Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify5.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	23	15
2	57	15
3	136	15
4	280	15
5	511	15
6	1297	15
7	4347	15
done	5001	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: 62.0b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

62.0b

(- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate--r+`
3×	`sub-neg` `add-log-exp`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `diff-log` `add-cbrt-cube` `flip--`

Counts

1 → 16

Calls

1 calls:

5.0ms

(- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0)))

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0)))

simplify1.3min

Counts

19 → 19

Iterations

Useful iterations: 4 (46.0ms)

Iter	Nodes	Cost
0	13	17
1	29	16
2	67	16
3	176	16
4	509	16
5	1855	16
done	5000	16
0	12	16
1	24	16
2	58	16
3	137	16
4	283	16
5	514	16
6	1295	16
7	4330	16
done	5000	16
0	12	16
1	27	16
2	73	16
3	195	16
4	505	16
5	1686	16
done	5000	16
0	13	33
1	25	33
2	59	33
3	138	33
4	284	33
5	514	33
6	1294	33
7	4369	33
done	5000	33
0	12	16
1	24	16
2	58	16
3	137	16
4	283	16
5	514	16
6	1295	16
7	4330	16
done	5000	16
0	13	47
1	26	47
2	74	17
3	274	17
4	1421	17
done	5000	17
0	12	16
1	24	16
2	58	16
3	137	16
4	283	16
5	514	16
6	1295	16
7	4330	16
done	5000	16
0	12	16
1	24	16
2	58	16
3	137	16
4	283	16
5	514	16
6	1295	16
7	4330	16
done	5000	16
0	14	19
1	44	19
2	166	19
3	753	19
4	3538	19
done	5000	19
0	15	47
1	50	37
2	178	35
3	655	35
4	2330	35
done	5000	35
0	6	10
1	15	10
2	47	10
3	109	10
4	159	9
5	201	9
6	328	9
7	542	9
8	1479	9
done	5000	9
0	13	31
1	42	31
2	137	29
3	492	27
4	1770	25
done	5001	25
0	11	15
1	22	15
2	45	15
3	91	15
4	176	15
5	384	15
6	1115	15
7	4064	15
done	5000	15
0	9	13
1	20	13
2	43	11
3	88	9
4	171	9
5	395	9
6	1243	9
7	4463	9
done	5000	9
0	9	13
1	20	13
2	43	11
3	88	9
4	171	9
5	395	9
6	1243	9
7	4463	9
done	5000	9
0	9	13
1	20	13
2	43	11
3	88	9
4	171	9
5	395	9
6	1243	9
7	4463	9
done	5000	9
0	9	13
1	20	13
2	43	11
3	88	9
4	171	9
5	395	9
6	1243	9
7	4463	9
done	5000	9
0	6	10
1	15	10
2	47	10
3	109	10
4	159	9
5	201	9
6	328	9
7	542	9
8	1479	9
done	5000	9
0	13	15
1	30	15
2	78	15
3	143	15
4	191	15
5	261	15
6	493	15
7	1059	15
8	2372	15
done	5000	15
0	24	28
1	58	26
2	125	24
3	287	23
4	732	22
5	1717	22
done	5001	22
0	25	28
1	59	27
2	124	25
3	306	23
4	779	23
5	1811	23
done	5000	23

prune37.0ms

Filtered

15 candidates to 19 candidates (-26.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	1	20

Merged error: 52.0b

Counts

20 → 1

localize12.0ms

Local error

Found 1 expressions with local error:

23.0b

(- (* 9.0 (pow x 4.0)) (pow y 4))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-log-exp`
1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `flip3--` `*-un-lft-identity` `diff-log` `add-cbrt-cube` `flip--`

Counts

1 → 12

Calls

1 calls:

6.0ms

(- (* 9.0 (pow x 4.0)) (pow y 4))

series88.0ms

Counts

1 → 3

Calls

1 calls:

88.0ms

(- (* 9.0 (pow x 4.0)) (pow y 4))

simplify56.2s

Counts

15 → 15

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	11
1	23	10
2	48	10
3	122	10
4	305	10
5	927	10
6	4390	10
done	5000	10
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	10	10
1	23	10
2	51	10
3	132	10
4	299	10
5	914	10
6	4325	10
done	5001	10
0	11	21
1	21	21
2	41	21
3	99	21
4	175	21
5	359	21
6	1087	21
7	3933	21
done	5000	21
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	11	29
1	22	29
2	56	11
3	204	11
4	900	11
done	5001	11
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	12	13
1	37	13
2	121	13
3	429	13
4	1535	13
done	5001	13
0	13	29
1	40	25
2	110	23
3	347	19
4	1012	19
5	3403	19
done	5000	19
0	4	4
1	8	4
2	18	4
3	52	4
4	68	4
5	80	4
6	107	4
7	175	4
8	363	4
9	1028	4
10	3826	4
done	5000	4
0	11	19
1	34	15
2	85	13
3	239	13
4	694	13
5	2362	13
done	5000	13
0	9	9
1	18	9
2	34	9
3	78	9
4	151	9
5	336	9
6	1041	9
7	3841	9
done	5000	9
0	4	4
1	8	4
2	18	4
3	52	4
4	68	4
5	80	4
6	107	4
7	175	4
8	363	4
9	1028	4
10	3826	4
done	5000	4
0	1	1
done	1	1
0	19	22
1	46	20
2	85	18
3	187	17
4	429	16
5	1086	16
6	2827	16
done	5000	16
0	20	22
1	47	21
2	84	19
3	203	17
4	472	17
5	1164	17
6	2917	17
done	5000	17

prune43.0ms

Filtered

13 candidates to 15 candidates (-15.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	15	1	16

Merged error: 52.0b

Counts

16 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

1.0b	(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4)) 3))
23.0b	(- (* 9.0 (pow x 4.0)) (pow y 4))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`pow1` `add-exp-log` `cube-div` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

2 → 35

Calls

2 calls:

8.0ms	(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4)) 3))
10.0ms	(- (* 9.0 (pow x 4.0)) (pow y 4))

series182.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4)) 3))
92.0ms	(- (* 9.0 (pow x 4.0)) (pow y 4))

simplify2.3min

Counts

41 → 41

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	11	11
1	23	10
2	48	10
3	122	10
4	305	10
5	927	10
6	4390	10
done	5000	10
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	10	10
1	23	10
2	51	10
3	132	10
4	299	10
5	914	10
6	4325	10
done	5001	10
0	11	21
1	21	21
2	41	21
3	99	21
4	175	21
5	359	21
6	1087	21
7	3933	21
done	5000	21
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	11	29
1	22	29
2	56	11
3	204	11
4	900	11
done	5001	11
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	12	13
1	37	13
2	121	13
3	429	13
4	1535	13
done	5001	13
0	13	29
1	40	25
2	110	23
3	347	19
4	1012	19
5	3403	19
done	5000	19
0	4	4
1	8	4
2	18	4
3	52	4
4	68	4
5	80	4
6	107	4
7	175	4
8	363	4
9	1028	4
10	3826	4
done	5000	4
0	11	19
1	34	15
2	85	13
3	239	13
4	694	13
5	2362	13
done	5000	13
0	9	9
1	18	9
2	34	9
3	78	9
4	151	9
5	336	9
6	1041	9
7	3841	9
done	5000	9
0	4	4
1	8	4
2	18	4
3	52	4
4	68	4
5	80	4
6	107	4
7	175	4
8	363	4
9	1028	4
10	3826	4
done	5000	4
0	13	13
1	30	10
2	68	10
3	222	10
4	934	10
done	5000	10
0	13	13
1	30	10
2	73	10
3	242	10
4	996	10
done	5001	10
0	14	24
1	33	21
2	74	13
3	177	13
4	460	13
5	1865	12
done	5000	12
0	13	13
1	30	10
2	56	10
3	124	10
4	225	10
5	459	10
6	1382	10
done	5000	10
0	13	13
1	30	10
2	56	10
3	133	10
4	278	10
5	732	10
6	2459	10
done	5001	10
0	13	13
1	30	10
2	56	10
3	133	10
4	278	10
5	732	10
6	2459	10
done	5001	10
0	4	4
1	14	1
2	18	1
done	18	1
0	12	12
1	29	9
2	67	9
3	221	9
4	934	9
done	5000	9
0	11	20
1	21	20
2	47	20
3	146	20
4	464	20
5	1911	20
done	5000	20
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	14	26
1	30	20
2	68	20
3	222	20
4	933	20
done	5000	20
0	13	13
1	30	10
2	68	10
3	222	10
4	934	10
done	5000	10
0	14	24
1	33	21
2	74	13
3	177	13
4	460	13
5	1865	12
done	5000	12
0	13	13
1	30	10
2	56	10
3	124	10
4	225	10
5	459	10
6	1382	10
done	5000	10
0	13	13
1	30	10
2	56	10
3	133	10
4	278	10
5	732	10
6	2459	10
done	5001	10
0	13	13
1	30	10
2	56	10
3	133	10
4	278	10
5	732	10
6	2459	10
done	5001	10
0	4	4
1	14	1
2	18	1
done	18	1
0	12	12
1	29	9
2	67	9
3	221	9
4	934	9
done	5000	9
0	10	10
1	20	10
2	40	10
3	98	10
4	175	10
5	357	10
6	1072	10
7	3906	10
done	5001	10
0	11	20
1	21	20
2	47	20
3	146	20
4	464	20
5	1911	20
done	5000	20
0	13	13
1	30	13
2	69	13
3	223	13
4	930	13
done	5000	13
0	13	13
1	30	13
2	69	13
3	223	13
4	930	13
done	5000	13
0	2	2
1	4	1
done	4	1
0	12	12
1	29	9
2	67	9
3	221	9
4	934	9
done	5000	9
0	14	14
1	27	12
2	53	12
3	122	12
4	228	12
5	468	12
6	1386	12
done	5000	12
0	14	14
1	27	12
2	53	12
3	122	12
4	228	12
5	468	12
6	1386	12
done	5000	12
0	14	16
1	44	13
2	143	13
3	643	13
4	4958	13
done	5000	13
0	16	32
1	50	25
2	154	23
3	714	19
done	5000	19
0	14	22
1	44	15
2	127	13
3	526	13
4	3768	13
done	5000	13
0	12	12
1	28	9
2	66	9
3	194	9
4	765	9
5	4143	9
done	5001	9
0	14	27
1	31	21
2	69	21
3	223	21
4	932	21
done	5000	21
0	13	13
1	30	10
2	68	10
3	222	10
4	934	10
done	5000	10
0	14	38
1	29	11
2	67	11
3	221	11
4	938	11
done	5000	11
0	13	13
1	30	10
2	68	10
3	222	10
4	934	10
done	5000	10
0	13	13
1	30	10
2	68	10
3	222	10
4	934	10
done	5000	10
0	1	1
done	1	1
0	19	22
1	46	20
2	85	18
3	187	17
4	429	16
5	1086	16
6	2827	16
done	5000	16
0	20	22
1	47	21
2	84	19
3	203	17
4	472	17
5	1164	17
6	2917	17
done	5000	17
0	1	1
done	1	1
0	19	22
1	46	20
2	85	18
3	187	17
4	429	16
5	1086	16
6	2827	16
done	5000	16
0	20	22
1	47	21
2	84	19
3	203	17
4	472	17
5	1164	17
6	2917	17
done	5000	17

prune106.0ms

Filtered

32 candidates to 41 candidates (-28.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	1	42

Merged error: 52.0b

Counts

42 → 1

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	19
1	21	19
2	24	19
3	28	19
done	28	19

end0.0ms

sample755.0ms

Algorithm

intervals

Results

333.0ms	8000×	body	80	valid
169.0ms	8000×	pre	80	true

Details

sample28.0ms

simplify5.4s

prune3.0ms

localize9.0ms

rewrite6.0ms

series52.0ms

simplify1.3min

prune37.0ms

localize12.0ms

rewrite6.0ms

series88.0ms

simplify56.2s

prune43.0ms

localize16.0ms

rewrite19.0ms

series182.0ms

simplify2.3min

prune106.0ms

simplify4.0ms

end0.0ms

sample755.0ms

Profiling