	5000	19
0	17	45
1	37	32
2	84	32
3	175	32
4	399	32
5	1124	32
6	3956	32
done	5000	32
0	15	30
1	32	19
2	65	19
3	140	19
4	330	19
5	1110	19
6	4827	19
done	5000	19
0	13	15
1	25	15
2	47	15
3	83	15
4	149	15
5	331	15
6	1012	15
7	3809	15
done	5000	15
0	3	3
1	6	1
done	6	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	33
1	26	33
2	44	33
3	73	33
4	115	33
5	223	33
6	601	33
7	2023	33
done	5000	33
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	47
1	27	30
2	56	17
3	95	17
4	156	17
5	321	17
6	962	17
7	3486	17
done	5000	17
0	15	32
1	27	16
2	45	16
3	76	16
4	118	16
5	224	16
6	605	16
7	2012	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	16	19
1	39	19
2	80	19
3	161	19
4	406	19
5	1437	19
done	5000	19
0	17	45
1	37	32
2	84	32
3	175	32
4	399	32
5	1124	32
6	3956	32
done	5000	32
0	15	30
1	32	19
2	65	19
3	140	19
4	330	19
5	1110	19
6	4827	19
done	5000	19
0	13	15
1	25	15
2	47	15
3	83	15
4	149	15
5	331	15
6	1012	15
7	3809	15
done	5000	15
0	3	3
1	6	1
done	6	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	3	3
1	8	3
2	14	3
3	24	3
4	48	3
5	115	3
6	340	3
7	1268	3
done	5000	3
0	23	26
1	50	24
2	114	24
3	313	21
4	1065	18
5	3516	17
done	5001	17
0	23	26
1	47	26
2	105	26
3	278	24
4	976	22
5	4314	21
done	5000	21
0	3	3
1	8	3
2	14	3
3	24	3
4	48	3
5	115	3
6	340	3
7	1268	3
done	5000	3
0	23	26
1	50	24
2	114	24
3	313	21
4	1065	18
5	3516	17
done	5001	17
0	23	26
1	47	26
2	105	26
3	278	24
4	976	22
5	4314	21
done	5000	21
0	2	2
done	2	2
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	2	2
done	2	2
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11

prune376.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	88	10	98

Merged error: 14.7b

Counts

98 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
10.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-div`
30×	`pow1`
28×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
15×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
14×	`add-sqr-sqrt`
10×	`associate-*r/`
9×	`add-cube-cbrt` `sqrt-pow1` `flip3-+` `flip-+`
5×	`rem-sqrt-square` `pow1/2`
4×	`frac-times` `add-log-exp`
3×	`distribute-lft-out`
2×	`associate-*l/`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 96

Calls

4 calls:

8.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
32.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
12.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series231.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
53.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
67.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
73.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify4.8min

Counts

108 → 108

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	35
1	27	35
2	45	35
3	76	35
4	118	35
5	224	35
6	605	35
7	2019	35
done	5000	35
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	50
1	28	32
2	49	18
3	82	18
4	129	18
5	243	18
6	632	18
7	2078	18
done	5000	18
0	16	34
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	33
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	2	2
1	4	1
done	4	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	17	20
1	40	20
2	81	20
3	162	20
4	398	20
5	1418	20
done	5000	20
0	18	46
1	38	33
2	85	33
3	176	33
4	401	33
5	1145	33
6	4004	33
done	5000	33
0	16	31
1	33	20
2	66	20
3	141	20
4	330	20
5	1128	20
6	4992	20
done	5000	20
0	14	16
1	26	16
2	48	16
3	86	16
4	152	16
5	336	16
6	1022	16
7	3844	16
done	5000	16
0	3	3
1	4	1
done	4	1
0	3	3
1	6	1
done	6	1
0	4	5
1	10	3
2	11	1
done	11	1
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	35
1	27	35
2	45	35
3	76	35
4	118	35
5	224	35
6	605	35
7	2019	35
done	5000	35
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	50
1	28	32
2	49	18
3	82	18
4	129	18
5	243	18
6	632	18
7	2078	18
done	5000	18
0	16	34
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	16	33
1	28	17
2	46	17
3	75	17
4	117	17
5	221	17
6	597	17
7	2024	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	3	3
1	5	1
done	5	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	2	2
1	4	1
done	4	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	17	20
1	40	20
2	81	20
3	162	20
4	398	20
5	1418	20
done	5000	20
0	18	46
1	38	33
2	85	33
3	176	33
4	401	33
5	1145	33
6	4004	33
done	5000	33
0	16	31
1	33	20
2	66	20
3	141	20
4	330	20
5	1128	20
6	4992	20
done	5000	20
0	14	16
1	26	16
2	48	16
3	86	16
4	152	16
5	336	16
6	1022	16
7	3844	16
done	5000	16
0	3	3
1	4	1
done	4	1
0	3	3
1	6	1
done	6	1
0	4	5
1	10	3
2	11	1
done	11	1
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	15	17
1	26	17
2	44	17
3	73	17
4	115	17
5	223	17
6	601	17
7	2023	17
done	5000	17
0	19	42
1	38	24
2	85	24
3	173	24
4	253	24
5	355	24
6	742	24
7	2156	24
done	5000	24
0	19	42
1	38	24
2	85	24
3	173	24
4	253	24
5	355	24
6	742	24
7	2156	24
done	5000	24
0	19	42
1	38	24
2	85	24
3	173	24
4	253	24
5	355	24
6	742	24
7	2156	24
done	5000	24
0	19	42
1	38	24
2	85	24
3	173	24
4	253	24
5	355	24
6	742	24
7	2156	24
done	5000	24
0	19	42
1	38	24
2	85	24
3	173	24
4	253	24
5	355	24
6	742	24
7	2156	24
done	5000	24
0	19	42
1	38	24
2	85	24
3	173	24
4	253	24
5	355	24
6	742	24
7	2156	24
done	5000	24
0	23	47
1	44	31
2	92	31
3	182	31
4	263	31
5	372	31
6	761	31
7	2181	31
done	5001	31
0	23	46
1	43	28
2	89	28
3	179	28
4	269	28
5	374	28
6	751	28
7	2186	28
done	5001	28
0	22	46
1	44	30
2	83	30
3	163	30
4	260	30
5	371	30
6	754	30
7	2157	30
done	5001	30
0	22	45
1	43	27
2	82	27
3	160	27
4	249	27
5	364	27
6	743	27
7	2173	27
done	5001	27
0	21	45
1	42	29
2	81	29
3	155	29
4	273	29
5	391	29
6	769	29
7	2187	29
done	5000	29
0	21	44
1	41	26
2	81	26
3	152	26
4	266	26
5	396	26
6	772	26
7	2183	26
done	5000	26
0	20	43
1	42	25
2	103	25
3	234	25
4	430	25
5	616	25
6	998	25
7	2380	25
done	5000	25
0	20	43
1	41	25
2	102	25
3	239	25
4	477	25
5	1078	25
6	2753	25
done	5001	25
0	27	128
1	63	74
2	219	45
3	1205	32
done	5000	32
0	27	128
1	64	74
2	217	32
3	1236	32
done	5000	32
0	25	128
1	65	74
2	221	43
3	1270	30
done	5000	30
0	25	128
1	66	74
2	217	30
3	1295	30
done	5000	30
0	23	128
1	59	74
2	215	41
3	1296	28
done	5000	28
0	23	128
1	60	74
2	212	28
3	1300	28
done	5000	28
0	21	87
1	40	51
2	87	51
3	175	51
4	248	51
5	353	51
6	738	51
7	2154	51
done	5000	51
0	20	43
1	39	25
2	86	25
3	175	25
4	251	25
5	355	25
6	737	25
7	2157	25
done	5000	25
0	21	128
1	50	74
2	194	26
3	1263	26
done	5000	26
0	20	43
1	39	25
2	86	25
3	175	25
4	251	25
5	355	25
6	737	25
7	2157	25
done	5000	25
0	20	43
1	39	25
2	86	25
3	175	25
4	251	25
5	355	25
6	737	25
7	2157	25
done	5000	25
0	18	25
1	35	25
2	72	25
3	128	25
4	171	25
5	275	25
6	653	25
7	2069	25
done	5000	25
0	16	38
1	30	20
2	51	20
3	80	20
4	122	20
5	224	20
6	597	20
7	2014	20
done	5000	20
0	22	50
1	53	28
2	123	28
3	267	28
4	548	28
5	1565	28
done	5001	28
0	27	61
1	64	50
2	148	50
3	351	50
4	794	50
5	2427	50
done	5000	50
0	27	61
1	64	50
2	148	50
3	349	50
4	794	50
5	2433	50
done	5000	50
0	21	72
1	46	28
2	108	28
3	243	28
4	471	28
5	1255	28
done	5000	28
0	25	46
1	58	46
2	133	46
3	311	46
4	635	46
5	1671	46
done	5000	46
0	24	57
1	50	46
2	116	46
3	283	46
4	563	46
5	1362	46
done	5002	46
0	25	46
1	58	46
2	133	46
3	311	46
4	642	46
5	1670	46
done	5001	46
0	24	57
1	50	46
2	116	46
3	285	46
4	547	46
5	1325	46
done	5000	46
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	33
1	26	33
2	44	33
3	73	33
4	115	33
5	223	33
6	601	33
7	2023	33
done	5000	33
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	15	47
1	27	30
2	56	17
3	95	17
4	156	17
5	321	17
6	962	17
7	3486	17
done	5000	17
0	15	32
1	27	16
2	45	16
3	76	16
4	118	16
5	224	16
6	605	16
7	2012	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	2	2
1	4	1
done	4	1
0	13	15
1	24	15
2	42	15
3	71	15
4	113	15
5	219	15
6	596	15
7	2016	15
done	5000	15
0	16	19
1	39	19
2	80	19
3	161	19
4	406	19
5	1437	19
done	5000	19
0	17	45
1	37	32
2	84	32
3	175	32
4	399	32
5	1124	32
6	3956	32
done	5000	32
0	15	30
1	32	19
2	65	19
3	140	19
4	330	19
5	1110	19
6	4827	19
done	5000	19
0	13	15
1	25	15
2	47	15
3	83	15
4	149	15
5	331	15
6	1012	15
7	3809	15
done	5000	15
0	3	3
1	6	1
done	6	1
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	14	16
1	25	16
2	43	16
3	74	16
4	116	16
5	220	16
6	600	16
7	2021	16
done	5001	16
0	3	3
1	8	3
2	14	3
3	24	3
4	48	3
5	115	3
6	340	3
7	1268	3
done	5000	3
0	23	26
1	50	24
2	114	24
3	313	21
4	1065	18
5	3516	17
done	5001	17
0	23	26
1	47	26
2	105	26
3	278	24
4	976	22
5	4314	21
done	5000	21
0	3	3
1	8	3
2	14	3
3	24	3
4	48	3
5	115	3
6	340	3
7	1268	3
done	5000	3
0	23	26
1	50	24
2	114	24
3	313	21
4	1065	18
5	3516	17
done	5001	17
0	23	26
1	47	26
2	105	26
3	278	24
4	976	22
5	4314	21
done	5000	21
0	1	1
done	1	1
0	11	11
1	19	11
2	39	11
3	63	11
4	64	11
done	64	11
0	11	11
1	19	11
2	39	11
3	63	11
4	64	11
done	64	11
0	2	2
done	2	2
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11
0	11	11
1	21	11
2	42	11
3	69	11
4	80	11
done	80	11

prune415.0ms

Filtered

78 candidates to 108 candidates (-38.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	108	10	118

Merged error: 14.7b

Counts

118 → 10

regimes702.0ms

Accuracy

88.4% (0.6b remaining)

Error of 13.7b against oracle of 13.1b and baseline of 18.4b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	118
1	50	118
done	50	118

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1515×	body	1280	valid
790.0ms	1268×	body	640	valid
529.0ms	4323×	body	80	valid
265.0ms	596×	body	320	valid
86.0ms	308×	body	160	valid

Details

sample125.0ms

simplify3.4s

prune5.0ms

localize29.0ms

rewrite41.0ms

series142.0ms

simplify5.2min

prune332.0ms

localize18.0ms

rewrite43.0ms

series136.0ms

simplify5.0min

prune304.0ms

localize21.0ms

rewrite41.0ms

series223.0ms

simplify4.2min

prune376.0ms

localize20.0ms

rewrite66.0ms

series231.0ms

simplify4.8min

prune415.0ms

regimes702.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample3.4s

Profiling