Details

sample97.0ms

Algorithm

intervals

Results

56.0ms	69×	body	2560	valid
13.0ms	37×	body	1280	valid
7.0ms	39×	body	640	valid
3.0ms	72×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	16×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	29	8
done	29	8

prune4.0ms

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: 34.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
19.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series20.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
17.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify33.8s

Counts

48 → 48

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	11
1	16	10
2	27	10
3	34	10
4	40	10
5	49	10
6	62	10
7	78	10
8	81	10
done	81	10
0	8	10
1	14	10
2	22	10
3	32	10
4	38	10
5	46	10
6	58	10
7	72	10
8	87	10
done	87	10
0	7	9
1	17	9
2	31	9
3	44	9
4	59	9
5	68	9
6	77	9
7	90	9
8	106	9
9	109	9
done	109	9
0	7	9
1	14	9
2	25	9
3	32	9
4	38	9
5	44	9
6	48	9
7	64	9
8	68	9
9	77	9
10	90	9
11	115	9
12	141	9
13	157	9
14	168	9
15	184	9
16	191	9
done	191	9
0	10	26
1	27	26
2	112	14
3	428	10
4	1327	10
done	5000	10
0	10	26
1	28	26
2	113	12
3	445	10
4	1415	10
done	5000	10
0	8	19
1	15	19
2	23	19
3	28	19
4	31	19
done	31	19
0	7	9
1	14	9
2	22	9
3	27	9
4	30	9
done	30	9
0	8	26
1	22	26
2	79	10
3	348	10
4	1388	10
5	4591	10
done	5000	10
0	7	9
1	14	9
2	22	9
3	27	9
4	30	9
done	30	9
0	7	9
1	14	9
2	22	9
3	27	9
4	30	9
done	30	9
0	5	5
1	7	5
2	11	5
3	13	5
4	14	4
done	14	4
0	3	4
1	6	4
done	6	4
0	4	5
1	6	5
done	6	5
0	4	6
1	6	6
done	6	6
0	7	13
1	11	13
2	14	13
3	15	13
done	15	13
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	3	3
1	5	3
done	5	3
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6
0	7	8
1	8	8
done	8	8
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	3	3
1	5	3
done	5	3
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6
0	4	5
1	8	5
done	8	5
0	6	8
1	10	8
2	16	8
3	19	8
4	21	8
done	21	8
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6
0	7	9
1	11	9
2	14	9
3	15	9
done	15	9
0	7	9
1	11	9
2	14	9
3	15	9
done	15	9
0	6	8
1	10	8
2	16	8
3	19	8
4	21	8
done	21	8
0	8	10
1	12	10
2	18	10
3	21	10
4	23	10
done	23	10
0	6	8
1	10	8
2	16	8
3	19	8
4	21	8
done	21	8
0	10	18
1	26	15
2	79	15
3	150	15
4	194	15
5	199	15
6	200	15
done	200	15
0	6	8
1	16	8
2	31	8
3	33	8
done	33	8
0	6	6
1	8	5
2	10	5
3	13	5
4	16	5
5	22	5
6	26	5
7	42	5
8	46	5
9	51	5
10	58	5
11	76	5
12	97	5
13	115	5
14	118	5
done	118	5
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	10	5
2	13	5
3	16	5
4	22	5
5	26	5
6	42	5
7	46	5
8	51	5
9	58	5
10	77	5
11	98	5
12	111	5
13	114	5
done	114	5
0	6	11
1	8	11
2	9	11
done	9	11
0	5	5
1	7	5
2	8	5
done	8	5
0	6	14
1	9	14
2	24	6
3	67	6
4	176	6
5	500	6
6	1723	6
7	4988	6
done	5000	6
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	500	8
6	2253	8
done	5001	8
0	8	14
1	15	11
2	23	11
3	26	11
4	27	11
done	27	11
0	3	3
done	3	3
0	6	9
1	11	9
2	18	9
3	33	9
4	58	9
5	99	9
6	161	9
7	329	9
8	1606	9
done	5000	9
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	6	6
1	8	6
2	9	6
done	9	6
0	4	4
1	6	4
2	7	4
done	7	4
0	3	3
done	3	3
0	12	13
1	27	13
2	74	13
3	119	13
4	164	13
5	210	13
6	331	13
7	780	13
8	2534	13
done	5000	13
0	7	8
1	17	8
2	40	8
3	50	8
4	59	8
5	70	8
6	92	8
7	156	8
8	366	8
9	1279	8
done	5000	8
0	7	8
1	17	8
2	40	8
3	50	8
4	59	8
5	70	8
6	92	8
7	156	8
8	366	8
9	1279	8
done	5000	8
0	15	17
1	35	17
2	92	17
3	193	17
4	496	17
5	1268	17
6	3919	17
done	5001	17
0	4	4
1	6	4
2	7	4
done	7	4
0	4	4
1	6	4
2	7	4
done	7	4

prune100.0ms

Filtered

38 candidates to 48 candidates (-26.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	6	49

Merged error: 0.0b

Counts

49 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.1b	(* 1/24 (pow x 2))
12.8b	(- (+ 1/2 (* 1/720 (pow x 4))) (* 1/24 (pow x 2)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

6.0ms	(* 1/720 (pow x 4))
11.0ms	(* 1/24 (pow x 2))
6.0ms	(- (+ 1/2 (* 1/720 (pow x 4))) (* 1/24 (pow x 2)))

series14.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* 1/720 (pow x 4))
3.0ms	(* 1/24 (pow x 2))
6.0ms	(- (+ 1/2 (* 1/720 (pow x 4))) (* 1/24 (pow x 2)))

simplify4.2min

Counts

75 → 75

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	15	16
1	34	15
2	86	14
3	187	14
4	507	14
5	2131	14
done	5001	14
0	14	15
1	32	14
2	83	14
3	175	14
4	404	14
5	1360	14
done	5000	14
0	13	14
1	28	14
2	75	14
3	120	14
4	164	14
5	210	14
6	329	14
7	776	14
8	2545	14
done	5000	14
0	13	14
1	31	14
2	90	14
3	174	14
4	333	14
5	999	14
done	5000	14
0	14	29
1	29	29
2	76	29
3	121	29
4	169	29
5	215	29
6	334	29
7	780	29
8	2539	29
done	5000	29
0	13	14
1	28	14
2	75	14
3	120	14
4	164	14
5	210	14
6	329	14
7	776	14
8	2545	14
done	5000	14
0	14	41
1	30	41
2	103	15
3	347	15
4	2142	15
done	5001	15
0	13	14
1	28	14
2	75	14
3	120	14
4	164	14
5	210	14
6	329	14
7	776	14
8	2545	14
done	5000	14
0	13	14
1	28	14
2	75	14
3	120	14
4	164	14
5	210	14
6	329	14
7	776	14
8	2545	14
done	5000	14
0	15	17
1	44	17
2	149	17
3	505	15
4	1977	15
done	5000	15
0	16	41
1	50	35
2	166	35
3	511	27
4	1574	27
5	3844	27
done	5000	27
0	6	6
1	17	5
2	45	5
3	63	5
4	69	5
5	79	5
6	101	5
7	165	5
8	376	5
9	1309	5
done	5001	5
0	14	27
1	44	21
2	149	21
3	453	21
4	1437	15
5	4003	15
done	5001	15
0	12	13
1	26	13
2	65	13
3	92	13
4	118	13
5	150	13
6	220	13
7	401	13
8	1044	13
9	3768	13
done	5001	13
0	10	11
1	22	11
2	64	11
3	107	11
4	144	11
5	177	11
6	245	11
7	443	11
8	1100	11
9	3835	11
done	5000	11
0	6	6
1	17	5
2	45	5
3	63	5
4	69	5
5	79	5
6	101	5
7	165	5
8	376	5
9	1309	5
done	5001	5
0	7	7
1	9	7
done	9	7
0	7	7
1	9	7
done	9	7
0	7	7
1	15	7
2	25	7
3	34	7
4	40	7
5	50	7
6	72	7
7	133	7
8	345	7
9	1259	7
done	5000	7
0	6	6
1	15	6
2	35	6
3	50	6
4	58	6
5	68	6
6	90	6
7	153	6
8	367	6
9	1307	6
done	5000	6
0	6	6
1	14	6
2	35	6
3	56	6
4	101	6
5	196	6
6	438	6
7	1258	6
8	4496	6
done	5000	6
0	9	17
1	26	9
2	80	7
3	170	7
4	314	5
5	590	5
6	1249	5
7	3580	5
done	5000	5
0	7	13
1	13	13
2	29	13
3	34	13
4	40	13
5	50	13
6	74	13
7	136	13
8	358	13
9	1301	13
done	5001	13
0	6	6
1	12	6
2	28	6
3	35	6
4	41	6
5	51	6
6	73	6
7	134	6
8	346	6
9	1277	6
done	5001	6
0	7	17
1	24	15
2	94	7
3	236	7
4	417	7
5	548	5
6	1185	5
7	3183	5
done	5000	5
0	6	6
1	12	6
2	28	6
3	35	6
4	41	6
5	51	6
6	73	6
7	134	6
8	346	6
9	1277	6
done	5001	6
0	6	6
1	12	6
2	28	6
3	35	6
4	41	6
5	51	6
6	73	6
7	134	6
8	346	6
9	1277	6
done	5001	6
0	7	7
1	13	7
2	29	4
3	44	4
4	79	4
5	199	4
6	651	4
7	2611	4
done	5000	4
0	7	7
1	13	7
2	29	4
3	44	4
4	79	4
5	199	4
6	651	4
7	2611	4
done	5000	4
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	7	7
1	13	7
2	23	5
3	28	5
4	34	5
5	44	5
6	68	5
7	134	5
8	346	5
9	1274	5
done	5000	5
0	7	7
1	13	7
2	23	5
3	28	5
4	34	5
5	44	5
6	68	5
7	134	5
8	346	5
9	1274	5
done	5000	5
0	7	8
1	13	6
2	26	4
3	40	4
4	76	4
5	200	4
6	658	4
7	2471	4
done	5001	4
0	7	8
1	13	6
2	26	4
3	40	4
4	76	4
5	200	4
6	658	4
7	2471	4
done	5001	4
0	7	9
1	13	9
2	33	9
3	74	9
4	172	6
5	424	6
6	1335	6
done	5001	6
0	6	6
1	12	6
2	28	3
3	45	3
4	83	3
5	205	3
6	642	3
7	2582	3
done	5000	3
0	5	5
1	12	1
2	16	1
done	16	1
0	3	3
1	4	3
done	4	3
0	7	11
1	15	11
2	25	11
3	30	11
4	36	11
5	46	11
6	70	11
7	130	11
8	339	11
9	1266	11
done	5000	11
0	6	6
1	12	6
2	22	4
3	27	4
4	33	4
5	43	4
6	65	4
7	124	4
8	349	4
9	1270	4
done	5000	4
0	3	3
1	6	1
done	6	1
0	6	7
1	12	5
2	25	3
3	41	3
4	78	3
5	194	3
6	648	3
7	2425	3
done	5000	3
0	6	6
1	12	6
2	28	6
3	35	6
4	41	6
5	51	6
6	73	6
7	134	6
8	346	6
9	1277	6
done	5001	6
0	6	6
1	12	6
2	28	6
3	35	6
4	41	6
5	51	6
6	73	6
7	134	6
8	346	6
9	1277	6
done	5001	6
0	5	5
1	11	5
2	27	5
3	32	5
4	38	5
5	48	5
6	70	5
7	129	5
8	346	5
9	1272	5
done	5000	5
0	7	7
1	9	7
done	9	7
0	7	7
1	9	7
done	9	7
0	7	7
1	14	7
2	24	7
3	51	7
4	79	7
5	109	7
6	132	7
7	193	7
8	371	7
9	981	7
10	3406	7
done	5000	7
0	6	6
1	14	6
2	30	6
3	79	6
4	124	6
5	158	6
6	189	6
7	282	6
8	559	6
9	1481	6
done	5001	6
0	6	6
1	13	6
2	29	6
3	81	6
4	152	6
5	318	6
6	777	6
7	2529	6
done	5001	6
0	9	17
1	25	9
2	62	7
3	210	7
4	640	7
5	1416	7
6	3385	5
done	5001	5
0	7	13
1	12	13
2	23	13
3	59	13
4	78	13
5	90	13
6	118	13
7	186	13
8	370	13
9	1009	13
10	3761	13
done	5000	13
0	6	6
1	11	6
2	22	6
3	58	6
4	76	6
5	88	6
6	116	6
7	186	6
8	372	6
9	1015	6
10	3762	6
done	5001	6
0	7	17
1	23	15
2	74	7
3	289	7
4	919	7
5	1658	7
6	3651	5
done	5000	5
0	6	6
1	11	6
2	22	6
3	58	6
4	76	6
5	88	6
6	116	6
7	186	6
8	372	6
9	1015	6
10	3762	6
done	5001	6
0	6	6
1	11	6
2	22	6
3	58	6
4	76	6
5	88	6
6	116	6
7	186	6
8	372	6
9	1015	6
10	3762	6
done	5001	6
0	7	7
1	12	7
2	23	7
3	59	6
4	99	6
5	217	6
6	663	6
7	2548	6
done	5000	6
0	7	7
1	12	7
2	23	7
3	59	6
4	99	6
5	217	6
6	663	6
7	2548	6
done	5000	6
0	7	7
1	12	7
2	20	7
3	40	7
4	51	7
5	63	7
6	83	7
7	125	7
8	235	7
9	611	7
10	2249	7
done	5001	7
0	7	7
1	12	7
2	20	7
3	40	7
4	51	7
5	63	7
6	83	7
7	125	7
8	235	7
9	611	7
10	2249	7
done	5001	7
0	8	8
1	13	6
2	25	6
3	30	6
4	36	6
5	46	6
6	70	6
7	129	6
8	337	6
9	1271	6
done	5000	6
0	8	8
1	13	6
2	25	6
3	30	6
4	36	6
5	46	6
6	70	6
7	129	6
8	337	6
9	1271	6
done	5000	6
0	7	9
1	12	9
2	23	9
3	63	9
4	165	9
5	535	9
6	1815	6
done	5000	6
0	6	6
1	11	6
2	22	6
3	58	5
4	101	5
5	210	5
6	653	5
7	2629	5
done	5000	5
0	5	5
1	12	1
done	12	1
0	7	11
1	14	11
2	23	11
3	43	11
4	52	11
5	64	11
6	84	11
7	126	11
8	239	11
9	616	11
10	2259	11
done	5001	11
0	6	6
1	11	6
2	19	6
3	39	6
4	48	6
5	60	6
6	80	6
7	122	6
8	233	6
9	612	6
10	2256	6
done	5000	6
0	3	3
1	6	1
done	6	1
0	7	7
1	12	5
2	24	5
3	29	5
4	35	5
5	45	5
6	67	5
7	129	5
8	345	5
9	1261	5
done	5000	5
0	6	6
1	11	6
2	22	6
3	58	6
4	79	6
5	91	6
6	119	6
7	187	6
8	375	6
9	1018	6
10	3752	6
done	5000	6
0	6	6
1	11	6
2	22	6
3	58	6
4	79	6
5	91	6
6	119	6
7	187	6
8	375	6
9	1018	6
10	3752	6
done	5000	6
0	5	5
1	10	5
2	21	5
3	57	5
4	76	5
5	88	5
6	116	5
7	182	5
8	361	5
9	1011	5
10	3772	5
done	5000	5
0	12	13
1	27	13
2	74	13
3	119	13
4	164	13
5	210	13
6	331	13
7	780	13
8	2534	13
done	5000	13
0	12	13
1	27	13
2	74	13
3	119	13
4	166	13
5	244	13
6	486	13
7	1109	13
8	3018	13
done	5001	13
0	12	13
1	27	13
2	74	13
3	119	13
4	166	13
5	244	13
6	486	13
7	1109	13
8	3018	13
done	5001	13
0	5	5
1	11	5
2	27	5
3	32	5
4	38	5
5	48	5
6	70	5
7	129	5
8	346	5
9	1272	5
done	5000	5
0	5	5
1	11	5
2	27	5
3	32	5
4	38	5
5	48	5
6	70	5
7	129	5
8	346	5
9	1272	5
done	5000	5
0	5	5
1	11	5
2	27	5
3	32	5
4	38	5
5	48	5
6	70	5
7	129	5
8	346	5
9	1272	5
done	5000	5
0	5	5
1	10	5
2	21	5
3	57	5
4	76	5
5	88	5
6	116	5
7	182	5
8	361	5
9	1011	5
10	3772	5
done	5000	5
0	5	5
1	10	5
2	21	5
3	57	5
4	76	5
5	88	5
6	116	5
7	182	5
8	361	5
9	1011	5
10	3772	5
done	5000	5
0	5	5
1	10	5
2	21	5
3	57	5
4	76	5
5	88	5
6	116	5
7	182	5
8	361	5
9	1011	5
10	3772	5
done	5000	5

prune140.0ms

Filtered

53 candidates to 75 candidates (-41.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	75	6	81

Merged error: 0.0b

Counts

81 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
2.6b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

7.0ms	(/ (- 1.0 (cos x)) x)
16.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
4.0ms	(- 1.0 (cos x))

series21.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (- 1.0 (cos x)) x)
11.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms	(- 1.0 (cos x))

simplify1.2min

Counts

123 → 123

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	8	5
2	10	5
3	13	5
4	16	5
5	22	5
6	26	5
7	42	5
8	46	5
9	51	5
10	58	5
11	76	5
12	97	5
13	115	5
14	118	5
done	118	5
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	10	5
2	13	5
3	16	5
4	22	5
5	26	5
6	42	5
7	46	5
8	51	5
9	58	5
10	77	5
11	98	5
12	111	5
13	114	5
done	114	5
0	6	11
1	8	11
2	9	11
done	9	11
0	5	5
1	7	5
2	8	5
done	8	5
0	6	14
1	9	14
2	24	6
3	67	6
4	176	6
5	500	6
6	1723	6
7	4988	6
done	5000	6
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	500	8
6	2253	8
done	5001	8
0	8	14
1	15	11
2	23	11
3	26	11
4	27	11
done	27	11
0	3	3
done	3	3
0	6	9
1	11	9
2	18	9
3	33	9
4	58	9
5	99	9
6	161	9
7	329	9
8	1606	9
done	5000	9
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	6	6
1	8	6
2	9	6
done	9	6
0	4	4
1	6	4
2	7	4
done	7	4
0	3	3
done	3	3
0	8	10
1	20	10
2	37	8
3	124	8
4	262	8
5	326	8
6	407	8
7	430	8
8	434	8
done	434	8
0	9	12
1	15	12
2	20	11
3	31	11
4	40	10
5	49	10
6	63	10
7	73	10
8	76	10
done	76	10
0	9	11
1	17	11
2	26	10
3	38	10
4	50	10
5	58	10
6	68	10
7	76	10
8	86	10
9	89	10
done	89	10
0	10	13
1	20	12
2	45	11
3	107	11
4	216	10
5	281	10
6	299	10
done	299	10
0	10	12
1	22	11
2	45	10
3	89	10
4	209	10
5	296	10
6	315	10
done	315	10
0	11	14
1	23	13
2	46	11
3	107	11
4	243	10
5	333	10
6	347	10
done	347	10
0	11	13
1	25	12
2	45	11
3	91	10
4	209	10
5	284	10
6	300	10
7	315	10
done	315	10
0	11	13
1	22	12
2	36	11
3	84	11
4	157	10
5	209	10
6	229	10
done	229	10
0	10	12
1	24	11
2	38	10
3	72	10
4	148	10
5	212	10
6	266	10
done	266	10
0	9	11
1	24	11
2	49	9
3	154	9
4	346	9
5	501	9
6	648	9
7	726	9
8	730	9
done	730	9
0	9	11
1	23	11
2	46	9
3	169	9
4	412	9
5	761	9
6	1877	9
done	5001	9
0	14	32
1	39	28
2	153	14
3	974	12
4	4330	10
done	5000	10
0	14	32
1	41	28
2	127	12
3	613	12
4	3126	12
done	5000	12
0	14	32
1	39	32
2	157	16
3	733	12
4	3246	12
done	5001	12
0	12	32
1	38	32
2	126	14
3	520	14
4	2492	10
done	5001	10
0	10	23
1	22	23
2	39	19
3	126	19
4	259	19
5	323	19
6	404	19
7	427	19
8	432	19
done	432	19
0	9	11
1	21	11
2	38	9
3	125	9
4	264	9
5	327	9
6	408	9
7	431	9
8	435	9
done	435	9
0	10	32
1	32	32
2	122	10
3	574	10
4	2419	10
done	5001	10
0	9	11
1	21	11
2	38	9
3	125	9
4	264	9
5	327	9
6	408	9
7	431	9
8	435	9
done	435	9
0	9	11
1	21	11
2	38	9
3	125	9
4	264	9
5	327	9
6	408	9
7	431	9
8	435	9
done	435	9
0	6	6
1	11	4
2	21	4
3	32	4
4	41	4
5	47	4
done	47	4
0	2	3
done	2	3
0	10	12
1	18	12
2	21	12
3	23	12
done	23	12
0	10	12
1	18	12
2	21	12
3	23	12
done	23	12
0	11	13
1	18	13
2	22	13
3	26	13
4	27	13
done	27	13
0	11	13
1	18	13
2	22	13
3	26	13
4	27	13
done	27	13
0	11	13
1	21	12
2	27	12
3	31	10
4	45	10
done	45	10
0	11	13
1	21	12
2	27	12
3	31	10
4	45	10
done	45	10
0	11	14
1	20	13
2	29	13
3	41	11
4	91	7
5	95	7
done	95	7
0	11	14
1	20	13
2	29	13
3	41	11
4	91	7
5	95	7
done	95	7
0	10	12
1	20	12
2	26	10
3	41	10
4	48	10
done	48	10
0	10	12
1	20	12
2	26	10
3	41	10
4	48	10
done	48	10
0	10	13
1	19	13
2	28	11
3	69	11
4	122	7
5	123	7
done	123	7
0	10	13
1	19	13
2	28	11
3	69	11
4	122	7
5	123	7
done	123	7
0	10	19
1	22	19
2	33	17
3	63	17
4	80	17
done	80	17
0	9	11
1	19	11
2	25	9
3	40	9
4	45	9
done	45	9
0	12	21
1	27	21
2	69	19
3	215	19
4	511	19
5	824	19
6	846	19
done	846	19
0	11	18
1	22	18
2	41	16
3	118	16
4	235	16
5	301	16
6	312	16
done	312	16
0	10	17
1	21	15
2	48	13
3	173	13
4	256	13
5	262	13
done	262	13
0	11	15
1	22	15
2	42	13
3	115	13
4	242	13
5	389	13
6	399	13
done	399	13
0	10	12
1	19	12
2	29	10
3	68	10
4	119	10
5	163	10
6	173	10
done	173	10
0	9	11
1	18	9
2	32	7
3	76	7
4	103	7
5	107	7
done	107	7
0	7	11
1	16	11
2	34	9
3	79	9
4	127	9
done	127	9
0	6	8
1	13	8
2	22	6
3	41	6
4	50	6
done	50	6
0	5	7
1	12	3
2	16	3
3	23	3
done	23	3
0	12	16
1	22	16
2	49	14
3	133	14
4	314	14
5	528	14
6	633	14
7	737	14
8	743	14
done	743	14
0	11	13
1	19	13
2	36	11
3	87	11
4	169	11
5	237	11
6	275	11
7	301	11
done	301	11
0	10	12
1	18	10
2	47	8
3	109	8
4	147	8
5	154	8
6	166	8
7	200	8
8	232	8
9	244	8
done	244	8
0	7	11
1	16	11
2	34	9
3	79	9
4	127	9
done	127	9
0	6	8
1	13	8
2	22	6
3	41	6
4	50	6
done	50	6
0	5	7
1	12	3
2	16	3
3	23	3
done	23	3
0	4	5
1	9	3
done	9	3
0	7	8
1	14	8
2	30	6
3	69	6
4	105	6
5	135	6
6	141	6
7	142	6
done	142	6
0	9	11
1	19	11
2	31	11
3	48	11
4	71	11
5	90	11
6	97	11
7	98	11
done	98	11
0	9	11
1	19	11
2	31	11
3	48	11
4	71	11
5	90	11
6	97	11
7	98	11
done	98	11
0	10	12
1	22	11
2	40	11
3	88	9
4	227	9
5	380	9
6	514	9
7	625	9
8	649	9
done	649	9
0	10	12
1	22	11
2	40	11
3	88	9
4	227	9
5	380	9
6	514	9
7	625	9
8	649	9
done	649	9
0	9	11
1	21	10
2	38	10
3	81	8
4	215	8
5	289	8
6	387	8
7	415	8
8	422	8
done	422	8
0	10	12
1	22	11
2	40	11
3	88	9
4	227	9
5	380	9
6	514	9
7	625	9
8	649	9
done	649	9
0	10	12
1	22	11
2	40	11
3	88	9
4	227	9
5	380	9
6	514	9
7	625	9
8	649	9
done	649	9
0	9	11
1	21	10
2	38	10
3	81	8
4	215	8
5	289	8
6	387	8
7	415	8
8	422	8
done	422	8
0	9	11
1	21	11
2	39	9
3	112	9
4	254	9
5	397	9
6	535	9
7	639	9
8	661	9
done	661	9
0	9	11
1	21	11
2	39	9
3	112	9
4	254	9
5	397	9
6	535	9
7	639	9
8	661	9
done	661	9
0	8	10
1	20	10
2	37	8
3	124	8
4	262	8
5	326	8
6	407	8
7	430	8
8	434	8
done	434	8
0	8	10
1	20	10
2	37	8
3	124	8
4	262	8
5	326	8
6	407	8
7	430	8
8	434	8
done	434	8
0	8	10
1	20	10
2	37	8
3	124	8
4	262	8
5	326	8
6	407	8
7	430	8
8	434	8
done	434	8
0	7	8
1	14	8
2	30	6
3	69	6
4	105	6
5	135	6
6	141	6
7	142	6
done	142	6
0	7	8
1	17	6
2	36	6
3	61	6
4	98	6
5	126	6
6	142	6
7	143	6
done	143	6
0	7	8
1	11	8
2	13	8
done	13	8
0	6	7
1	14	7
2	19	7
3	22	7
done	22	7
0	6	7
1	11	7
2	17	7
3	21	7
4	24	7
5	30	7
6	34	7
7	50	7
8	54	7
9	61	7
10	70	7
11	90	7
12	111	7
13	129	7
14	136	7
15	142	7
16	146	7
done	146	7
0	9	20
1	20	20
2	68	10
3	203	8
4	562	8
5	2033	8
done	5001	8
0	7	15
1	12	15
2	15	15
3	17	15
done	17	15
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	7	20
1	19	20
2	50	8
3	176	8
4	571	8
5	1720	8
done	5000	8
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	5	5
1	7	5
2	11	5
3	13	5
4	14	4
done	14	4
0	2	2
done	2	2
0	3	3
done	3	3
0	3	4
done	3	4
0	9	17
1	17	17
2	27	17
3	33	17
done	33	17
0	7	8
1	9	8
2	10	8
done	10	8
0	8	14
1	12	14
2	15	14
3	16	14
done	16	14
0	7	8
1	9	8
2	10	8
done	10	8
0	8	13
1	14	11
2	21	11
3	26	11
done	26	11
0	6	7
1	8	7
2	9	7
done	9	7
0	8	11
1	12	11
2	13	11
done	13	11
0	7	8
1	9	8
2	10	8
done	10	8
0	7	8
1	9	8
2	10	8
done	10	8
0	7	8
1	9	8
2	10	8
done	10	8
0	7	7
1	11	5
2	14	5
done	14	5
0	6	7
1	8	7
2	9	7
done	9	7
0	5	7
1	9	7
done	9	7
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	4	4
1	6	4
done	6	4
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	2	3
1	4	1
done	4	1
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6
0	9	12
1	12	12
done	12	12
0	8	9
1	13	9
2	16	9
3	18	9
done	18	9
0	8	9
1	9	9
done	9	9
0	8	9
1	13	9
2	16	9
3	18	9
done	18	9
0	8	8
1	11	6
2	13	6
done	13	6
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	5	7
1	9	7
done	9	7
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	4	4
1	6	4
done	6	4
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	2	3
1	4	1
done	4	1
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6
0	3	3
1	5	3
done	5	3
0	5	6
1	7	6
2	8	6
done	8	6
0	7	10
1	14	10
2	22	10
3	27	10
4	30	10
done	30	10
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	6	6
1	13	4
2	18	4
3	19	4
done	19	4
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	5	6
1	7	6
2	8	6
done	8	6
0	7	8
1	9	8
2	10	8
done	10	8
0	5	6
1	7	6
2	8	6
done	8	6
0	9	16
1	23	13
2	52	13
3	78	13
4	87	13
5	89	13
done	89	13
0	5	6
1	13	6
2	14	6
done	14	6
0	15	17
1	35	17
2	92	17
3	193	17
4	496	17
5	1268	17
6	3919	17
done	5001	17
0	4	4
1	6	4
2	7	4
done	7	4
0	4	4
1	6	4
2	7	4
done	7	4
0	12	13
1	27	13
2	74	13
3	119	13
4	164	13
5	210	13
6	331	13
7	780	13
8	2534	13
done	5000	13
0	7	8
1	17	8
2	40	8
3	50	8
4	59	8
5	70	8
6	92	8
7	156	8
8	366	8
9	1279	8
done	5000	8
0	7	8
1	17	8
2	40	8
3	50	8
4	59	8
5	70	8
6	92	8
7	156	8
8	366	8
9	1279	8
done	5000	8
0	13	15
1	33	15
2	75	15
3	158	15
4	347	15
5	861	15
6	2839	15
done	5000	15
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6
0	7	8
1	16	7
2	30	7
3	54	7
4	86	6
5	113	6
6	169	6
7	196	6
8	240	6
9	343	6
10	423	6
11	439	6
done	439	6

prune150.0ms

Filtered

87 candidates to 123 candidates (-41.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Merged error: 0.0b

Counts

129 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
5.0ms	(- 1.0 (cos x))

series37.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

simplify1.2min

Counts

69 → 69

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	8	5
2	10	5
3	13	5
4	16	5
5	22	5
6	26	5
7	42	5
8	46	5
9	51	5
10	58	5
11	76	5
12	97	5
13	115	5
14	118	5
done	118	5
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	10	5
2	13	5
3	16	5
4	22	5
5	26	5
6	42	5
7	46	5
8	51	5
9	58	5
10	77	5
11	98	5
12	111	5
13	114	5
done	114	5
0	6	11
1	8	11
2	9	11
done	9	11
0	5	5
1	7	5
2	8	5
done	8	5
0	6	14
1	9	14
2	24	6
3	67	6
4	176	6
5	500	6
6	1723	6
7	4988	6
done	5000	6
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	500	8
6	2253	8
done	5001	8
0	8	14
1	15	11
2	23	11
3	26	11
4	27	11
done	27	11
0	3	3
done	3	3
0	6	9
1	11	9
2	18	9
3	33	9
4	58	9
5	99	9
6	161	9
7	329	9
8	1606	9
done	5000	9
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	6	6
1	8	6
2	9	6
done	9	6
0	4	4
1	6	4
2	7	4
done	7	4
0	3	3
done	3	3
0	6	6
1	8	5
2	10	5
3	13	5
4	16	5
5	22	5
6	26	5
7	42	5
8	46	5
9	51	5
10	58	5
11	76	5
12	97	5
13	115	5
14	118	5
done	118	5
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	10	5
2	13	5
3	16	5
4	22	5
5	26	5
6	42	5
7	46	5
8	51	5
9	58	5
10	77	5
11	98	5
12	111	5
13	114	5
done	114	5
0	6	11
1	8	11
2	9	11
done	9	11
0	5	5
1	7	5
2	8	5
done	8	5
0	6	14
1	9	14
2	24	6
3	67	6
4	176	6
5	500	6
6	1723	6
7	4988	6
done	5000	6
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	500	8
6	2253	8
done	5001	8
0	8	14
1	15	11
2	23	11
3	26	11
4	27	11
done	27	11
0	3	3
done	3	3
0	6	9
1	11	9
2	18	9
3	33	9
4	58	9
5	99	9
6	161	9
7	329	9
8	1606	9
done	5000	9
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	6	6
1	8	6
2	9	6
done	9	6
0	4	4
1	6	4
2	7	4
done	7	4
0	3	3
done	3	3
0	6	6
1	8	5
2	10	5
3	13	5
4	16	5
5	22	5
6	26	5
7	42	5
8	46	5
9	51	5
10	58	5
11	76	5
12	97	5
13	115	5
14	118	5
done	118	5
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	10	5
2	13	5
3	16	5
4	22	5
5	26	5
6	42	5
7	46	5
8	51	5
9	58	5
10	77	5
11	98	5
12	111	5
13	114	5
done	114	5
0	6	11
1	8	11
2	9	11
done	9	11
0	5	5
1	7	5
2	8	5
done	8	5
0	6	14
1	9	14
2	24	6
3	67	6
4	176	6
5	500	6
6	1723	6
7	4988	6
done	5000	6
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	500	8
6	2253	8
done	5001	8
0	8	14
1	15	11
2	23	11
3	26	11
4	27	11
done	27	11
0	3	3
done	3	3
0	6	9
1	11	9
2	18	9
3	33	9
4	58	9
5	99	9
6	161	9
7	329	9
8	1606	9
done	5000	9
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	6	6
1	8	6
2	9	6
done	9	6
0	4	4
1	6	4
2	7	4
done	7	4
0	3	3
done	3	3
0	6	6
1	8	6
2	9	6
done	9	6
0	6	6
1	8	6
2	9	6
done	9	6
0	7	12
1	9	12
2	10	12
done	10	12
0	6	6
1	8	6
2	9	6
done	9	6
0	6	6
1	8	6
2	9	6
done	9	6
0	6	6
1	8	6
2	9	6
done	9	6
0	2	2
1	4	1
done	4	1
0	5	5
1	7	5
2	8	5
done	8	5
0	7	7
1	8	7
done	8	7
0	7	7
1	9	7
2	10	7
done	10	7
0	2	2
1	4	1
done	4	1
0	5	5
1	7	5
2	8	5
done	8	5
0	8	9
1	23	9
2	45	9
3	79	9
4	169	9
5	502	9
6	2259	9
done	5000	9
0	9	15
1	16	12
2	24	12
3	27	12
4	28	12
done	28	12
0	7	10
1	12	10
2	19	10
3	34	10
4	59	10
5	100	10
6	156	10
7	324	10
8	1598	10
done	5000	10
0	5	5
1	6	5
done	6	5
0	7	13
1	9	13
2	10	13
done	10	13
0	6	6
1	8	6
2	9	6
done	9	6
0	7	17
1	10	17
2	13	7
3	18	4
4	24	4
5	34	4
6	55	4
7	117	4
8	328	4
9	1251	4
done	5000	4
0	6	6
1	8	6
2	9	6
done	9	6
0	6	6
1	8	6
2	9	6
done	9	6
0	15	17
1	35	17
2	92	17
3	193	17
4	496	17
5	1268	17
6	3919	17
done	5001	17
0	4	4
1	6	4
2	7	4
done	7	4
0	4	4
1	6	4
2	7	4
done	7	4
0	15	17
1	35	17
2	92	17
3	193	17
4	496	17
5	1268	17
6	3919	17
done	5001	17
0	4	4
1	6	4
2	7	4
done	7	4
0	4	4
1	6	4
2	7	4
done	7	4
0	15	17
1	35	17
2	92	17
3	193	17
4	496	17
5	1268	17
6	3919	17
done	5001	17
0	4	4
1	6	4
2	7	4
done	7	4
0	4	4
1	6	4
2	7	4
done	7	4
0	21	44
1	53	44
2	138	44
3	360	27
4	1248	20
done	5001	20
0	6	6
1	14	5
2	21	5
3	31	5
4	55	5
5	113	5
6	317	5
7	1230	5
done	5000	5
0	6	6
1	14	5
2	21	5
3	31	5
4	55	5
5	113	5
6	317	5
7	1230	5
done	5000	5

prune125.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

regimes63.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.7b

bsearch32.0ms

Steps

Iters	Range		Point
9	2.685778245287387e-07	280.39199233801065	0.031662641678737835
8	-1.1417122487016937	-0.00029558442529086166	-0.03390686091718305

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	41
1	34	32
done	34	32

end0.0ms

sample2.0s

Algorithm

intervals

Results

897.0ms	1613×	body	2560	valid
390.0ms	1270×	body	1280	valid
272.0ms	1475×	body	640	valid
119.0ms	911×	body	320	valid
102.0ms	2266×	body	80	valid
48.0ms	465×	body	160	valid

Details

sample97.0ms

simplify20.0ms

prune4.0ms

localize9.0ms

rewrite16.0ms

series20.0ms

simplify33.8s

prune100.0ms

localize10.0ms

rewrite25.0ms

series14.0ms

simplify4.2min

prune140.0ms

localize8.0ms

rewrite32.0ms

series21.0ms

simplify1.2min

prune150.0ms

localize11.0ms

rewrite19.0ms

series37.0ms

simplify1.2min

prune125.0ms

regimes63.0ms

bsearch32.0ms

simplify3.0ms

end0.0ms

sample2.0s

Profiling