Details

sample65.0ms

Algorithm

intervals

Results

19.0ms	64×	body	1280	valid
12.0ms	32×	body	640	valid
10.0ms	257×	body	80	nan
6.0ms	131×	body	80	valid
3.0ms	23×	body	320	valid
0.0ms	6×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

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: 29.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (log (+ N 1.0)) (log N))
3.1b	(log (+ N 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

8.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series12.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(- (log (+ N 1.0)) (log N))
5.0ms	(log (+ N 1.0))

simplify42.8s

Counts

47 → 47

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	11	7
3	12	7
done	12	7
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	2	2
1	4	1
done	4	1
0	4	4
1	5	4
done	5	4
0	2	2
1	4	1
done	4	1
0	4	4
1	5	4
done	5	4
0	7	8
1	21	8
2	30	8
3	47	8
4	88	8
5	208	8
6	613	8
7	2441	8
done	5000	8
0	8	12
1	16	10
2	31	10
3	44	10
4	64	10
5	85	10
6	102	10
7	125	10
8	168	10
9	230	10
10	231	10
done	231	10
0	6	8
1	11	8
2	21	8
3	37	8
4	62	8
5	103	8
6	161	8
7	329	8
8	1610	8
done	5000	8
0	4	4
1	6	4
2	7	4
done	7	4
0	4	4
1	5	4
done	5	4
0	5	5
1	6	5
done	6	5
0	5	5
1	6	3
done	6	3
0	6	11
1	7	11
done	7	11
0	5	5
1	6	5
done	6	5
0	6	14
1	8	14
2	10	6
3	15	6
4	21	6
5	31	6
6	54	6
7	110	6
8	319	6
9	1259	6
done	5001	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	4	5
1	5	5
done	5	5
0	7	8
1	10	8
2	11	8
done	11	8
0	7	8
1	13	8
2	16	5
3	19	5
4	33	5
5	49	5
6	85	5
7	102	5
8	111	5
9	121	5
10	136	5
11	166	5
12	203	5
13	236	5
14	270	5
15	298	5
16	301	5
done	301	5
0	8	17
1	11	17
2	12	17
done	12	17
0	7	8
1	10	8
2	11	8
done	11	8
0	8	23
1	12	23
2	27	9
3	70	9
4	179	9
5	507	9
6	1717	9
7	4952	9
done	5000	9
0	7	8
1	10	8
2	11	8
done	11	8
0	7	8
1	10	8
2	11	8
done	11	8
0	9	11
1	25	11
2	47	11
3	81	11
4	165	11
5	497	11
6	2238	11
done	5000	11
0	10	23
1	18	20
2	26	20
3	29	18
4	30	18
done	30	18
0	3	3
done	3	3
0	8	15
1	14	15
2	21	15
3	36	15
4	61	15
5	102	15
6	166	15
7	334	15
8	1644	15
done	5000	15
0	6	7
1	8	7
done	8	7
0	8	9
1	10	9
done	10	9
0	8	9
1	11	9
2	12	9
done	12	9
0	6	7
1	9	7
2	10	7
done	10	7
0	6	7
1	9	7
2	10	7
done	10	7
0	6	7
1	9	7
2	10	7
done	10	7
0	6	7
1	9	7
2	10	7
done	10	7
0	8	11
1	13	11
2	20	10
3	30	10
4	36	10
5	44	10
6	56	10
7	70	10
8	85	10
done	85	10
0	7	8
1	10	8
2	11	8
done	11	8
0	7	7
1	12	6
2	13	4
3	20	4
done	20	4
0	7	8
1	10	8
2	11	8
done	11	8
0	7	8
1	10	8
2	11	8
done	11	8
0	6	7
1	9	7
2	10	7
done	10	7
0	6	7
1	9	7
2	10	7
done	10	7
0	10	15
1	19	13
2	34	13
3	47	13
4	67	13
5	88	13
6	105	13
7	128	13
8	171	13
9	233	13
10	234	13
done	234	13
0	6	7
1	9	7
2	10	7
done	10	7
0	3	3
done	3	3
0	12	16
1	29	16
2	86	16
3	175	16
4	337	16
5	535	14
6	648	14
7	794	14
8	1245	14
9	3100	14
done	5000	14
0	15	21
1	38	19
2	89	12
3	219	12
4	460	12
5	1268	10
done	5000	10
0	18	22
1	41	21
2	92	17
3	224	17
4	575	14
5	1648	10
done	5000	10
0	17	22
1	41	21
2	119	19
3	403	19
4	1587	19
done	5000	19
0	17	21
1	43	21
2	107	15
3	266	15
4	864	15
5	2906	13
done	5000	13
0	17	20
1	37	19
2	80	15
3	173	15
4	401	11
5	1092	7
done	5002	7

prune90.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Merged error: 0.0b

Counts

48 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.9b	(log (/ (+ N 1.0) N))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/ (+ N 1.0) N)
8.0ms	(log (/ (+ N 1.0) N))

series10.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

simplify25.7s

Counts

66 → 66

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	14
1	10	14
2	12	9
3	13	9
done	13	9
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	9	16
1	19	16
2	40	16
3	69	10
4	108	10
5	143	10
6	198	10
7	238	10
8	275	10
9	278	10
done	278	10
0	7	8
1	11	8
2	13	8
3	14	8
done	14	8
0	8	13
1	14	13
2	22	13
3	35	11
4	43	11
5	47	11
6	55	11
7	70	11
8	82	11
9	94	11
10	106	11
11	107	11
done	107	11
0	7	8
1	11	8
2	13	8
3	14	8
done	14	8
0	8	12
1	15	10
2	29	10
3	52	7
4	72	7
5	85	7
6	97	7
7	110	7
done	110	7
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	8	11
1	14	11
2	20	11
3	28	11
4	40	11
5	48	11
6	57	11
7	70	11
8	86	11
9	89	11
done	89	11
0	7	8
1	11	8
2	13	8
3	14	8
done	14	8
0	7	8
1	11	8
2	13	8
3	14	8
done	14	8
0	7	8
1	11	8
2	13	8
3	14	8
done	14	8
0	7	7
1	12	5
2	18	5
3	22	5
done	22	5
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	6	8
1	14	7
2	19	7
3	32	6
4	44	5
5	74	5
6	100	5
7	106	5
8	115	5
done	115	5
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	5	5
1	11	4
2	12	4
3	16	4
4	18	4
5	24	4
6	29	4
done	29	4
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	3	4
1	7	1
done	7	1
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	6	8
1	14	7
2	19	7
3	32	6
4	44	5
5	74	5
6	100	5
7	106	5
8	115	5
done	115	5
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	5	5
1	11	4
2	12	4
3	16	4
4	18	4
5	24	4
6	29	4
done	29	4
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	3	4
1	7	1
done	7	1
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	2	2
1	4	1
done	4	1
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	4	4
1	5	4
done	5	4
0	4	4
1	10	3
2	11	3
3	15	3
4	17	3
5	23	3
6	28	3
done	28	3
0	4	4
1	5	4
done	5	4
0	2	2
done	2	2
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	6	7
1	10	5
2	15	5
3	18	5
4	23	5
5	40	5
6	61	5
7	110	5
8	130	5
9	171	5
10	223	5
11	236	5
12	253	5
13	259	5
14	277	5
15	299	5
16	304	5
done	304	5
0	7	15
1	11	15
2	13	15
3	14	15
done	14	15
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	7	20
1	12	20
2	16	8
3	34	8
4	78	8
5	191	8
6	530	8
7	1790	8
done	5000	8
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	6	7
1	10	7
2	12	7
3	13	7
done	13	7
0	6	7
1	9	7
2	10	7
done	10	7
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	5	6
1	6	6
done	6	6
0	8	17
1	30	17
2	91	9
3	232	7
4	615	7
5	1678	7
6	4415	7
done	5000	7
0	6	13
1	7	13
done	7	13
0	5	6
1	6	6
done	6	6
0	6	17
1	14	17
2	46	7
3	118	7
4	295	7
5	588	7
6	1241	7
done	5001	7
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	4	4
1	8	4
2	10	4
3	11	4
done	11	4
0	2	2
done	2	2
0	8	15
1	15	15
2	24	15
3	30	15
done	30	15
0	6	7
1	7	7
done	7	7
0	7	12
1	10	12
2	12	12
3	13	12
done	13	12
0	6	7
1	7	7
done	7	7
0	7	11
1	12	9
2	18	9
3	23	9
done	23	9
0	5	6
1	6	6
done	6	6
0	7	10
1	10	10
done	10	10
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	6
1	9	4
2	11	4
done	11	4
0	5	6
1	6	6
done	6	6
0	5	7
1	9	7
done	9	7
0	5	6
1	6	6
done	6	6
0	4	4
1	6	4
done	6	4
0	5	6
1	6	6
done	6	6
0	2	3
1	4	1
done	4	1
0	4	5
1	5	5
done	5	5
0	5	7
1	9	7
done	9	7
0	5	6
1	6	6
done	6	6
0	4	4
1	6	4
done	6	4
0	5	6
1	6	6
done	6	6
0	2	3
1	4	1
done	4	1
0	4	5
1	5	5
done	5	5
0	3	3
1	5	3
done	5	3
0	4	5
1	5	5
done	5	5
0	6	9
1	9	9
done	9	9
0	5	6
1	6	6
done	6	6
0	5	5
1	8	3
2	10	3
done	10	3
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	4	5
1	5	5
done	5	5
0	4	5
1	5	5
done	5	5
0	8	13
1	23	11
2	50	11
3	97	11
4	142	11
5	190	11
6	300	11
7	442	11
8	966	11
9	3363	11
done	5000	11
0	4	5
1	7	5
2	13	5
3	18	5
4	22	5
done	22	5
0	14	19
1	34	19
2	97	19
3	195	19
4	389	19
5	672	17
6	1040	17
7	1604	17
8	2073	17
9	3932	17
done	5000	17
0	13	16
1	30	15
2	66	9
3	147	9
4	358	9
5	1135	7
done	5000	7
0	13	16
1	30	15
2	66	9
3	147	9
4	358	9
5	1135	7
done	5000	7
0	6	7
1	12	7
2	15	5
3	16	5
4	22	5
5	25	5
done	25	5
0	6	7
1	12	7
2	15	5
3	16	5
4	22	5
5	25	5
done	25	5
0	6	7
1	12	7
2	15	5
3	16	5
4	22	5
5	25	5
done	25	5

prune94.0ms

Filtered

47 candidates to 66 candidates (-40.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	3	68

Merged error: 0.0b

Counts

68 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.9b	(log (sqrt (/ (+ N 1.0) N)))
2.9b	(log (sqrt (/ (+ N 1.0) N)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
6.0ms	(sqrt (/ (+ N 1.0) N))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
4.0ms	(sqrt (/ (+ N 1.0) N))
6.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify49.2s

Counts

130 → 130

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	8	16
1	11	16
2	13	10
3	14	10
done	14	10
0	7	8
1	8	8
done	8	8
0	8	15
1	10	8
done	10	8
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	10	17
1	17	17
2	27	9
3	33	9
done	33	9
0	8	9
1	9	9
done	9	9
0	9	14
1	12	14
2	14	14
3	15	14
done	15	14
0	8	9
1	9	9
done	9	9
0	9	13
1	14	11
2	21	6
3	26	6
done	26	6
0	7	8
1	8	8
done	8	8
0	9	12
1	12	12
done	12	12
0	8	9
1	9	9
done	9	9
0	8	9
1	9	9
done	9	9
0	8	9
1	9	9
done	9	9
0	8	8
1	11	6
2	13	6
done	13	6
0	7	8
1	8	8
done	8	8
0	7	9
1	11	9
done	11	9
0	7	8
1	8	8
done	8	8
0	6	6
1	8	6
done	8	6
0	7	8
1	8	8
done	8	8
0	4	5
1	6	2
done	6	2
0	6	7
1	7	7
done	7	7
0	7	9
1	11	9
done	11	9
0	7	8
1	8	8
done	8	8
0	6	6
1	8	6
done	8	6
0	7	8
1	8	8
done	8	8
0	4	5
1	6	2
done	6	2
0	6	7
1	7	7
done	7	7
0	3	3
1	5	2
done	5	2
0	6	7
1	7	7
done	7	7
0	5	5
1	6	5
done	6	5
0	5	5
1	7	5
done	7	5
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	2	2
1	4	1
done	4	1
0	6	7
1	7	7
done	7	7
0	5	5
1	6	5
done	6	5
0	3	3
done	3	3
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	6	7
1	7	7
done	7	7
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	7	8
1	8	8
done	8	8
0	7	8
1	8	6
done	8	6
0	8	17
1	9	17
done	9	17
0	7	8
1	8	8
done	8	8
0	8	23
1	10	23
2	12	9
3	17	9
4	23	9
5	33	9
6	54	9
7	110	9
8	328	9
9	1244	9
done	5000	9
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	8	16
1	11	16
2	13	10
3	14	10
done	14	10
0	7	8
1	8	8
done	8	8
0	8	15
1	10	8
done	10	8
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	10	17
1	17	17
2	27	9
3	33	9
done	33	9
0	8	9
1	9	9
done	9	9
0	9	14
1	12	14
2	14	14
3	15	14
done	15	14
0	8	9
1	9	9
done	9	9
0	9	13
1	14	11
2	21	6
3	26	6
done	26	6
0	7	8
1	8	8
done	8	8
0	9	12
1	12	12
done	12	12
0	8	9
1	9	9
done	9	9
0	8	9
1	9	9
done	9	9
0	8	9
1	9	9
done	9	9
0	8	8
1	11	6
2	13	6
done	13	6
0	7	8
1	8	8
done	8	8
0	7	9
1	11	9
done	11	9
0	7	8
1	8	8
done	8	8
0	6	6
1	8	6
done	8	6
0	7	8
1	8	8
done	8	8
0	4	5
1	6	2
done	6	2
0	6	7
1	7	7
done	7	7
0	7	9
1	11	9
done	11	9
0	7	8
1	8	8
done	8	8
0	6	6
1	8	6
done	8	6
0	7	8
1	8	8
done	8	8
0	4	5
1	6	2
done	6	2
0	6	7
1	7	7
done	7	7
0	3	3
1	5	2
done	5	2
0	6	7
1	7	7
done	7	7
0	5	5
1	6	5
done	6	5
0	5	5
1	7	5
done	7	5
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	2	2
1	4	1
done	4	1
0	6	7
1	7	7
done	7	7
0	5	5
1	6	5
done	6	5
0	3	3
done	3	3
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	6	7
1	7	7
done	7	7
0	5	6
1	9	6
2	11	6
3	12	6
done	12	6
0	7	8
1	8	8
done	8	8
0	7	8
1	8	6
done	8	6
0	8	17
1	9	17
done	9	17
0	7	8
1	8	8
done	8	8
0	8	23
1	10	23
2	12	9
3	17	9
4	23	9
5	33	9
6	54	9
7	110	9
8	328	9
9	1244	9
done	5000	9
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	7	15
1	8	15
done	8	15
0	6	7
1	7	7
done	7	7
0	7	20
1	9	12
2	16	8
3	33	8
4	41	8
5	60	8
6	83	8
7	154	8
8	369	8
9	1301	8
done	5001	8
0	7	14
1	9	7
done	9	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	9	16
1	16	16
2	26	8
3	32	8
done	32	8
0	7	8
1	8	8
done	8	8
0	8	13
1	11	13
2	13	13
3	14	13
done	14	13
0	7	8
1	8	8
done	8	8
0	8	12
1	13	10
2	20	5
3	25	5
done	25	5
0	6	7
1	7	7
done	7	7
0	8	11
1	11	11
done	11	11
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	7	7
1	10	5
2	12	5
done	12	5
0	6	7
1	7	7
done	7	7
0	6	8
1	10	8
done	10	8
0	6	7
1	7	7
done	7	7
0	5	5
1	7	5
done	7	5
0	6	7
1	7	7
done	7	7
0	3	4
1	5	1
done	5	1
0	5	6
1	6	6
done	6	6
0	6	8
1	10	8
done	10	8
0	6	7
1	7	7
done	7	7
0	5	5
1	7	5
done	7	5
0	6	7
1	7	7
done	7	7
0	3	4
1	5	1
done	5	1
0	5	6
1	6	6
done	6	6
0	2	2
1	4	1
done	4	1
0	5	6
1	6	6
done	6	6
0	4	4
1	5	4
done	5	4
0	4	4
1	6	4
done	6	4
0	4	4
1	5	4
done	5	4
0	2	2
done	2	2
0	3	3
1	6	1
done	6	1
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	7	15
1	8	15
done	8	15
0	6	7
1	7	7
done	7	7
0	7	20
1	9	12
2	16	8
3	33	8
4	41	8
5	60	8
6	83	8
7	154	8
8	369	8
9	1301	8
done	5001	8
0	7	14
1	9	7
done	9	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	9	16
1	16	16
2	26	8
3	32	8
done	32	8
0	7	8
1	8	8
done	8	8
0	8	13
1	11	13
2	13	13
3	14	13
done	14	13
0	7	8
1	8	8
done	8	8
0	8	12
1	13	10
2	20	5
3	25	5
done	25	5
0	6	7
1	7	7
done	7	7
0	8	11
1	11	11
done	11	11
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	7	7
1	10	5
2	12	5
done	12	5
0	6	7
1	7	7
done	7	7
0	6	8
1	10	8
done	10	8
0	6	7
1	7	7
done	7	7
0	5	5
1	7	5
done	7	5
0	6	7
1	7	7
done	7	7
0	3	4
1	5	1
done	5	1
0	5	6
1	6	6
done	6	6
0	6	8
1	10	8
done	10	8
0	6	7
1	7	7
done	7	7
0	5	5
1	7	5
done	7	5
0	6	7
1	7	7
done	7	7
0	3	4
1	5	1
done	5	1
0	5	6
1	6	6
done	6	6
0	2	2
1	4	1
done	4	1
0	5	6
1	6	6
done	6	6
0	4	4
1	5	4
done	5	4
0	4	4
1	6	4
done	6	4
0	4	4
1	5	4
done	5	4
0	2	2
done	2	2
0	3	3
1	6	1
done	6	1
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	20	34
1	52	34
2	199	30
3	609	28
4	2145	26
done	5001	26
0	13	16
1	30	15
2	66	9
3	147	9
4	358	9
5	1135	7
done	5000	7
0	13	16
1	30	15
2	66	9
3	147	9
4	358	9
5	1135	7
done	5000	7
0	20	34
1	52	34
2	199	30
3	609	28
4	2145	26
done	5001	26
0	13	16
1	30	15
2	66	9
3	147	9
4	358	9
5	1135	7
done	5000	7
0	13	16
1	30	15
2	66	9
3	147	9
4	358	9
5	1135	7
done	5000	7
0	18	31
1	55	31
2	194	31
3	552	25
4	1702	23
done	5000	23
0	12	15
1	29	15
2	65	11
3	142	11
4	349	11
5	1086	9
done	5001	9
0	12	15
1	29	15
2	65	11
3	142	11
4	349	11
5	1086	9
done	5001	9
0	18	31
1	55	31
2	194	31
3	552	25
4	1702	23
done	5000	23
0	12	15
1	29	15
2	65	11
3	142	11
4	349	11
5	1086	9
done	5001	9
0	12	15
1	29	15
2	65	11
3	142	11
4	349	11
5	1086	9
done	5001	9

prune273.0ms

Filtered

96 candidates to 130 candidates (-35.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	130	3	133

Merged error: 0.0b

Counts

133 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt N)
0.5b	(cbrt N)
0.5b	(cbrt N)
3.8b	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-prod`
55×	`*-un-lft-identity`
49×	`times-frac`
46×	`associate-+r+`
37×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`sqrt-prod`
11×	`associate-+l+` `distribute-lft-out`
8×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`log-div` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 107

Calls

4 calls:

2.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
25.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt N)
26.0ms	(cbrt N)
30.0ms	(cbrt N)
55.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify3.3min

Counts

119 → 119

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	9	18
1	16	18
2	29	18
3	50	12
4	68	8
5	73	5
6	77	5
7	83	5
8	93	5
9	114	5
10	174	5
11	384	5
12	1313	5
done	5001	5
0	12	21
1	20	21
2	34	21
3	75	21
4	161	15
5	318	15
6	416	14
7	476	14
8	497	14
done	497	14
0	12	21
1	23	21
2	43	18
3	116	18
4	268	14
5	624	11
6	1136	8
7	2555	5
done	5001	5
0	13	43
1	21	43
2	35	43
3	76	43
4	161	31
5	319	31
6	417	29
7	479	29
8	500	29
done	500	29
0	12	21
1	20	21
2	34	21
3	75	21
4	161	15
5	318	15
6	416	14
7	476	14
8	497	14
done	497	14
0	13	62
1	34	62
2	80	22
3	245	22
4	1178	16
done	5001	16
0	12	21
1	20	21
2	34	21
3	75	21
4	161	15
5	318	15
6	416	14
7	476	14
8	497	14
done	497	14
0	12	21
1	20	21
2	34	21
3	75	21
4	161	15
5	318	15
6	416	14
7	476	14
8	497	14
done	497	14
0	14	24
1	35	24
2	50	24
3	98	24
4	255	24
5	865	24
6	4088	24
done	5000	24
0	15	62
1	30	53
2	55	53
3	149	50
4	593	35
5	2608	28
done	5000	28
0	13	41
1	25	41
2	46	41
3	146	41
4	621	35
5	2645	26
done	5001	26
0	11	20
1	20	20
2	33	20
3	77	20
4	203	20
5	435	11
6	643	4
7	2614	4
done	5000	4
0	11	20
1	19	20
2	33	20
3	74	20
4	159	14
5	316	14
6	414	13
7	474	13
8	495	13
done	495	13
0	11	20
1	19	20
2	33	20
3	74	20
4	159	14
5	316	14
6	414	13
7	474	13
8	495	13
done	495	13
0	11	20
1	19	20
2	33	20
3	74	20
4	159	14
5	316	14
6	414	13
7	474	13
8	495	13
done	495	13
0	11	20
1	19	20
2	33	20
3	74	20
4	159	14
5	316	14
6	414	13
7	474	13
8	495	13
done	495	13
0	13	30
1	21	30
2	37	23
3	73	23
4	146	21
5	276	21
6	496	21
7	654	21
8	789	21
9	812	21
10	813	21
done	813	21
0	12	21
1	18	21
2	28	21
3	51	21
4	87	21
5	138	21
6	184	21
7	241	21
8	300	21
9	312	21
10	313	21
done	313	21
0	14	31
1	26	31
2	48	31
3	118	28
4	355	26
5	1032	26
6	2094	26
7	2486	26
8	2547	26
done	2547	26
0	15	28
1	27	28
2	49	28
3	119	25
4	356	23
5	1038	23
6	2094	23
7	2484	23
8	2544	23
done	2544	23
0	15	27
1	29	26
2	51	26
3	119	20
4	455	18
5	2426	18
done	5000	18
0	15	32
1	31	32
2	66	32
3	171	24
4	554	22
5	1931	22
6	4450	22
done	5000	22
0	14	28
1	26	28
2	48	28
3	118	25
4	355	23
5	1032	23
6	2094	23
7	2486	23
8	2547	23
done	2547	23
0	14	26
1	27	24
2	54	24
3	144	20
4	479	18
5	1069	18
6	1317	18
7	1332	18
done	1332	18
0	15	30
1	26	25
2	42	25
3	90	25
4	218	25
5	519	25
6	882	25
7	1049	25
8	1080	25
done	1080	25
0	16	27
1	27	22
2	43	22
3	91	22
4	219	22
5	518	22
6	878	22
7	1045	22
8	1076	22
done	1076	22
0	16	26
1	29	20
2	45	20
3	93	20
4	221	20
5	520	20
6	878	20
7	1045	18
8	1243	18
done	1243	18
0	16	31
1	29	26
2	49	26
3	114	25
4	318	25
5	953	23
6	1897	23
7	2281	23
8	2340	23
done	2340	23
0	15	27
1	26	22
2	42	22
3	90	22
4	218	22
5	519	22
6	882	22
7	1049	22
8	1080	22
done	1080	22
0	15	25
1	27	18
2	46	18
3	100	18
4	270	18
5	568	18
6	676	18
7	718	18
done	718	18
0	13	25
1	23	25
2	39	25
3	87	25
4	215	25
5	515	25
6	870	25
7	1037	25
8	1069	25
done	1069	25
0	14	22
1	24	22
2	40	22
3	88	22
4	216	22
5	514	22
6	872	22
7	1037	22
8	1069	22
done	1069	22
0	14	21
1	26	20
2	42	20
3	90	20
4	218	20
5	517	20
6	874	20
7	1041	18
8	1239	18
done	1239	18
0	14	26
1	26	26
2	46	26
3	111	25
4	315	25
5	947	23
6	1901	23
7	2274	23
8	2332	23
done	2332	23
0	13	22
1	23	22
2	39	22
3	87	22
4	215	22
5	515	22
6	870	22
7	1037	22
8	1069	22
done	1069	22
0	13	20
1	24	18
2	43	18
3	97	18
4	267	18
5	562	18
6	667	18
7	708	18
done	708	18
0	14	22
1	26	21
2	42	21
3	90	21
4	218	21
5	517	21
6	874	21
7	1041	21
8	1077	19
9	1275	19
done	1275	19
0	15	19
1	27	18
2	43	18
3	91	18
4	219	18
5	518	18
6	875	18
7	1042	18
8	1077	16
9	1275	16
done	1275	16
0	14	18
1	26	16
2	42	16
3	90	13
4	204	11
5	889	11
6	3497	11
7	3499	11
done	3499	11
0	15	23
1	29	22
2	49	22
3	114	19
4	357	18
5	1656	16
done	5001	16
0	14	19
1	26	18
2	42	18
3	90	18
4	218	18
5	517	18
6	874	18
7	1041	18
8	1077	16
9	1275	16
done	1275	16
0	13	17
1	24	13
2	34	11
3	65	11
4	104	11
5	154	11
6	192	11
7	256	11
8	292	11
done	292	11
0	14	22
1	26	21
2	42	21
3	90	21
4	218	21
5	517	21
6	874	21
7	1041	21
8	1077	19
9	1275	19
done	1275	19
0	15	19
1	27	18
2	43	18
3	91	18
4	219	18
5	518	18
6	875	18
7	1042	18
8	1077	16
9	1275	16
done	1275	16
0	14	18
1	26	16
2	42	16
3	90	13
4	204	11
5	889	11
6	3497	11
7	3499	11
done	3499	11
0	15	23
1	29	22
2	49	22
3	114	19
4	357	18
5	1656	16
done	5001	16
0	14	19
1	26	18
2	42	18
3	90	18
4	218	18
5	517	18
6	874	18
7	1041	18
8	1077	16
9	1275	16
done	1275	16
0	13	17
1	24	13
2	34	11
3	65	11
4	104	11
5	154	11
6	192	11
7	256	11
8	292	11
done	292	11
0	13	25
1	23	25
2	39	25
3	87	25
4	215	25
5	515	25
6	870	25
7	1037	25
8	1069	25
done	1069	25
0	14	22
1	24	22
2	40	22
3	88	22
4	216	22
5	514	22
6	872	22
7	1037	22
8	1069	22
done	1069	22
0	14	21
1	26	20
2	42	20
3	90	20
4	218	20
5	517	20
6	874	20
7	1041	18
8	1239	18
done	1239	18
0	14	26
1	26	26
2	46	26
3	111	25
4	315	25
5	947	23
6	1901	23
7	2274	23
8	2332	23
done	2332	23
0	13	22
1	23	22
2	39	22
3	87	22
4	215	22
5	515	22
6	870	22
7	1037	22
8	1069	22
done	1069	22
0	13	20
1	24	18
2	43	18
3	97	18
4	267	18
5	562	18
6	667	18
7	708	18
done	708	18
0	13	21
1	26	20
2	42	19
3	97	19
4	249	19
5	543	19
6	726	19
7	732	19
done	732	19
0	14	18
1	27	17
2	43	16
3	98	16
4	250	16
5	543	16
6	734	16
7	740	16
done	740	16
0	13	17
1	26	14
2	42	13
3	84	11
4	172	11
5	310	11
6	312	11
done	312	11
0	14	22
1	29	21
2	49	20
3	125	18
4	368	16
5	1040	16
6	1505	16
7	1519	16
done	1519	16
0	13	18
1	26	17
2	42	16
3	97	16
4	249	16
5	543	16
6	726	16
7	732	16
done	732	16
0	12	16
1	23	13
2	33	11
3	63	11
4	102	11
5	150	11
6	185	11
7	249	11
8	287	11
done	287	11
0	11	14
1	20	13
2	30	11
3	61	11
4	103	11
5	151	11
6	186	11
7	250	11
8	287	11
done	287	11
0	10	17
1	16	17
2	26	17
3	47	13
4	77	10
5	123	10
6	175	10
7	218	10
8	245	10
done	245	10
0	12	21
1	18	21
2	24	21
3	33	21
4	43	21
5	52	21
6	57	21
7	66	21
8	83	21
9	102	21
10	110	21
done	110	21
0	12	21
1	18	21
2	24	21
3	33	21
4	43	21
5	52	21
6	57	21
7	66	21
8	83	21
9	102	21
10	110	21
done	110	21
0	11	18
1	18	18
2	29	18
3	55	18
4	107	18
5	192	18
6	279	18
7	333	18
8	353	18
done	353	18
0	12	18
1	19	18
2	30	18
3	56	18
4	108	18
5	193	18
6	280	18
7	334	18
8	353	18
done	353	18
0	11	18
1	18	18
2	29	18
3	55	18
4	107	18
5	192	18
6	279	18
7	333	18
8	353	18
done	353	18
0	8	17
1	14	10
2	21	10
3	40	10
4	73	10
5	126	10
6	185	10
7	235	10
8	268	10
done	268	10
0	8	17
1	14	10
2	21	10
3	40	10
4	73	10
5	126	10
6	185	10
7	235	10
8	268	10
done	268	10
0	11	18
1	18	18
2	29	18
3	55	18
4	107	18
5	192	18
6	279	18
7	333	18
8	353	18
done	353	18
0	8	17
1	14	10
2	21	10
3	40	10
4	73	10
5	126	10
6	185	10
7	235	10
8	268	10
done	268	10
0	11	20
1	19	20
2	33	20
3	74	20
4	159	14
5	316	14
6	414	13
7	474	13
8	495	13
done	495	13
0	12	17
1	25	16
2	40	15
3	96	14
4	213	11
5	416	11
6	515	11
7	528	11
done	528	11
0	10	17
1	16	17
2	26	17
3	47	13
4	77	10
5	123	10
6	175	10
7	218	10
8	245	10
done	245	10
0	10	15
1	17	15
2	28	14
3	43	14
4	68	14
5	95	11
6	131	11
7	164	11
8	197	11
9	198	11
done	198	11
0	3	3
done	3	3
0	3	3
done	3	3
0	4	6
done	4	6
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	2	2
1	4	1
done	4	1
0	2	2
done	2	2
0	4	7
done	4	7
0	3	3
done	3	3
0	4	8
1	5	8
2	7	4
3	12	1
4	16	1
5	22	1
6	32	1
7	55	1
8	122	1
9	333	1
10	1272	1
done	5000	1
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	4	6
done	4	6
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	2	2
1	4	1
done	4	1
0	2	2
done	2	2
0	4	7
done	4	7
0	3	3
done	3	3
0	4	8
1	5	8
2	7	4
3	12	1
4	16	1
5	22	1
6	32	1
7	55	1
8	122	1
9	333	1
10	1272	1
done	5000	1
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	4	6
done	4	6
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	2	2
1	4	1
done	4	1
0	2	2
done	2	2
0	4	7
done	4	7
0	3	3
done	3	3
0	4	8
1	5	8
2	7	4
3	12	1
4	16	1
5	22	1
6	32	1
7	55	1
8	122	1
9	333	1
10	1272	1
done	5000	1
0	3	3
done	3	3
0	3	3
done	3	3
0	30	45
1	70	43
2	190	34
3	758	32
4	3439	23
done	5000	21
0	41	71
1	113	67
2	335	55
3	1480	48
done	5001	47
0	47	79
1	129	75
2	384	67
3	1748	62
done	5000	62
0	8	8
1	20	7
2	28	5
3	50	2
4	87	2
5	174	2
6	360	2
7	911	2
8	3082	2
done	5000	2
0	9	10
1	19	8
2	35	5
3	72	2
4	126	2
5	264	2
6	568	2
7	1635	2
done	5000	2
0	12	13
1	23	12
2	40	11
3	95	10
4	227	9
5	544	7
6	1185	6
7	3475	6
done	5001	6
0	8	8
1	20	7
2	28	5
3	50	2
4	87	2
5	174	2
6	360	2
7	911	2
8	3082	2
done	5000	2
0	9	10
1	19	8
2	35	5
3	72	2
4	126	2
5	264	2
6	568	2
7	1635	2
done	5000	2
0	12	13
1	23	12
2	40	11
3	95	10
4	227	9
5	544	7
6	1185	6
7	3475	6
done	5001	6
0	8	8
1	20	7
2	28	5
3	50	2
4	87	2
5	174	2
6	360	2
7	911	2
8	3082	2
done	5000	2
0	9	10
1	19	8
2	35	5
3	72	2
4	126	2
5	264	2
6	568	2
7	1635	2
done	5000	2
0	12	13
1	23	12
2	40	11
3	95	10
4	227	9
5	544	7
6	1185	6
7	3475	6
done	5001	6

prune226.0ms

Filtered

84 candidates to 119 candidates (-41.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	119	3	122

Merged error: 0.0b

Counts

122 → 3

regimes39.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.4b

bsearch12.0ms

Steps

Iters	Range		Point
7	280.39199233801065	54027.26876101495	7318.376323178768

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	32
1	24	32
done	24	32

end0.0ms

sample1.7s

Algorithm

intervals

Results

533.0ms	1803×	body	1280	valid
290.0ms	7974×	body	80	nan
253.0ms	1235×	body	640	valid
195.0ms	4084×	body	80	valid
79.0ms	597×	body	320	valid
24.0ms	281×	body	160	valid

Details

sample65.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite13.0ms

series12.0ms

simplify42.8s

prune90.0ms

localize5.0ms

rewrite17.0ms

series10.0ms

simplify25.7s

prune94.0ms

localize8.0ms

rewrite29.0ms

series22.0ms

simplify49.2s

prune273.0ms

localize15.0ms

rewrite36.0ms

series137.0ms

simplify3.3min

prune226.0ms

regimes39.0ms

bsearch12.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling