Details

sample90.0ms

Algorithm

intervals

Results

46.0ms	120×	body	1280	valid
24.0ms	90×	body	640	valid
6.0ms	33×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	13×	body	160	valid

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	15
1	18	15
2	43	15
3	87	15
4	150	15
5	196	15
6	282	15
7	444	15
8	685	15
9	709	15
10	734	15
11	792	15
12	872	15
13	975	15
14	1109	15
15	1173	15
16	1409	15
17	1472	15
18	1825	15
19	3684	15
done	5000	15

prune3.0ms

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: 63.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* n (log n))
0.3b	(* (+ n 1.0) (log (+ n 1.0)))
3.9b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`log-prod`
25×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
14×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r` `associate--l+`
7×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`associate--r+`
5×	`distribute-lft-out` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `log-pow` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 81

Calls

3 calls:

5.0ms	(* n (log n))
10.0ms	(* (+ n 1.0) (log (+ n 1.0)))
10.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series43.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* n (log n))
6.0ms	(* (+ n 1.0) (log (+ n 1.0)))
20.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify1.4min

Counts

90 → 90

Iterations

Useful iterations: 2 (2.0ms)

Iter	Nodes	Cost
0	10	15
1	19	14
2	45	11
3	92	11
4	233	11
5	794	11
done	5000	11
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	9	14
1	17	14
2	44	11
3	89	11
4	193	11
5	654	11
6	3735	11
done	5000	11
0	10	29
1	15	29
2	30	29
3	42	29
4	50	29
5	57	29
6	67	29
7	92	29
8	129	29
9	203	29
10	224	29
11	241	29
12	278	29
13	298	29
done	298	29
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	10	41
1	16	41
2	45	15
3	164	15
4	879	15
done	5000	15
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	11	17
1	35	17
2	127	17
3	481	17
4	1343	17
5	3520	17
done	5000	17
0	12	41
1	40	36
2	117	36
3	275	32
4	558	32
5	1197	32
6	2982	32
done	5000	32
0	4	5
1	9	5
2	11	5
done	11	5
0	10	27
1	32	27
2	97	27
3	254	27
4	527	27
5	1342	27
6	4040	27
done	5000	27
0	8	13
1	12	13
2	20	13
3	28	13
4	32	13
5	34	13
done	34	13
0	10	17
1	17	17
2	38	16
3	73	16
4	138	16
5	181	16
6	239	16
7	362	16
8	604	16
9	683	16
10	688	16
done	688	16
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	9	13
1	16	12
2	31	10
3	43	8
4	66	8
5	70	8
6	90	8
7	119	8
8	148	8
9	208	8
10	221	8
11	223	8
done	223	8
0	10	17
1	17	17
2	38	16
3	73	16
4	138	16
5	181	16
6	239	16
7	362	16
8	604	16
9	683	16
10	688	16
done	688	16
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	9	13
1	16	12
2	31	10
3	43	8
4	66	8
5	70	8
6	90	8
7	119	8
8	148	8
9	208	8
10	221	8
11	223	8
done	223	8
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	9	14
1	14	14
2	29	14
3	41	14
4	49	14
5	56	14
6	66	14
7	91	14
8	128	14
9	202	14
10	223	14
11	240	14
12	277	14
13	297	14
done	297	14
0	8	13
1	13	13
2	28	13
3	40	13
4	48	13
5	55	13
6	65	13
7	90	13
8	127	13
9	201	13
10	222	13
11	239	13
12	276	13
13	296	13
done	296	13
0	8	13
1	13	13
2	28	13
3	40	13
4	48	13
5	55	13
6	65	13
7	90	13
8	127	13
9	201	13
10	222	13
11	239	13
12	276	13
13	296	13
done	296	13
0	9	14
1	20	14
2	32	14
3	41	14
4	50	14
5	61	14
6	80	14
7	112	14
8	159	14
9	205	14
10	225	14
11	261	14
12	282	14
done	282	14
0	9	14
1	20	14
2	32	14
3	41	14
4	50	14
5	61	14
6	80	14
7	112	14
8	159	14
9	205	14
10	225	14
11	261	14
12	282	14
done	282	14
0	8	13
1	19	13
2	31	13
3	40	13
4	49	13
5	60	13
6	79	13
7	111	13
8	158	13
9	204	13
10	224	13
11	260	13
12	281	13
done	281	13
0	8	13
1	19	13
2	31	13
3	40	13
4	49	13
5	60	13
6	79	13
7	111	13
8	158	13
9	204	13
10	224	13
11	260	13
12	281	13
done	281	13
0	4	5
1	9	5
2	11	5
done	11	5
0	5	8
1	7	8
2	15	8
done	15	8
0	6	10
1	8	10
done	8	10
0	6	9
1	10	9
2	19	9
done	19	9
0	6	9
1	10	9
2	29	7
3	43	7
4	70	7
5	136	7
6	336	7
7	960	7
8	3782	7
done	5000	7
0	9	26
1	29	26
2	90	12
3	256	12
4	979	10
5	3629	10
done	5000	10
0	7	19
1	9	19
2	17	19
done	17	19
0	6	9
1	8	9
2	16	9
done	16	9
0	7	26
1	19	26
2	80	10
3	291	10
4	726	10
5	1840	10
6	4312	10
done	5000	10
0	6	9
1	8	9
2	16	9
done	16	9
0	6	9
1	8	9
2	16	9
done	16	9
0	7	10
1	9	10
done	9	10
0	7	10
1	9	10
done	9	10
0	7	14
1	11	14
2	25	11
3	49	11
4	91	11
5	107	11
done	107	11
0	6	9
1	8	9
2	16	9
done	16	9
0	6	9
1	8	9
2	16	9
done	16	9
0	6	9
1	8	9
2	16	9
done	16	9
0	6	6
1	10	5
2	18	1
done	18	1
0	5	8
1	7	8
2	15	8
done	15	8
0	6	6
1	10	5
2	18	1
done	18	1
0	5	8
1	7	8
2	15	8
done	15	8
0	7	14
1	17	14
2	32	11
3	58	11
4	94	11
5	103	11
done	103	11
0	6	9
1	14	9
2	15	9
done	15	9
0	6	9
1	14	9
2	15	9
done	15	9
0	6	9
1	14	9
2	15	9
done	15	9
0	6	6
1	16	5
2	17	1
done	17	1
0	5	8
1	13	8
2	14	8
done	14	8
0	6	6
1	16	5
2	17	1
done	17	1
0	5	8
1	13	8
2	14	8
done	14	8
0	5	5
1	9	3
2	20	3
3	28	3
done	28	3
0	7	15
1	11	15
2	21	15
3	33	15
4	35	15
done	35	15
0	6	9
1	8	9
2	16	9
done	16	9
0	5	5
1	9	3
2	20	3
3	28	3
done	28	3
0	6	9
1	8	9
done	8	9
0	6	9
1	8	9
done	8	9
0	5	8
1	7	8
2	15	8
done	15	8
0	5	8
1	7	8
2	15	8
done	15	8
0	9	12
1	25	12
2	42	12
3	83	12
4	162	12
5	401	12
6	1260	12
done	5000	12
0	8	12
1	14	12
2	30	12
3	76	12
4	159	12
5	245	12
6	396	12
7	767	12
8	3351	12
done	5000	12
0	3	4
1	4	4
done	4	4
0	4	6
1	5	6
done	5	6
0	4	5
1	7	5
2	8	5
done	8	5
0	4	5
1	7	5
2	14	3
3	24	3
4	47	3
5	103	3
6	242	3
7	701	3
8	2681	3
done	5000	3
0	7	14
1	14	14
2	39	8
3	76	8
4	134	6
5	258	6
6	662	6
7	2440	6
done	5000	6
0	5	11
1	6	11
done	6	11
0	4	5
1	5	5
done	5	5
0	5	14
1	16	14
2	45	6
3	91	6
4	107	6
5	153	6
6	293	6
7	755	6
8	2745	6
done	5001	6
0	4	5
1	5	5
done	5	5
0	4	5
1	5	5
done	5	5
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	8
1	8	8
2	14	7
3	20	7
4	24	7
done	24	7
0	4	5
1	5	5
done	5	5
0	4	5
1	5	5
done	5	5
0	4	5
1	5	5
done	5	5
0	4	4
1	7	3
done	7	1
0	3	4
1	4	4
done	4	4
0	5	8
1	8	8
2	14	7
3	20	7
4	24	7
done	24	7
0	4	5
1	5	5
done	5	5
0	4	5
1	5	5
done	5	5
0	4	5
1	5	5
done	5	5
0	4	4
1	7	3
done	7	1
0	3	4
1	4	4
done	4	4
0	3	3
1	6	1
done	6	1
0	5	9
1	8	9
2	10	9
done	10	9
0	4	5
1	5	5
done	5	5
0	3	3
1	6	1
done	6	1
0	4	5
1	5	5
done	5	5
0	4	5
1	5	5
done	5	5
0	3	4
1	4	4
done	4	4
0	24	39
1	63	34
2	185	30
3	721	30
4	2929	26
done	5000	25
0	19	27
1	47	25
2	110	19
3	290	16
4	659	16
5	1571	16
done	5001	16
0	21	31
1	46	29
2	106	24
3	350	24
4	1025	17
5	2925	10
done	5000	10
0	17	29
1	45	27
2	141	25
3	342	25
4	661	22
5	1034	22
6	1621	20
7	2730	20
8	4486	20
done	5000	20
0	17	31
1	43	27
2	113	15
3	273	13
4	520	12
5	951	12
6	1335	12
7	1618	12
8	2187	12
9	2335	12
10	2573	12
11	3882	12
done	5001	12
0	20	33
1	48	26
2	113	21
3	376	21
4	1177	17
5	4910	14
done	5000	14
0	6	7
1	10	6
2	18	4
3	24	4
done	24	4
0	7	9
1	15	7
2	25	4
3	44	4
4	52	4
5	69	4
6	104	4
done	104	4
0	7	9
1	12	9
2	23	9
3	42	6
4	66	4
5	186	4
6	967	4
7	2285	4
done	5000	4

prune151.0ms

Filtered

68 candidates to 90 candidates (-32.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	1	91

Merged error: 0.0b

Counts

91 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (+ (+ (/ 0.5 n) 1.0) (* 1.0 (log n))) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
3×	`add-sqr-sqrt` `*-un-lft-identity` `diff-log` `sum-log`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `associate--l+` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 17

Calls

1 calls:

13.0ms

(- (+ (+ (/ 0.5 n) 1.0) (* 1.0 (log n))) 1.0)

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(- (+ (+ (/ 0.5 n) 1.0) (* 1.0 (log n))) 1.0)

simplify1.3min

Counts

20 → 20

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	22	15
2	54	13
3	130	12
4	349	10
5	1030	8
6	4777	8
done	5000	8
0	12	15
1	22	14
2	49	13
3	122	12
4	322	10
5	912	8
6	4276	8
done	5000	8
0	11	14
1	21	13
2	50	13
3	122	12
4	274	10
5	707	8
6	3533	8
done	5000	8
0	10	13
1	19	13
2	43	13
3	84	13
4	114	11
5	167	9
6	618	9
7	3043	9
done	5000	9
0	10	13
1	22	13
2	57	13
3	136	12
4	261	10
5	528	8
6	2421	8
done	5000	8
0	11	27
1	20	27
2	44	27
3	85	27
4	119	23
5	172	19
6	625	19
7	3058	19
done	5000	19
0	10	13
1	19	13
2	43	13
3	84	13
4	114	11
5	167	9
6	618	9
7	3043	9
done	5000	9
0	11	38
1	21	38
2	71	14
3	381	14
4	2683	12
done	5000	12
0	10	13
1	19	13
2	43	13
3	84	13
4	114	11
5	167	9
6	618	9
7	3043	9
done	5000	9
0	10	13
1	19	13
2	43	13
3	84	13
4	114	11
5	167	9
6	618	9
7	3043	9
done	5000	9
0	12	16
1	32	16
2	91	16
3	351	16
4	1752	16
done	5000	16
0	13	38
1	31	36
2	113	36
3	438	27
4	2613	27
done	5000	27
0	2	2
done	2	2
0	11	25
1	27	25
2	101	25
3	424	25
4	2062	21
done	5001	21
0	9	12
1	17	12
2	34	12
3	51	12
4	63	10
5	83	10
6	84	10
done	84	10
0	11	14
1	17	14
2	26	14
3	30	14
4	36	14
5	42	14
done	42	14
0	11	14
1	18	14
2	28	14
3	32	14
4	38	14
5	44	14
done	44	14
0	9	12
1	18	12
2	42	12
3	85	12
4	117	10
5	170	8
6	620	8
7	3074	8
done	5000	8
0	5	6
1	8	6
2	9	6
done	9	6
0	2	2
done	2	2
0	12	15
1	23	14
2	34	10
3	37	8
4	51	8
5	59	8
done	59	8
0	12	17
1	27	15
2	48	11
3	70	8
4	108	8
5	146	8
6	183	8
7	248	8
8	343	8
9	365	8
10	414	8
11	609	8
12	1135	8
13	2429	8
done	5000	8
0	14	17
1	28	17
2	46	15
3	71	13
4	134	13
5	238	10
6	374	8
7	1394	8
done	5000	8

prune35.0ms

Filtered

16 candidates to 20 candidates (-25.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	1	21

Merged error: 0b

Counts

21 → 1

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts: 0 → 0

prune2.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Merged error: 0b

Counts

1 → 1

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	9	8
done	9	8

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	3594×	body	1280	valid
709.0ms	2654×	body	640	valid
257.0ms	1344×	body	320	valid
100.0ms	8000×	pre	80	true
47.0ms	408×	body	160	valid

Details

sample90.0ms

simplify5.6s

prune3.0ms

localize11.0ms

rewrite28.0ms

series43.0ms

simplify1.4min

prune151.0ms

localize9.0ms

rewrite14.0ms

series27.0ms

simplify1.3min

prune35.0ms

localize6.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune2.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling