Details

sample104.0ms

Algorithm

intervals

Results

22.0ms	102×	body	2560	nan
20.0ms	512×	body	80	nan
16.0ms	256×	body	80	valid
15.0ms	86×	body	1280	nan
4.0ms	31×	body	640	nan
2.0ms	16×	body	320	nan
1.0ms	12×	body	160	nan

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

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: 31.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
29.7b	(sqrt (- (* x x) 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

7.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series10.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))

simplify38.0s

Counts

34 → 34

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	9	7
done	9	7
0	6	7
1	8	7
2	9	7
done	9	7
0	7	15
1	9	15
2	10	15
done	10	15
0	6	7
1	8	7
2	9	7
done	9	7
0	7	20
1	10	12
2	20	8
3	34	8
4	44	8
5	54	8
6	75	8
7	135	8
8	341	8
9	1267	8
done	5000	8
0	7	14
1	10	7
2	11	7
done	11	7
0	6	7
1	8	7
2	9	7
done	9	7
0	6	7
1	8	7
2	9	7
done	9	7
0	6	7
1	8	7
2	9	7
done	9	7
0	2	2
1	4	1
done	4	1
0	5	6
1	7	6
2	8	6
done	8	6
0	5	5
1	6	5
done	6	5
0	5	5
1	7	5
2	8	5
done	8	5
0	8	10
1	25	10
2	65	8
3	124	8
4	291	8
5	932	8
6	4503	8
done	5000	8
0	9	18
1	22	16
2	36	14
3	50	12
4	70	12
5	99	12
6	181	12
7	423	12
8	1393	12
done	5000	12
0	7	12
1	16	12
2	27	10
3	51	8
4	99	8
5	189	8
6	350	8
7	832	8
8	3577	8
done	5001	8
0	5	6
1	6	6
done	6	6
0	3	3
1	6	1
done	6	1
0	6	7
1	8	7
2	9	7
done	9	7
0	6	7
1	8	7
2	9	7
done	9	7
0	8	10
1	13	9
2	15	9
done	15	9
0	7	9
1	10	9
2	11	9
done	11	9
0	7	9
1	13	9
2	15	9
done	15	9
0	8	19
1	11	19
2	12	19
done	12	19
0	7	9
1	10	9
2	11	9
done	11	9
0	8	26
1	24	26
2	56	10
3	121	10
4	327	10
5	1236	10
6	4808	10
done	5000	10
0	7	9
1	10	9
2	11	9
done	11	9
0	7	9
1	10	9
2	11	9
done	11	9
0	9	12
1	24	12
2	34	12
3	60	12
4	119	12
5	258	12
6	668	12
7	2518	12
done	5000	12
0	9	26
1	19	18
2	47	18
3	99	16
4	188	14
5	304	14
6	415	14
7	541	14
8	576	14
done	576	14
0	7	17
1	14	9
2	29	9
3	61	3
4	96	1
5	136	1
6	188	1
7	253	1
8	319	1
9	364	1
10	375	1
11	377	1
done	377	1
0	6	8
1	10	8
2	12	8
done	12	8
0	6	8
1	9	8
2	10	8
done	10	8
0	18	25
1	44	25
2	128	25
3	425	25
4	1931	22
done	5000	22
0	12	15
1	33	15
2	68	11
3	160	11
4	411	11
5	1335	11
done	5000	11
0	12	15
1	33	15
2	66	11
3	124	11
4	267	11
5	731	11
6	2897	11
done	5000	11
0	11	15
1	23	15
2	47	15
3	62	15
4	85	15
5	106	15
6	132	15
7	202	15
8	432	15
9	1373	15
done	5000	15
0	14	17
1	35	17
2	70	13
3	160	13
4	403	13
5	1317	13
done	5000	13
0	17	21
1	44	21
2	90	15
3	171	15
4	397	15
5	1197	15
done	5000	15

prune68.0ms

Filtered

29 candidates to 34 candidates (-17.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	1	35

Merged error: 0b

Counts

35 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
10×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 53

Calls

2 calls:

3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
15.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series23.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.6min

Counts

59 → 59

Iterations

Useful iterations: 8 (308.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	25	9
3	53	9
4	94	9
5	149	9
6	214	9
7	321	7
8	536	5
9	1471	5
10	4633	5
done	5000	5
0	8	11
1	12	11
2	13	11
done	13	11
0	6	9
1	10	9
2	25	9
3	53	9
4	94	9
5	149	9
6	214	9
7	321	7
8	536	5
9	1471	5
10	4633	5
done	5000	5
0	10	13
1	14	13
2	15	13
done	15	13
0	9	12
1	16	12
2	18	12
done	18	12
0	9	12
1	15	12
2	22	12
3	30	12
4	53	12
5	109	12
6	251	12
7	714	12
8	2712	12
done	5001	12
0	12	35
1	22	21
2	70	15
3	236	15
4	617	13
5	1302	13
6	2754	13
done	5000	13
0	10	25
1	14	25
2	15	25
done	15	25
0	9	12
1	13	12
2	14	12
done	14	12
0	10	35
1	24	35
2	54	13
3	151	13
4	410	13
5	795	13
6	1515	13
7	3090	13
done	5001	13
0	6	9
1	10	9
2	25	9
3	53	9
4	94	9
5	149	9
6	214	9
7	321	7
8	536	5
9	1471	5
10	4633	5
done	5000	5
0	9	12
1	13	12
2	14	12
done	14	12
0	9	12
1	13	12
2	14	12
done	14	12
0	11	19
1	28	19
2	50	19
3	80	19
4	169	19
5	496	19
6	2257	19
done	5001	19
0	13	31
1	27	23
2	49	23
3	63	19
4	84	19
5	105	19
6	127	19
7	142	19
8	177	19
9	221	19
10	278	19
11	313	19
12	340	19
13	371	19
14	393	19
done	393	19
0	13	20
1	31	16
2	45	16
3	77	16
4	145	16
5	303	16
6	759	16
7	2751	16
done	5001	16
0	12	21
1	22	17
2	37	17
3	50	15
4	70	15
5	91	15
6	107	15
7	119	15
8	145	15
9	174	15
10	199	15
11	208	15
12	218	15
13	237	15
14	251	15
done	251	15
0	13	20
1	32	16
2	57	16
3	102	16
4	218	16
5	596	16
6	2410	16
done	5000	16
0	12	21
1	22	17
2	31	17
3	34	15
4	35	15
done	35	15
0	8	21
1	13	5
2	19	5
3	34	5
4	61	5
5	100	5
6	145	5
7	282	5
8	1354	5
done	5000	5
0	8	11
1	12	11
2	13	11
done	13	11
0	10	13
1	14	13
2	15	13
done	15	13
0	10	13
1	14	13
2	15	13
done	15	13
0	10	13
1	14	13
2	15	13
done	15	13
0	10	13
1	14	13
2	15	13
done	15	13
0	10	13
1	14	13
2	15	13
done	15	13
0	10	13
1	14	13
2	15	13
done	15	13
0	10	13
1	14	13
2	15	13
done	15	13
0	10	13
1	14	13
2	15	13
done	15	13
0	10	19
1	16	19
2	19	19
done	19	19
0	10	18
1	15	12
2	16	12
done	16	12
0	9	12
1	13	12
2	14	12
done	14	12
0	8	8
1	12	7
done	12	7
0	10	13
1	13	13
done	13	13
0	10	13
1	13	13
done	13	13
0	8	8
1	12	7
done	12	7
0	9	12
1	13	12
2	14	12
done	14	12
0	7	7
1	11	5
2	14	5
done	14	5
0	9	12
1	13	12
2	14	12
done	14	12
0	9	12
1	13	12
2	14	12
done	14	12
0	9	12
1	13	12
2	14	12
done	14	12
0	8	11
1	12	11
2	13	11
done	13	11
0	8	11
1	12	11
2	13	11
done	13	11
0	9	12
1	13	12
2	14	12
done	14	12
0	8	11
1	12	11
2	13	11
done	13	11
0	11	15
1	28	15
2	50	15
3	80	15
4	168	15
5	495	15
6	2257	15
done	5001	15
0	10	16
1	16	12
2	20	12
3	35	12
4	62	12
5	101	12
6	154	12
7	291	12
8	1365	12
done	5000	12
0	11	15
1	28	15
2	38	15
3	55	15
4	96	15
5	211	15
6	622	15
7	2457	15
done	5001	15
0	10	16
1	17	12
2	27	12
3	54	12
4	81	12
5	138	12
6	269	12
7	1304	12
done	5000	12
0	11	15
1	20	14
2	28	14
3	40	14
4	75	14
5	165	14
6	416	14
7	1276	14
8	4972	14
done	5000	14
0	10	14
1	15	14
2	16	14
done	16	14
0	10	14
1	18	14
2	24	14
3	31	14
4	49	14
5	103	14
6	236	14
7	613	14
8	1971	14
done	5000	14
0	11	29
1	16	29
2	17	29
done	17	29
0	10	14
1	15	14
2	16	14
done	16	14
0	11	41
1	29	41
2	78	15
3	231	15
4	601	15
5	1613	15
done	5002	15
0	10	14
1	15	14
2	16	14
done	16	14
0	10	14
1	15	14
2	16	14
done	16	14
0	12	17
1	33	17
2	72	17
3	149	17
4	382	17
5	1218	17
6	4136	17
done	5000	17
0	13	41
1	34	29
2	77	27
3	161	25
4	323	25
5	729	25
6	1616	25
7	3534	25
done	5001	25
0	11	27
1	27	27
2	58	13
3	165	13
4	377	13
5	789	13
6	2200	11
done	5001	11
0	9	13
1	15	13
2	23	13
done	23	13
0	21	37
1	52	34
2	153	25
3	599	25
4	4050	21
done	5001	21
0	17	21
1	43	21
2	120	17
3	377	17
4	1855	15
done	5000	15
0	21	37
1	55	37
2	213	34
3	573	34
4	2610	28
done	5000	28
0	14	23
1	31	21
2	72	15
3	107	15
4	180	15
5	359	15
6	888	15
7	3030	15
done	5001	15
0	18	23
1	45	23
2	122	19
3	379	19
4	1856	17
done	5000	17
0	11	16
1	27	16
2	77	16
3	190	16
4	627	16
5	2655	14
done	5000	14

prune152.0ms

Filtered

46 candidates to 59 candidates (-28.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	1	60

Merged error: 0b

Counts

60 → 1

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
done	13	14

end0.0ms

sample3.1s

Algorithm

intervals

Results

670.0ms	3048×	body	2560	nan
646.0ms	16596×	body	80	nan
471.0ms	2597×	body	1280	nan
376.0ms	8000×	body	80	valid
185.0ms	1253×	body	640	nan
72.0ms	661×	body	320	nan
27.0ms	319×	body	160	nan

Details

sample104.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite13.0ms

series10.0ms

simplify38.0s

prune68.0ms

localize12.0ms

rewrite23.0ms

series23.0ms

simplify1.6min

prune152.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling