Details

sample147.0ms

Algorithm

intervals

Results

70.0ms	127×	body	1280	valid
20.0ms	256×	pre	80	true
17.0ms	67×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	29×	body	80	valid
1.0ms	7×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	64	9
8	82	9
9	99	9
10	107	9
done	107	9

prune9.0ms

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: 14.8b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
4.3b	(tan (+ y z))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series118.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(+ x (- (tan (+ y z)) (tan a)))
38.0ms	(- (tan (+ y z)) (tan a))
29.0ms	(tan (+ y z))

simplify37.2s

Counts

51 → 51

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5
done	6	5
0	7	7
1	12	7
2	19	7
done	19	7
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
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	9	9
1	12	8
2	14	8
3	17	8
4	20	8
5	26	8
6	30	8
7	46	8
8	50	8
9	55	8
10	62	8
11	81	8
12	102	8
13	115	8
14	118	8
done	118	8
0	8	8
1	11	8
2	12	8
done	12	8
0	8	8
1	14	8
2	17	8
3	20	8
4	26	8
5	30	8
6	46	8
7	50	8
8	55	8
9	62	8
10	80	8
11	101	8
12	117	8
13	120	8
done	120	8
0	9	17
1	12	17
2	13	17
done	13	17
0	8	8
1	11	8
2	12	8
done	12	8
0	9	23
1	13	23
2	28	9
3	71	9
4	180	9
5	508	9
6	1712	9
7	4969	9
done	5000	9
0	8	8
1	11	8
2	12	8
done	12	8
0	8	8
1	11	8
2	12	8
done	12	8
0	14	19
1	24	19
2	52	19
3	103	19
4	270	19
5	637	19
6	959	19
7	1278	19
8	1573	19
9	1747	19
10	1751	19
done	1751	19
0	10	10
1	16	10
2	29	10
3	50	10
4	109	10
5	225	10
6	269	10
done	269	10
0	11	15
1	16	15
2	23	15
done	23	15
0	7	7
1	9	7
done	9	7
0	10	11
1	26	11
2	48	11
3	82	11
4	169	11
5	502	11
6	2263	11
done	5000	11
0	11	23
1	19	20
2	27	20
3	28	18
4	29	18
done	29	18
0	3	3
done	3	3
0	9	15
1	15	15
2	22	15
3	37	15
4	62	15
5	103	15
6	169	15
7	337	15
8	1640	15
done	5000	15
0	7	7
1	9	7
done	9	7
0	9	9
1	11	9
done	11	9
0	9	9
1	12	9
2	13	9
done	13	9
0	7	7
1	10	7
2	11	7
done	11	7
0	3	3
done	3	3
0	12	12
1	18	11
2	29	10
3	45	10
4	70	10
5	100	10
6	142	10
7	253	10
8	357	10
9	452	10
10	470	10
done	470	10
0	11	11
1	20	10
2	31	10
3	52	10
4	79	10
5	107	10
6	175	10
7	261	10
8	371	10
9	441	10
10	464	10
done	464	10
0	10	10
1	16	10
2	23	10
3	32	10
4	38	10
5	48	10
6	55	10
7	65	10
8	83	10
9	100	10
10	108	10
done	108	10
0	10	10
1	19	10
2	34	10
3	58	10
4	86	10
5	118	10
6	197	10
7	271	10
8	407	10
9	440	10
10	441	10
done	441	10
0	11	21
1	17	21
2	24	21
3	33	21
4	39	21
5	49	21
6	56	21
7	66	21
8	84	21
9	101	21
10	109	21
done	109	21
0	10	10
1	16	10
2	23	10
3	32	10
4	38	10
5	48	10
6	55	10
7	65	10
8	83	10
9	100	10
10	108	10
done	108	10
0	11	29
1	30	29
2	81	11
3	305	11
4	1571	11
done	5000	11
0	10	10
1	16	10
2	23	10
3	32	10
4	38	10
5	48	10
6	55	10
7	65	10
8	83	10
9	100	10
10	108	10
done	108	10
0	10	10
1	16	10
2	23	10
3	32	10
4	38	10
5	48	10
6	55	10
7	65	10
8	83	10
9	100	10
10	108	10
done	108	10
0	12	13
1	29	13
2	51	13
3	110	13
4	267	13
5	787	13
6	3044	13
done	5001	13
0	13	29
1	24	21
2	56	21
3	149	21
4	476	21
5	1506	21
6	4444	21
done	5000	21
0	11	19
1	19	19
2	39	19
3	113	19
4	389	19
5	1205	19
done	5001	19
0	9	9
1	16	9
2	24	9
3	37	9
4	41	9
5	49	9
6	64	9
7	90	9
8	99	9
done	99	9
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	64	9
8	82	9
9	99	9
10	107	9
done	107	9
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	64	9
8	82	9
9	99	9
10	107	9
done	107	9
0	6	6
1	8	6
done	8	6
0	6	6
1	8	6
done	8	6
0	6	6
1	8	6
done	8	6
0	8	9
1	21	9
2	45	9
3	76	9
4	127	9
5	272	9
6	805	9
7	3085	9
done	5000	9
0	6	9
1	7	9
done	7	9
0	6	9
1	7	9
done	7	9
0	5	5
1	10	5
2	17	5
3	23	5
4	29	5
5	38	5
6	51	5
7	64	5
8	73	5
9	82	5
10	97	5
11	102	5
12	106	5
13	107	5
done	107	5
0	11	15
1	14	15
2	17	15
done	17	15
0	11	15
1	14	15
2	17	15
done	17	15
0	5	5
1	9	5
2	15	5
done	15	5
0	13	17
1	19	17
2	28	17
3	34	17
4	40	17
5	51	17
6	66	17
7	86	17
8	102	17
9	110	17
10	127	17
11	131	17
done	131	17
0	13	17
1	19	17
2	28	17
3	34	17
4	40	17
5	51	17
6	66	17
7	86	17
8	102	17
9	110	17
10	127	17
11	131	17
done	131	17

prune104.0ms

Filtered

40 candidates to 51 candidates (-27.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.1b

Counts

52 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

6.0ms	(+ (tan y) (tan z))
14.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
14.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series345.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (tan y) (tan z))
150.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
142.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms	(* (tan y) (tan z))

simplify1.6min

Counts

79 → 79

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	6	6
1	10	6
2	11	6
done	11	6
0	6	6
1	9	6
2	15	6
3	23	6
4	46	6
5	102	6
6	243	6
7	706	6
8	2720	6
done	5000	6
0	9	17
1	16	17
2	41	9
3	80	9
4	138	7
5	265	7
6	663	7
7	2444	7
done	5000	7
0	7	13
1	8	13
done	8	13
0	6	6
1	7	6
done	7	6
0	7	17
1	18	17
2	47	7
3	89	7
4	105	7
5	151	7
6	291	7
7	753	7
8	2738	7
done	5000	7
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	7	7
1	8	7
done	8	7
0	7	10
1	10	10
2	12	10
done	12	10
0	6	6
1	7	6
done	7	6
0	4	4
1	7	2
2	10	2
done	10	2
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
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	14	18
1	22	17
2	31	17
3	34	17
4	36	17
5	40	17
6	44	17
7	60	17
8	64	17
9	71	17
10	82	17
11	109	17
12	142	17
13	191	17
14	283	17
15	436	17
16	446	17
done	446	17
0	13	17
1	21	17
2	29	17
done	29	17
0	13	17
1	24	17
2	34	17
3	36	17
4	40	17
5	44	17
6	60	17
7	64	17
8	71	17
9	82	17
10	109	17
11	142	17
12	191	17
13	283	17
14	436	17
15	448	17
done	448	17
0	14	35
1	22	35
2	30	35
done	30	35
0	13	17
1	21	17
2	29	17
done	29	17
0	14	50
1	23	50
2	45	18
3	96	18
4	264	18
5	850	18
6	2837	18
done	5000	18
0	13	17
1	21	17
2	29	17
done	29	17
0	13	17
1	21	17
2	29	17
done	29	17
0	14	19
1	24	19
2	52	19
3	103	19
4	270	19
5	637	19
6	959	19
7	1278	19
8	1573	19
9	1747	19
10	1751	19
done	1751	19
0	10	10
1	16	10
2	29	10
3	50	10
4	109	10
5	225	10
6	269	10
done	269	10
0	15	20
1	39	20
2	86	20
3	216	20
4	595	20
5	2185	20
done	5000	20
0	16	50
1	35	47
2	67	47
3	105	36
4	171	36
5	358	36
6	1168	36
7	3484	36
done	5000	36
0	3	3
done	3	3
0	14	33
1	29	33
2	57	33
3	97	33
4	185	33
5	429	33
6	1388	33
7	4280	33
done	5000	33
0	12	16
1	19	16
2	26	16
done	26	16
0	14	18
1	21	18
2	28	18
done	28	18
0	14	18
1	22	18
2	30	18
done	30	18
0	15	19
1	22	19
2	29	19
done	29	19
0	15	19
1	23	19
2	31	19
done	31	19
0	12	16
1	20	16
2	28	16
done	28	16
0	3	3
done	3	3
0	17	21
1	28	20
2	46	19
3	62	19
4	86	19
5	116	19
6	160	19
7	275	19
8	387	19
9	540	19
10	810	19
11	1448	19
12	1521	19
done	1521	19
0	16	20
1	30	19
2	48	19
3	68	19
4	93	19
5	121	19
6	194	19
7	280	19
8	394	19
9	476	19
10	569	19
11	800	19
12	1420	19
13	1481	19
done	1481	19
0	15	19
1	26	19
2	40	19
3	49	19
4	55	19
5	65	19
6	72	19
7	84	19
8	106	19
9	131	19
10	151	19
11	212	19
12	343	19
13	383	19
14	404	19
done	404	19
0	15	19
1	29	19
2	51	19
3	74	19
4	100	19
5	132	19
6	211	19
7	285	19
8	425	19
9	472	19
10	485	19
11	552	19
12	783	19
13	1376	19
14	1466	19
done	1466	19
0	16	39
1	27	39
2	41	39
3	50	39
4	56	39
5	66	39
6	73	39
7	85	39
8	107	39
9	132	39
10	152	39
11	213	39
12	342	39
13	382	39
14	403	39
done	403	39
0	15	19
1	26	19
2	40	19
3	49	19
4	55	19
5	65	19
6	72	19
7	84	19
8	106	19
9	131	19
10	151	19
11	212	19
12	343	19
13	383	19
14	404	19
done	404	19
0	16	56
1	40	56
2	98	20
3	330	20
4	1720	20
done	5000	20
0	15	19
1	26	19
2	40	19
3	49	19
4	55	19
5	65	19
6	72	19
7	84	19
8	106	19
9	131	19
10	151	19
11	212	19
12	343	19
13	383	19
14	404	19
done	404	19
0	15	19
1	26	19
2	40	19
3	49	19
4	55	19
5	65	19
6	72	19
7	84	19
8	106	19
9	131	19
10	151	19
11	212	19
12	343	19
13	383	19
14	404	19
done	404	19
0	17	22
1	39	22
2	68	22
3	135	22
4	351	22
5	1124	22
6	4150	22
done	5000	22
0	18	56
1	34	39
2	73	39
3	174	39
4	548	39
5	1702	39
6	4971	39
done	5000	39
0	16	37
1	29	37
2	56	37
3	134	37
4	440	37
5	1363	37
done	5000	37
0	14	18
1	26	18
2	41	18
3	56	18
4	62	18
5	72	18
6	93	18
7	169	18
8	286	18
9	532	18
10	569	18
11	570	18
done	570	18
0	14	18
1	25	18
2	39	18
3	48	18
4	54	18
5	64	18
6	71	18
7	83	18
8	105	18
9	130	18
10	150	18
11	211	18
12	342	18
13	380	18
14	400	18
done	400	18
0	14	18
1	25	18
2	39	18
3	48	18
4	54	18
5	64	18
6	71	18
7	83	18
8	105	18
9	130	18
10	150	18
11	211	18
12	342	18
13	380	18
14	400	18
done	400	18
0	11	15
1	18	15
2	25	15
done	25	15
0	11	15
1	18	15
2	25	15
done	25	15
0	11	15
1	18	15
2	25	15
done	25	15
0	7	7
1	10	6
2	11	6
done	11	6
0	6	6
1	7	6
done	7	6
0	6	6
1	10	6
2	11	6
done	11	6
0	7	13
1	8	13
done	8	13
0	6	6
1	7	6
done	7	6
0	7	17
1	21	17
2	53	7
3	118	7
4	277	7
5	844	7
6	1946	7
7	2746	7
8	3229	7
9	4303	7
done	5000	7
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	9	11
1	12	11
done	12	11
0	5	5
1	6	5
done	6	5
0	8	9
1	22	9
2	31	9
3	48	9
4	87	9
5	204	9
6	609	9
7	2436	9
done	5000	9
0	9	17
1	17	14
2	32	14
3	45	14
4	65	14
5	86	14
6	103	14
7	136	14
8	191	14
9	223	14
done	223	14
0	7	11
1	12	11
2	19	11
3	34	11
4	59	11
5	100	11
6	158	11
7	326	11
8	1621	11
done	5000	11
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	6	5
done	6	5
0	13	19
1	39	19
2	103	17
3	255	17
4	565	15
5	1317	15
6	3948	15
done	5000	15
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11
0	5	5
1	10	5
2	17	5
3	23	5
4	29	5
5	38	5
6	51	5
7	64	5
8	73	5
9	82	5
10	97	5
11	102	5
12	106	5
13	107	5
done	107	5
0	21	45
1	44	45
2	100	45
3	219	45
4	802	45
5	3764	35
done	5000	35
0	21	45
1	44	45
2	100	45
3	219	45
4	802	45
5	3764	35
done	5000	35
0	5	5
1	9	5
2	15	5
done	15	5
0	23	47
1	49	47
2	118	47
3	268	47
4	876	47
5	3901	37
done	5001	37
0	23	47
1	49	47
2	118	47
3	268	47
4	876	47
5	3901	37
done	5001	37
0	8	9
1	21	9
2	45	9
3	76	9
4	127	9
5	272	9
6	805	9
7	3085	9
done	5000	9
0	9	11
1	10	11
done	10	11
0	9	11
1	10	11
done	10	11

prune165.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.1b

Counts

85 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan y) (tan z)) (cos a))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-*l/`
18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`tan-quot` `*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `times-frac` `pow-prod-down` `frac-add` `-commutative` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

9.0ms	(* (+ (tan y) (tan z)) (cos a))
6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
22.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (+ (tan y) (tan z)) (cos a))
26.0ms	(* (tan y) (tan z))
28.0ms	(* (tan y) (tan z))
181.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify3.2min

Counts

108 → 108

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	19	33
1	34	33
2	71	33
3	132	33
4	305	33
5	694	33
6	1047	33
7	1425	33
8	1852	33
9	2065	33
10	2144	33
11	2571	33
12	3872	33
done	5000	33
0	18	32
1	34	32
2	75	32
3	151	32
4	372	32
5	931	32
6	1411	32
7	1841	32
8	2056	32
9	2166	32
10	2630	32
11	3907	32
done	5000	32
0	17	31
1	36	31
2	115	31
3	286	22
4	925	20
5	4953	20
done	5000	20
0	17	31
1	33	31
2	107	31
3	282	22
4	948	20
done	5000	20
0	22	92
1	47	92
2	190	36
3	946	36
done	5000	36
0	20	92
1	49	92
2	218	34
3	1207	32
done	5000	32
0	18	63
1	34	63
2	105	63
3	264	45
4	882	41
5	4920	41
done	5000	41
0	17	31
1	33	31
2	104	31
3	263	22
4	882	20
5	4871	20
done	5000	20
0	18	92
1	41	92
2	170	32
3	813	23
done	5001	23
0	17	31
1	33	31
2	104	31
3	263	22
4	882	20
5	4871	20
done	5000	20
0	17	31
1	33	31
2	104	31
3	263	22
4	882	20
5	4871	20
done	5000	20
0	15	20
1	25	20
2	56	20
3	127	20
4	377	19
5	870	19
6	1270	19
7	1569	19
8	1906	19
9	1926	19
10	1930	19
done	1930	19
0	11	11
1	21	11
2	40	11
3	88	10
4	207	10
5	428	10
6	655	10
7	668	10
8	674	10
done	674	10
0	13	19
1	28	19
2	70	15
3	121	13
4	437	13
5	1796	13
done	5000	13
0	13	21
1	27	21
2	72	7
3	170	5
4	819	5
done	5001	5
0	17	49
1	29	49
2	62	49
3	120	49
4	289	49
5	687	49
6	1103	49
7	1551	49
8	1955	49
9	2289	49
10	2405	49
11	2414	49
done	2414	49
0	16	23
1	26	23
2	54	23
3	105	23
4	268	23
5	632	23
6	958	23
7	1277	23
8	1578	23
9	1766	23
10	1774	23
11	1782	23
12	1784	23
done	1784	23
0	16	28
1	26	28
2	54	28
3	105	28
4	268	28
5	632	28
6	961	28
7	1282	28
8	1580	28
9	1767	28
10	1779	28
11	1780	28
done	1780	28
0	16	23
1	26	23
2	54	23
3	105	23
4	268	23
5	632	23
6	958	23
7	1277	23
8	1578	23
9	1766	23
10	1774	23
11	1782	23
12	1784	23
done	1784	23
0	8	9
1	13	9
2	20	9
done	20	9
0	15	22
1	28	22
2	66	22
3	131	21
4	349	21
5	946	19
6	1846	19
7	3155	19
done	5001	19
0	11	12
1	19	12
2	34	12
3	55	12
4	116	12
5	240	12
6	284	12
done	284	12
0	16	30
1	29	30
2	73	30
3	168	30
4	513	29
5	1812	22
done	5001	21
0	15	27
1	28	27
2	66	27
3	143	19
4	546	19
5	3605	19
done	5000	19
0	17	31
1	30	31
2	71	31
3	153	31
4	417	31
5	1123	31
6	1812	31
7	2657	31
8	3063	31
9	3232	31
10	3249	31
done	3249	31
0	17	31
1	30	31
2	71	31
3	153	31
4	417	31
5	1123	31
6	1812	31
7	2657	31
8	3063	31
9	3232	31
10	3249	31
done	3249	31
0	16	30
1	29	30
2	73	30
3	168	30
4	513	29
5	1812	22
done	5001	21
0	20	34
1	54	32
2	173	32
3	533	31
4	1978	31
done	5000	31
0	19	38
1	46	36
2	155	36
3	517	35
4	1960	32
done	5001	27
0	20	40
1	57	32
2	238	32
3	1094	32
4	3828	32
done	5000	32
0	16	24
1	38	24
2	134	24
3	596	24
4	1980	24
done	5000	24
0	21	52
1	59	41
2	242	41
3	1274	41
done	5001	41
0	17	36
1	42	33
2	144	33
3	801	33
4	4389	33
done	5000	33
0	18	40
1	54	32
2	216	32
3	979	32
4	3893	32
done	5001	32
0	14	24
1	35	24
2	120	24
3	530	24
4	1967	24
done	5000	24
0	20	70
1	63	59
2	245	59
3	1099	59
done	5000	59
0	16	30
1	35	30
2	105	30
3	345	30
4	1319	30
done	5000	30
0	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	6	6
1	10	6
2	11	6
done	11	6
0	6	6
1	9	6
2	15	6
3	23	6
4	46	6
5	102	6
6	243	6
7	706	6
8	2720	6
done	5000	6
0	9	17
1	16	17
2	41	9
3	80	9
4	138	7
5	265	7
6	663	7
7	2444	7
done	5000	7
0	7	13
1	8	13
done	8	13
0	6	6
1	7	6
done	7	6
0	7	17
1	18	17
2	47	7
3	89	7
4	105	7
5	151	7
6	291	7
7	753	7
8	2738	7
done	5000	7
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	7	7
1	8	7
done	8	7
0	7	10
1	10	10
2	12	10
done	12	10
0	6	6
1	7	6
done	7	6
0	4	4
1	7	2
2	10	2
done	10	2
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
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	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	6	6
1	10	6
2	11	6
done	11	6
0	6	6
1	9	6
2	15	6
3	23	6
4	46	6
5	102	6
6	243	6
7	706	6
8	2720	6
done	5000	6
0	9	17
1	16	17
2	41	9
3	80	9
4	138	7
5	265	7
6	663	7
7	2444	7
done	5000	7
0	7	13
1	8	13
done	8	13
0	6	6
1	7	6
done	7	6
0	7	17
1	18	17
2	47	7
3	89	7
4	105	7
5	151	7
6	291	7
7	753	7
8	2738	7
done	5000	7
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	7	7
1	8	7
done	8	7
0	7	10
1	10	10
2	12	10
done	12	10
0	6	6
1	7	6
done	7	6
0	4	4
1	7	2
2	10	2
done	10	2
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
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	8	8
1	10	8
2	18	8
done	18	8
0	10	10
1	12	10
done	12	10
0	9	9
1	14	9
2	23	9
done	23	9
0	9	9
1	13	9
2	31	9
3	43	9
4	70	9
5	136	9
6	340	9
7	966	9
8	3773	9
done	5001	9
0	12	26
1	32	26
2	93	12
3	260	12
4	968	10
5	3627	10
done	5000	10
0	10	19
1	12	19
2	20	19
done	20	19
0	9	9
1	11	9
2	19	9
done	19	9
0	10	26
1	22	26
2	83	10
3	297	10
4	748	10
5	1869	10
6	4382	10
done	5000	10
0	9	9
1	11	9
2	19	9
done	19	9
0	9	9
1	11	9
2	19	9
done	19	9
0	10	10
1	12	10
done	12	10
0	10	10
1	12	10
done	12	10
0	10	13
1	14	13
2	24	13
3	36	13
done	36	13
0	9	9
1	11	9
2	19	9
done	19	9
0	7	7
1	11	5
2	22	5
3	30	5
done	30	5
0	9	9
1	11	9
done	11	9
0	9	9
1	11	9
done	11	9
0	8	8
1	10	8
2	18	8
done	18	8
0	8	8
1	10	8
2	18	8
done	18	8
0	12	14
1	16	14
2	24	14
3	40	14
4	42	14
done	42	14
0	11	12
1	26	12
2	43	12
3	84	12
4	166	12
5	403	12
6	1269	12
done	5000	12
0	10	14
1	16	14
2	33	14
3	79	14
4	162	14
5	248	14
6	416	14
7	787	14
8	3448	14
done	5000	14
0	5	5
1	10	5
2	17	5
3	23	5
4	29	5
5	38	5
6	51	5
7	64	5
8	73	5
9	82	5
10	97	5
11	102	5
12	106	5
13	107	5
done	107	5
0	26	52
1	68	52
2	186	52
3	442	52
4	975	46
5	2253	46
6	4917	46
done	5000	46
0	25	52
1	68	52
2	186	52
3	444	52
4	975	46
5	2290	46
done	5000	46
0	13	19
1	39	19
2	103	17
3	255	17
4	565	15
5	1317	15
6	3948	15
done	5000	15
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11
0	13	19
1	39	19
2	103	17
3	255	17
4	565	15
5	1317	15
6	3948	15
done	5000	15
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11
0	8	9
1	21	9
2	45	9
3	76	9
4	127	9
5	272	9
6	805	9
7	3085	9
done	5000	9
0	12	14
1	20	14
2	29	14
3	37	14
4	41	14
5	43	14
done	43	14
0	12	14
1	20	14
2	29	14
3	37	14
4	41	14
5	43	14
done	43	14

prune202.0ms

Filtered

89 candidates to 108 candidates (-21.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	107	11	118

Merged error: 0.1b

Counts

118 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(/ (- (cbrt (pow (* (+ (tan y) (tan z)) (cos a)) 3)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.6b	(pow (* (+ (tan y) (tan z)) (cos a)) 3)
6.7b	(cbrt (pow (* (+ (tan y) (tan z)) (cos a)) 3))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

21×	`associate-*l/`
14×	`add-exp-log` `add-cbrt-cube`
12×	`tan-quot` `cube-div` `add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `cbrt-div`
8×	`cbrt-prod` `associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`flip3-+` `frac-add` `flip-+` `add-log-exp`
3×	`pow-unpow` `times-frac` `associate-r` `associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `pow-exp` `associate-/r/` `rem-cube-cbrt` `sqr-pow`
1×	`frac-times` `pow-to-exp` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `clear-num` `associate-/r` `*-commutative` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
18.0ms	(/ (- (cbrt (pow (* (+ (tan y) (tan z)) (cos a)) 3)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
10.0ms	(pow (* (+ (tan y) (tan z)) (cos a)) 3)
6.0ms	(cbrt (pow (* (+ (tan y) (tan z)) (cos a)) 3))

series312.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (tan y) (tan z))
178.0ms	(/ (- (cbrt (pow (* (+ (tan y) (tan z)) (cos a)) 3)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
67.0ms	(pow (* (+ (tan y) (tan z)) (cos a)) 3)
42.0ms	(cbrt (pow (* (+ (tan y) (tan z)) (cos a)) 3))

simplify3.8min

Counts

110 → 110

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	12	12
1	25	9
2	72	9
3	231	9
4	702	9
5	1783	9
done	5000	9
0	12	12
1	25	9
2	72	9
3	245	9
4	730	9
5	1861	9
done	5000	9
0	8	8
1	17	5
2	39	5
3	81	5
4	168	5
5	404	5
6	1286	5
7	3395	5
done	5000	5
0	5	5
1	13	2
2	19	2
3	29	2
4	50	2
5	106	2
6	321	2
7	1236	2
done	5000	2
0	10	18
1	19	18
2	54	18
3	138	18
4	236	18
5	344	18
6	470	18
7	576	18
8	630	18
9	634	18
done	634	18
0	9	9
1	11	9
2	19	9
done	19	9
0	13	24
1	25	18
2	68	18
3	227	18
4	685	18
5	1761	18
done	5000	18
0	12	12
1	25	9
2	68	9
3	227	9
4	694	9
5	1762	9
done	5000	9
0	8	8
1	17	5
2	39	5
3	81	5
4	168	5
5	404	5
6	1286	5
7	3395	5
done	5000	5
0	5	5
1	13	2
2	19	2
3	29	2
4	50	2
5	106	2
6	321	2
7	1236	2
done	5000	2
0	9	9
1	11	9
2	19	9
done	19	9
0	10	18
1	19	18
2	54	18
3	138	18
4	236	18
5	344	18
6	470	18
7	576	18
8	630	18
9	634	18
done	634	18
0	12	12
1	25	12
2	69	12
3	228	12
4	688	12
5	1797	12
done	5000	12
0	12	12
1	25	12
2	69	12
3	228	12
4	688	12
5	1797	12
done	5000	12
0	2	2
1	4	1
done	4	1
0	11	11
1	24	8
2	67	8
3	230	8
4	701	8
5	1750	8
done	5000	8
0	13	13
1	20	11
2	34	11
3	44	11
4	65	11
5	125	11
6	345	11
7	1249	11
done	5000	11
0	13	13
1	20	11
2	34	11
3	44	11
4	65	11
5	125	11
6	345	11
7	1249	11
done	5000	11
0	15	17
1	30	14
2	73	14
3	244	14
4	879	14
5	3619	14
done	5000	14
0	8	8
1	20	5
2	55	5
3	132	5
4	241	5
5	625	5
6	2425	5
done	5000	5
0	13	15
1	36	12
2	85	12
3	273	12
4	1183	12
done	5000	12
0	12	20
1	28	14
2	65	14
3	202	14
4	1033	14
done	5001	14
0	13	17
1	30	14
2	85	14
3	373	14
4	2618	14
done	5001	14
0	8	8
1	18	5
2	37	5
3	85	5
4	209	5
5	582	5
6	1982	5
done	5001	5
0	13	25
1	26	19
2	69	19
3	227	19
4	684	19
5	1768	19
done	5001	19
0	12	12
1	25	9
2	68	9
3	227	9
4	694	9
5	1762	9
done	5000	9
0	13	35
1	24	10
2	67	10
3	226	10
4	684	10
5	1750	10
done	5001	10
0	12	12
1	25	9
2	68	9
3	227	9
4	694	9
5	1762	9
done	5000	9
0	12	12
1	25	9
2	68	9
3	227	9
4	694	9
5	1762	9
done	5000	9
0	12	12
1	15	12
2	23	12
done	23	12
0	11	11
1	17	11
2	32	11
3	33	11
done	33	11
0	11	11
1	17	11
2	32	11
3	33	11
done	33	11
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	12	14
1	18	14
2	33	14
3	57	14
4	113	14
5	272	14
6	886	14
7	3359	14
done	5000	14
0	11	11
1	17	11
2	30	11
3	48	11
4	87	11
5	197	11
6	561	11
7	2175	11
done	5000	11
0	10	10
1	19	8
2	34	8
3	45	8
4	69	8
5	133	8
6	358	8
7	1296	8
done	5000	8
0	7	7
1	16	7
2	38	7
3	80	7
4	167	7
5	403	7
6	1271	7
7	3337	7
done	5001	7
0	4	4
1	12	4
2	18	4
3	28	4
4	49	4
5	111	4
6	325	4
7	1243	4
done	5000	4
0	9	17
1	18	17
2	53	17
3	137	17
4	236	17
5	342	17
6	470	17
7	575	17
8	631	17
9	633	17
done	633	17
0	11	11
1	26	11
2	82	11
3	287	11
4	854	11
5	2164	11
done	5001	11
0	11	11
1	24	11
2	75	11
3	283	11
4	931	11
5	2651	11
done	5000	11
0	12	23
1	24	17
2	67	17
3	226	17
4	675	17
5	1737	17
done	5000	17
0	11	11
1	24	8
2	67	8
3	230	8
4	701	8
5	1750	8
done	5000	8
0	12	32
1	29	21
2	116	12
3	815	12
done	5000	12
0	7	7
1	16	7
2	38	7
3	80	7
4	167	7
5	403	7
6	1271	7
7	3337	7
done	5001	7
0	4	4
1	12	4
2	18	4
3	28	4
4	49	4
5	111	4
6	325	4
7	1243	4
done	5000	4
0	14	16
1	29	16
2	72	16
3	244	16
4	875	16
5	3633	16
done	5001	16
0	7	7
1	19	7
2	54	7
3	125	7
4	246	7
5	628	7
6	2397	7
done	5000	7
0	12	14
1	35	14
2	84	14
3	273	14
4	1184	14
done	5001	14
0	11	19
1	27	16
2	64	16
3	201	16
4	1029	16
done	5000	16
0	12	16
1	29	16
2	84	16
3	371	16
4	2613	16
done	5000	16
0	7	7
1	17	7
2	36	7
3	84	7
4	208	7
5	581	7
6	1983	7
done	5000	7
0	9	17
1	18	17
2	53	17
3	137	17
4	236	17
5	342	17
6	470	17
7	575	17
8	631	17
9	633	17
done	633	17
0	11	11
1	24	11
2	68	11
3	231	11
4	700	11
5	1766	11
done	5000	11
0	11	11
1	24	11
2	68	11
3	231	11
4	700	11
5	1766	11
done	5000	11
0	12	12
1	19	10
2	33	10
3	43	10
4	64	10
5	120	10
6	339	10
7	1246	10
done	5000	10
0	12	12
1	19	10
2	33	10
3	43	10
4	64	10
5	120	10
6	339	10
7	1246	10
done	5000	10
0	22	36
1	48	33
2	120	33
3	345	33
4	963	33
5	2415	33
done	5000	33
0	21	35
1	48	32
2	124	32
3	361	32
4	1050	32
5	3103	32
done	5000	32
0	20	34
1	50	31
2	164	31
3	499	22
4	1615	20
done	5000	20
0	20	34
1	47	31
2	156	31
3	493	22
4	1636	20
done	5000	20
0	25	101
1	61	92
2	234	36
3	1192	36
done	5000	36
0	23	101
1	63	92
2	265	34
3	1414	32
done	5001	32
0	21	69
1	48	63
2	154	63
3	475	45
4	1576	41
done	5000	41
0	20	34
1	47	31
2	153	31
3	474	22
4	1575	20
done	5001	20
0	21	101
1	55	92
2	218	32
3	1009	23
done	5000	23
0	20	34
1	47	31
2	153	31
3	474	22
4	1575	20
done	5001	20
0	20	34
1	47	31
2	153	31
3	474	22
4	1575	20
done	5001	20
0	18	23
1	39	20
2	105	20
3	344	20
4	1049	19
5	2589	19
done	5001	19
0	11	11
1	21	11
2	40	11
3	88	10
4	207	10
5	428	10
6	655	10
7	668	10
8	674	10
done	674	10
0	16	22
1	37	19
2	111	19
3	322	15
4	981	13
5	3165	13
done	5001	13
0	13	21
1	27	21
2	72	7
3	170	5
4	819	5
done	5001	5
0	20	55
1	43	49
2	111	49
3	325	49
4	943	49
5	2375	49
done	5000	49
0	19	26
1	40	23
2	103	23
3	315	23
4	916	23
5	2341	23
done	5000	23
0	19	31
1	40	28
2	103	28
3	315	28
4	916	28
5	2341	28
done	5000	28
0	19	26
1	40	23
2	103	23
3	315	23
4	916	23
5	2341	23
done	5000	23
0	8	9
1	13	9
2	20	9
done	20	9
0	18	25
1	42	22
2	115	22
3	341	21
4	1000	21
5	2637	19
done	5001	19
0	11	12
1	19	12
2	34	12
3	55	12
4	116	12
5	240	12
6	284	12
done	284	12
0	19	33
1	43	30
2	122	30
3	371	30
4	1192	29
5	4019	22
done	5000	21
0	18	30
1	42	27
2	115	27
3	353	19
4	1197	19
done	5000	19
0	20	34
1	44	31
2	120	31
3	356	31
4	1106	31
5	3304	31
done	5000	31
0	20	34
1	44	31
2	120	31
3	356	31
4	1106	31
5	3304	31
done	5000	31
0	19	33
1	43	30
2	122	30
3	371	30
4	1192	29
5	4019	22
done	5000	21
0	22	37
1	64	32
2	215	32
3	735	31
4	2572	31
done	5001	31
0	22	41
1	60	36
2	204	36
3	726	35
4	2647	32
done	5001	27
0	23	43
1	69	32
2	272	32
3	1246	32
4	4038	32
done	5001	32
0	19	27
1	50	24
2	174	24
3	756	24
4	2268	24
done	5001	24
0	24	55
1	70	41
2	275	41
3	1453	41
done	5000	41
0	20	39
1	53	33
2	177	33
3	996	33
done	5000	33
0	21	43
1	65	32
2	245	32
3	1068	32
4	4117	32
done	5000	32
0	17	27
1	46	24
2	147	24
3	620	24
4	2153	24
done	5000	24
0	23	79
1	67	59
2	242	59
3	1095	58
done	5000	58
0	19	33
1	49	30
2	152	30
3	528	30
4	1936	30
done	5001	30
0	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	6	6
1	10	6
2	11	6
done	11	6
0	6	6
1	9	6
2	15	6
3	23	6
4	46	6
5	102	6
6	243	6
7	706	6
8	2720	6
done	5000	6
0	9	17
1	16	17
2	41	9
3	80	9
4	138	7
5	265	7
6	663	7
7	2444	7
done	5000	7
0	7	13
1	8	13
done	8	13
0	6	6
1	7	6
done	7	6
0	7	17
1	18	17
2	47	7
3	89	7
4	105	7
5	151	7
6	291	7
7	753	7
8	2738	7
done	5000	7
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	7	7
1	8	7
done	8	7
0	7	7
1	8	7
done	8	7
0	7	10
1	10	10
2	12	10
done	12	10
0	6	6
1	7	6
done	7	6
0	4	4
1	7	2
2	10	2
done	10	2
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
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	8	9
1	21	9
2	45	9
3	76	9
4	127	9
5	272	9
6	805	9
7	3085	9
done	5000	9
0	12	14
1	20	14
2	29	14
3	37	14
4	41	14
5	43	14
done	43	14
0	12	14
1	20	14
2	29	14
3	37	14
4	41	14
5	43	14
done	43	14
0	13	19
1	39	19
2	103	19
3	153	17
4	230	13
5	356	13
6	609	13
7	1649	13
done	5000	13
0	15	18
1	30	18
2	83	18
3	313	18
4	1257	18
done	5000	18
0	15	18
1	30	18
2	83	18
3	313	18
4	1257	18
done	5000	18
0	5	5
1	10	5
2	17	5
3	23	5
4	29	5
5	38	5
6	51	5
7	64	5
8	73	5
9	82	5
10	97	5
11	102	5
12	106	5
13	107	5
done	107	5
0	26	52
1	68	52
2	186	52
3	442	52
4	975	46
5	2253	46
6	4917	46
done	5000	46
0	25	52
1	68	52
2	186	52
3	444	52
4	975	46
5	2290	46
done	5000	46
0	13	19
1	39	19
2	103	17
3	255	17
4	565	15
5	1317	15
6	3948	15
done	5000	15
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11
0	9	11
1	18	11
2	39	11
3	66	11
4	77	11
done	77	11

prune197.0ms

Filtered

93 candidates to 110 candidates (-18.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	110	11	121

Merged error: 0.1b

Counts

121 → 11

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	32
1	26	32
done	26	32

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.9s	3963×	body	1280	valid
577.0ms	8000×	pre	80	true
508.0ms	2013×	body	640	valid
119.0ms	666×	body	320	valid
65.0ms	1056×	body	80	valid
36.0ms	302×	body	160	valid

Details

sample147.0ms

simplify82.0ms

prune9.0ms

localize13.0ms

rewrite22.0ms

series118.0ms

simplify37.2s

prune104.0ms

localize17.0ms

rewrite46.0ms

series345.0ms

simplify1.6min

prune165.0ms

localize22.0ms

rewrite47.0ms

series275.0ms

simplify3.2min

prune202.0ms

localize30.0ms

rewrite43.0ms

series312.0ms

simplify3.8min

prune197.0ms

regimes1.0s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling