Details

sample94.0ms

Algorithm

intervals

Results

41.0ms	113×	body	1280	valid
24.0ms	31×	body	2560	valid
10.0ms	47×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	8×	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: 38.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
4.2b	(tan (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

8.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series55.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- (tan (+ x eps)) (tan x))
24.0ms	(tan (+ x eps))

simplify28.8s

Counts

31 → 31

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	8	9
1	11	8
2	13	8
3	16	8
4	19	8
5	25	8
6	29	8
7	45	8
8	49	8
9	54	8
10	61	8
11	80	8
12	101	8
13	113	8
14	116	8
done	116	8
0	7	8
1	10	8
2	11	8
done	11	8
0	7	8
1	13	8
2	16	8
3	19	8
4	25	8
5	29	8
6	45	8
7	49	8
8	54	8
9	61	8
10	79	8
11	100	8
12	113	8
13	116	8
done	116	8
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	13	19
1	23	19
2	51	19
3	102	19
4	263	19
5	632	19
6	955	19
7	1276	19
8	1571	19
9	1749	19
10	1753	19
done	1753	19
0	9	10
1	15	10
2	28	10
3	49	10
4	108	10
5	222	10
6	266	10
done	266	10
0	10	15
1	15	15
2	22	15
done	22	15
0	6	7
1	8	7
done	8	7
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	3	3
done	3	3
0	8	9
1	21	9
2	45	9
3	76	9
4	127	9
5	274	9
6	797	9
7	3091	9
done	5001	9
0	6	9
1	7	9
done	7	9
0	6	9
1	7	9
done	7	9
0	9	13
1	25	13
2	58	13
3	78	11
4	111	9
5	146	9
6	188	9
7	308	9
8	722	9
9	2569	9
done	5000	9
0	10	15
1	13	15
2	16	15
done	16	15
0	10	15
1	13	15
2	16	15
done	16	15

prune69.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 16.1b

Counts

32 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

9.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(+ (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
25.0ms	(+ (tan x) (tan eps))
29.0ms	(* (tan x) (tan eps))
125.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6min

Counts

98 → 98

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	12	18
1	20	17
2	28	17
3	31	17
4	33	17
5	37	17
6	41	17
7	57	17
8	61	17
9	68	17
10	79	17
11	105	17
12	138	17
13	181	17
14	260	17
15	409	17
16	418	17
done	418	17
0	11	17
1	19	17
2	26	17
done	26	17
0	11	17
1	22	17
2	31	17
3	33	17
4	37	17
5	41	17
6	57	17
7	61	17
8	68	17
9	79	17
10	105	17
11	138	17
12	184	17
13	263	17
14	413	17
15	432	17
done	432	17
0	12	35
1	20	35
2	27	35
done	27	35
0	11	17
1	19	17
2	26	17
done	26	17
0	12	50
1	21	50
2	42	18
3	93	18
4	257	18
5	805	18
6	2816	18
done	5001	18
0	11	17
1	19	17
2	26	17
done	26	17
0	11	17
1	19	17
2	26	17
done	26	17
0	13	19
1	23	19
2	51	19
3	102	19
4	263	19
5	632	19
6	955	19
7	1276	19
8	1571	19
9	1749	19
10	1753	19
done	1753	19
0	9	10
1	15	10
2	28	10
3	49	10
4	108	10
5	222	10
6	266	10
done	266	10
0	13	20
1	37	20
2	83	20
3	213	20
4	588	20
5	2159	20
done	5001	20
0	14	50
1	33	47
2	63	47
3	91	36
4	159	36
5	341	36
6	1139	36
7	3678	36
done	5000	36
0	3	3
done	3	3
0	12	33
1	27	33
2	54	33
3	94	33
4	175	33
5	409	33
6	1387	33
7	4546	33
done	5001	33
0	10	16
1	17	16
2	24	16
done	24	16
0	12	18
1	19	18
2	26	18
done	26	18
0	12	18
1	20	18
2	28	18
done	28	18
0	13	19
1	20	19
2	27	19
done	27	19
0	13	19
1	21	19
2	29	19
done	29	19
0	10	16
1	18	16
2	25	16
done	25	16
0	3	3
done	3	3
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	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	11	15
1	19	15
2	27	15
done	27	15
0	10	14
1	19	14
2	28	14
3	29	14
done	29	14
0	10	14
1	16	14
2	23	14
done	23	14
0	13	41
1	40	41
2	115	17
3	331	15
4	1167	15
5	4822	15
done	5000	15
0	11	29
1	17	29
2	24	29
done	24	29
0	10	14
1	16	14
2	23	14
done	23	14
0	11	41
1	24	41
2	63	15
3	141	15
4	351	15
5	913	15
6	3413	15
done	5001	15
0	10	14
1	16	14
2	23	14
done	23	14
0	10	14
1	16	14
2	23	14
done	23	14
0	6	6
1	10	6
2	12	6
3	13	6
done	13	6
0	8	8
1	13	8
2	24	8
3	34	7
4	44	7
done	44	7
0	13	31
1	25	31
2	41	31
3	47	31
done	47	31
0	11	15
1	17	15
2	24	15
done	24	15
0	12	22
1	20	22
2	29	22
3	30	22
done	30	22
0	11	15
1	17	15
2	24	15
done	24	15
0	9	15
1	14	13
2	20	13
3	25	13
done	25	13
0	10	14
1	16	14
2	23	14
done	23	14
0	12	24
1	20	24
2	27	24
done	27	24
0	11	15
1	17	15
2	24	15
done	24	15
0	11	15
1	17	15
2	24	15
done	24	15
0	11	15
1	17	15
2	24	15
done	24	15
0	8	8
1	11	6
2	13	6
done	13	6
0	10	14
1	16	14
2	23	14
done	23	14
0	10	19
1	17	19
2	24	19
done	24	19
0	10	14
1	16	14
2	23	14
done	23	14
0	9	10
1	14	10
2	21	10
done	21	10
0	10	14
1	16	14
2	23	14
done	23	14
0	2	3
1	4	1
done	4	1
0	9	13
1	15	13
2	22	13
done	22	13
0	10	19
1	17	19
2	24	19
done	24	19
0	10	14
1	16	14
2	23	14
done	23	14
0	9	10
1	14	10
2	21	10
done	21	10
0	10	14
1	16	14
2	23	14
done	23	14
0	2	3
1	4	1
done	4	1
0	9	13
1	15	13
2	22	13
done	22	13
0	8	9
1	13	9
2	20	9
done	20	9
0	9	13
1	18	13
2	31	13
3	39	13
4	55	13
5	61	13
done	61	13
0	11	23
1	19	23
2	26	23
done	26	23
0	10	14
1	16	14
2	23	14
done	23	14
0	7	7
1	10	5
2	12	5
done	12	5
0	10	14
1	19	14
2	32	14
3	40	14
4	56	14
5	62	14
done	62	14
0	10	14
1	19	14
2	32	14
3	40	14
4	56	14
5	62	14
done	62	14
0	9	13
1	18	13
2	31	13
3	39	13
4	55	13
5	61	13
done	61	13
0	9	13
1	18	13
2	31	13
3	39	13
4	55	13
5	61	13
done	61	13
0	12	17
1	34	15
2	83	15
3	267	15
4	655	15
5	1583	15
done	5000	15
0	11	21
1	27	19
2	59	19
3	119	19
4	168	19
5	386	19
6	787	19
7	1243	19
8	3134	19
done	5000	19
0	11	13
1	20	13
2	39	13
3	84	13
4	305	13
5	585	13
6	773	13
done	773	13
0	12	25
1	30	22
2	79	22
3	273	22
4	1205	22
5	3127	22
done	5000	22
0	9	13
1	17	13
2	36	13
3	86	13
4	302	13
5	590	13
6	932	13
7	1443	13
8	1907	13
9	2034	13
done	2034	13
0	9	13
1	25	13
2	58	13
3	78	11
4	111	9
5	146	9
6	188	9
7	308	9
8	722	9
9	2569	9
done	5000	9
0	18	45
1	40	45
2	94	45
3	213	45
4	804	45
5	3783	35
done	5001	35
0	18	45
1	40	45
2	94	45
3	213	45
4	804	45
5	3783	35
done	5001	35
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	274	9
6	797	9
7	3091	9
done	5001	9
0	9	11
1	10	11
done	10	11
0	9	11
1	10	11
done	10	11
0	8	9
1	21	9
2	45	9
3	76	9
4	127	9
5	274	9
6	797	9
7	3091	9
done	5001	9
0	15	25
1	27	25
2	59	25
3	122	25
4	190	25
5	215	25
6	218	25
done	218	25
0	15	25
1	27	25
2	59	25
3	122	25
4	190	25
5	215	25
6	218	25
done	218	25

prune180.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	87	11	98
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 16.0b

Counts

105 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

5.0ms	(+ (tan x) (tan eps))
7.0ms	(/ (* (tan x) (sin eps)) (cos eps))
6.0ms	(* (tan x) (sin eps))
21.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (tan x) (tan eps))
30.0ms	(/ (* (tan x) (sin eps)) (cos eps))
18.0ms	(* (tan x) (sin eps))
125.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify1.8min

Counts

82 → 82

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	25	20
2	35	20
3	52	20
4	67	20
5	74	20
6	78	20
7	94	20
8	98	20
9	105	20
10	117	20
11	144	20
12	177	20
13	227	20
14	325	20
15	496	20
16	511	20
done	511	20
0	14	20
1	24	20
2	33	20
3	47	20
4	60	20
5	63	20
done	63	20
0	14	20
1	27	20
2	38	20
3	54	20
4	71	20
5	78	20
6	94	20
7	98	20
8	105	20
9	117	20
10	143	20
11	176	20
12	229	20
13	327	20
14	497	20
15	518	20
done	518	20
0	15	41
1	25	41
2	34	41
3	48	41
4	61	41
5	64	41
done	64	41
0	14	20
1	24	20
2	33	20
3	47	20
4	60	20
5	63	20
done	63	20
0	15	59
1	26	59
2	49	21
3	114	21
4	291	21
5	848	21
6	2883	21
done	5000	21
0	14	20
1	24	20
2	33	20
3	47	20
4	60	20
5	63	20
done	63	20
0	14	20
1	24	20
2	33	20
3	47	20
4	60	20
5	63	20
done	63	20
0	16	22
1	28	22
2	58	22
3	115	22
4	324	22
5	943	22
6	2223	22
7	2664	22
8	3137	22
9	3409	22
10	3590	22
11	3614	22
done	3614	22
0	11	13
1	19	13
2	34	13
3	61	13
4	166	13
5	474	13
6	999	13
7	1173	13
8	1279	13
9	1321	13
done	1321	13
0	16	23
1	42	23
2	90	23
3	234	23
4	639	23
5	2465	23
done	5000	23
0	17	59
1	38	56
2	70	56
3	116	42
4	221	42
5	544	42
6	2119	42
done	5000	42
0	3	3
done	3	3
0	15	39
1	32	39
2	61	39
3	115	39
4	231	39
5	578	39
6	2274	39
done	5000	39
0	13	19
1	22	19
2	31	19
3	45	19
4	58	19
5	61	19
done	61	19
0	15	21
1	24	21
2	33	21
3	47	21
4	60	21
5	63	21
done	63	21
0	15	21
1	25	21
2	35	21
3	49	21
4	62	21
5	65	21
done	65	21
0	16	22
1	25	22
2	34	22
3	48	22
4	61	22
5	64	22
done	64	22
0	16	22
1	26	22
2	36	22
3	50	22
4	63	22
5	66	22
done	66	22
0	13	19
1	23	19
2	32	19
3	46	19
4	59	19
5	62	19
done	62	19
0	3	3
done	3	3
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	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	10	11
1	15	11
2	22	11
3	28	11
4	34	11
5	43	11
6	56	11
7	74	11
8	90	11
9	97	11
10	114	11
11	116	11
done	116	11
0	9	10
1	15	10
2	21	10
3	30	10
4	33	10
5	39	10
6	48	10
7	61	10
8	79	10
9	95	10
10	102	10
11	119	10
12	121	10
done	121	10
0	8	9
1	14	9
2	26	9
3	45	9
4	61	9
5	69	9
6	81	9
7	99	9
8	115	9
9	122	9
10	139	9
11	141	9
done	141	9
0	8	9
1	11	9
2	15	9
3	20	9
4	29	9
5	42	9
6	75	9
7	158	9
8	374	9
9	1023	9
10	4626	9
done	5000	9
0	13	26
1	28	26
2	124	14
3	556	14
4	2274	12
done	5000	12
0	11	26
1	30	26
2	131	12
3	694	10
4	2622	10
5	4848	10
done	5000	10
0	9	19
1	12	19
2	16	19
3	19	19
4	20	19
done	20	19
0	8	9
1	11	9
2	15	9
3	18	9
4	19	9
done	19	9
0	9	26
1	19	26
2	60	10
3	237	10
4	994	10
5	2956	10
done	5000	10
0	8	9
1	11	9
2	15	9
3	18	9
4	19	9
done	19	9
0	8	9
1	11	9
2	15	9
3	18	9
4	19	9
done	19	9
0	6	6
1	11	6
2	13	6
done	13	6
0	3	3
done	3	3
0	7	10
1	9	10
done	9	10
0	5	6
done	5	6
0	6	6
done	6	6
0	5	6
done	5	6
0	4	4
1	6	2
2	8	2
done	8	2
0	4	5
done	4	5
0	4	4
1	6	4
done	6	4
0	7	8
1	10	8
2	12	8
done	12	8
0	9	13
1	17	13
2	31	13
3	44	13
4	48	13
done	48	13
0	8	9
1	11	9
2	15	9
3	18	9
4	19	9
done	19	9
0	7	7
1	12	5
2	20	5
3	29	5
4	34	5
done	34	5
0	4	5
done	4	5
0	5	5
1	6	5
done	6	5
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	9	13
1	25	13
2	58	13
3	78	11
4	111	9
5	146	9
6	188	9
7	308	9
8	722	9
9	2569	9
done	5000	9
0	18	45
1	40	45
2	94	45
3	213	45
4	804	45
5	3783	35
done	5001	35
0	18	45
1	40	45
2	94	45
3	213	45
4	804	45
5	3783	35
done	5001	35
0	14	19
1	41	19
2	116	17
3	351	17
4	965	17
5	2481	17
done	5001	17
0	7	8
1	10	8
2	14	8
3	17	8
4	18	8
done	18	8
0	7	8
1	10	8
2	14	8
3	17	8
4	18	8
done	18	8
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	274	9
6	797	9
7	3091	9
done	5001	9
0	9	11
1	10	11
done	10	11
0	9	11
1	10	11
done	10	11

prune140.0ms

Filtered

65 candidates to 82 candidates (-26.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 16.0b

Counts

95 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.9b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`tan-quot`
19×	`*-un-lft-identity`
18×	`associate-r`
15×	`add-exp-log`
14×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1` `frac-sub` `add-log-exp`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`flip3-+` `frac-add` `prod-exp` `flip-+`
4×	`unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rec-exp` `diff-log` `1-exp` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

15.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
5.0ms	(+ (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
13.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series249.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
28.0ms	(+ (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))
126.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify4.5min

Counts

111 → 111

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	26	19
2	54	17
3	114	17
4	240	17
5	520	17
6	1566	17
done	5000	17
0	12	19
1	23	19
2	41	17
3	83	17
4	125	17
5	195	17
6	450	17
7	961	17
8	3984	17
done	5000	17
0	12	19
1	26	19
2	50	17
3	111	17
4	216	17
5	436	17
6	1328	17
7	4689	17
done	5001	17
0	13	39
1	24	39
2	42	35
3	84	35
4	124	35
5	194	35
6	454	35
7	968	35
8	3991	35
done	5000	35
0	12	19
1	23	19
2	41	17
3	83	17
4	125	17
5	195	17
6	448	17
7	956	17
8	3979	17
done	5000	17
0	13	56
1	25	56
2	57	18
3	182	18
4	804	18
5	4214	18
done	5001	18
0	12	19
1	23	19
2	41	17
3	83	17
4	125	17
5	195	17
6	448	17
7	956	17
8	3979	17
done	5000	17
0	12	19
1	23	19
2	41	17
3	83	17
4	125	17
5	195	17
6	448	17
7	956	17
8	3979	17
done	5000	17
0	20	33
1	41	31
2	116	31
3	346	31
4	1181	27
5	3589	22
done	5000	22
0	12	16
1	24	16
2	58	16
3	142	16
4	484	16
5	1068	16
6	1416	16
7	1428	16
done	1428	16
0	22	43
1	55	38
2	136	38
3	459	38
4	2223	38
done	5000	38
0	14	28
1	29	25
2	65	25
3	244	25
4	1241	25
5	4715	25
done	5000	25
0	18	33
1	39	31
2	116	31
3	377	25
4	1293	25
5	3477	25
done	5000	25
0	11	16
1	22	16
2	47	16
3	141	16
4	515	16
5	1183	16
6	2042	16
7	3200	16
8	4572	16
9	4981	16
10	4982	16
done	4982	16
0	13	19
1	23	19
2	51	19
3	102	19
4	263	19
5	632	19
6	955	19
7	1276	19
8	1571	19
9	1749	19
10	1753	19
done	1753	19
0	9	10
1	15	10
2	28	10
3	49	10
4	108	10
5	222	10
6	266	10
done	266	10
0	14	21
1	27	19
2	72	19
3	139	19
4	306	19
5	549	19
6	774	19
7	1145	19
8	1349	19
9	1359	19
done	1359	19
0	9	10
1	15	10
2	28	10
3	49	10
4	108	10
5	222	10
6	266	10
done	266	10
0	20	33
1	39	33
2	88	28
3	207	28
4	414	28
5	811	28
6	1308	28
7	2099	28
8	3743	28
done	5000	28
0	6	8
1	8	8
2	11	8
done	11	8
0	22	43
1	54	40
2	117	38
3	310	38
4	892	38
5	2727	38
done	5000	38
0	11	20
1	20	17
2	43	17
3	84	17
4	147	17
5	205	17
6	267	17
7	349	17
8	517	17
9	745	17
10	772	17
11	774	17
done	774	17
0	18	33
1	38	33
2	98	31
3	323	31
4	978	31
5	2522	25
done	5000	25
0	7	8
1	10	8
2	17	8
3	22	8
4	26	8
done	26	8
0	14	22
1	41	22
2	121	20
3	393	20
4	1404	20
5	4286	20
done	5001	20
0	15	56
1	40	53
2	115	47
3	305	36
4	727	36
5	1827	36
done	5000	36
0	3	3
done	3	3
0	13	37
1	34	37
2	101	33
3	299	33
4	802	33
5	1927	33
done	5001	33
0	11	18
1	21	18
2	39	16
3	77	16
4	119	16
5	188	16
6	426	16
7	878	16
8	3526	16
done	5000	16
0	3	3
done	3	3
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	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	10	15
1	19	15
2	37	13
3	67	13
4	107	13
5	168	13
6	409	13
7	855	13
8	3469	13
done	5001	13
0	12	16
1	20	15
2	27	15
done	27	15
0	13	17
1	23	16
2	40	15
3	49	15
4	67	15
5	93	15
6	98	15
7	107	15
8	124	15
done	124	15
0	13	18
1	24	17
2	38	15
3	55	15
4	73	15
5	99	15
6	104	15
7	113	15
8	130	15
done	130	15
0	12	17
1	23	16
2	36	15
3	47	15
4	59	15
5	91	15
6	109	15
7	116	15
8	124	15
done	124	15
0	11	16
1	23	16
2	47	14
3	83	14
4	141	14
5	217	14
6	487	14
7	935	14
8	3570	14
done	5000	14
0	11	16
1	22	16
2	50	14
3	97	14
4	191	14
5	392	14
6	1100	14
7	3412	14
done	5000	14
0	16	47
1	48	43
2	143	17
3	542	17
4	2428	17
done	5000	17
0	14	47
1	45	47
2	131	19
3	399	19
4	1591	15
done	5000	15
0	12	33
1	21	33
2	39	29
3	69	29
4	109	29
5	170	29
6	411	29
7	856	29
8	3453	29
done	5000	29
0	11	16
1	20	16
2	38	14
3	68	14
4	106	14
5	167	14
6	407	14
7	851	14
8	3461	14
done	5001	14
0	12	47
1	31	47
2	124	15
3	475	15
4	1511	15
5	3675	15
done	5000	15
0	11	16
1	20	16
2	38	14
3	68	14
4	106	14
5	167	14
6	407	14
7	851	14
8	3461	14
done	5001	14
0	11	16
1	20	16
2	38	14
3	68	14
4	106	14
5	167	14
6	407	14
7	851	14
8	3461	14
done	5001	14
0	11	13
1	17	11
2	28	11
3	52	11
4	76	11
done	76	11
0	11	13
1	20	13
2	45	13
3	103	13
4	314	13
5	631	13
6	801	13
done	801	13
0	10	11
1	27	9
2	47	9
3	96	9
4	208	9
5	431	9
6	1137	9
7	3883	9
done	5000	9
0	12	25
1	24	22
2	54	22
3	163	22
4	805	22
5	2700	22
done	5000	22
0	9	13
1	17	11
2	37	11
3	94	11
4	182	11
5	239	11
6	343	11
7	568	11
8	2035	11
done	5001	11
0	9	13
1	17	13
2	36	13
3	86	13
4	302	13
5	591	13
6	939	13
7	1442	13
8	1881	13
9	2012	13
done	2012	13
0	12	17
1	19	17
2	26	17
done	26	17
0	12	17
1	19	17
2	26	17
done	26	17
0	13	18
1	22	17
2	32	17
3	36	15
4	47	15
done	47	15
0	13	18
1	22	17
2	32	17
3	36	15
4	47	15
done	47	15
0	12	17
1	21	17
2	31	15
3	46	15
4	49	15
done	49	15
0	12	17
1	21	17
2	31	15
3	46	15
4	49	15
done	49	15
0	12	27
1	21	27
2	38	27
3	50	27
4	54	27
done	54	27
0	11	16
1	18	16
2	33	16
done	33	16
0	14	29
1	29	27
2	73	25
3	143	23
4	224	23
5	262	23
6	275	23
7	276	23
done	276	23
0	13	20
1	24	18
2	49	16
3	82	14
4	126	14
5	146	14
6	159	14
7	160	14
done	160	14
0	10	13
1	18	9
2	41	7
3	53	5
4	57	5
done	57	5
0	13	26
1	24	25
2	50	25
3	88	23
4	171	23
5	227	23
6	243	23
7	244	23
done	244	23
0	12	17
1	21	16
2	39	16
3	55	14
4	90	14
5	113	14
6	126	14
7	127	14
done	127	14
0	9	10
1	15	7
2	28	5
3	40	5
done	40	5
0	12	25
1	23	25
2	48	23
3	101	23
4	178	23
5	217	23
6	230	23
7	231	23
done	231	23
0	11	16
1	20	16
2	38	14
3	65	14
4	94	14
5	114	14
6	127	14
7	128	14
done	128	14
0	8	9
1	14	7
2	27	5
3	39	5
done	39	5
0	7	7
1	11	5
2	22	5
3	30	5
done	30	5
0	7	7
1	11	5
2	22	5
3	30	5
done	30	5
0	13	19
1	38	17
2	98	15
3	305	15
4	771	15
5	2451	15
done	5000	15
0	12	23
1	31	21
2	78	19
3	192	19
4	387	19
5	907	19
6	2530	19
done	5000	19
0	11	16
1	20	16
2	30	14
3	48	14
4	58	14
5	87	14
6	164	14
7	206	14
8	246	14
done	246	14
0	11	16
1	20	16
2	30	14
3	48	14
4	58	14
5	87	14
6	164	14
7	206	14
8	246	14
done	246	14
0	10	15
1	19	15
2	37	13
3	67	13
4	107	13
5	168	13
6	409	13
7	855	13
8	3469	13
done	5001	13
0	10	15
1	19	15
2	37	13
3	67	13
4	107	13
5	168	13
6	409	13
7	855	13
8	3469	13
done	5001	13
0	7	7
1	11	5
2	22	5
3	30	5
done	30	5
0	16	21
1	27	21
2	45	19
3	91	19
4	159	19
5	288	19
6	460	19
7	742	19
8	1167	19
9	1371	19
10	1465	19
done	1465	19
0	13	19
1	35	19
2	62	17
3	133	17
4	306	17
5	947	17
6	3100	17
done	5001	17
0	12	21
1	25	21
2	53	19
3	158	19
4	385	19
5	868	19
6	1770	19
7	4326	19
done	5001	19
0	9	13
1	25	13
2	58	13
3	78	11
4	111	9
5	146	9
6	188	9
7	308	9
8	722	9
9	2569	9
done	5000	9
0	18	45
1	40	45
2	94	45
3	213	45
4	804	45
5	3783	35
done	5001	35
0	18	45
1	40	45
2	94	45
3	213	45
4	804	45
5	3783	35
done	5001	35
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	274	9
6	797	9
7	3091	9
done	5001	9
0	9	11
1	10	11
done	10	11
0	9	11
1	10	11
done	10	11
0	8	9
1	21	9
2	45	9
3	76	9
4	127	9
5	274	9
6	797	9
7	3091	9
done	5001	9
0	15	25
1	27	25
2	59	25
3	122	25
4	190	25
5	215	25
6	218	25
done	218	25
0	15	25
1	27	25
2	59	25
3	122	25
4	190	25
5	215	25
6	218	25
done	218	25

prune134.0ms

Filtered

84 candidates to 111 candidates (-32.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Merged error: 0.2b

Counts

123 → 10

regimes147.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	39
1	33	37
done	33	37

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3300×	body	1280	valid
494.0ms	641×	body	2560	valid
441.0ms	1895×	body	640	valid
113.0ms	749×	body	320	valid
55.0ms	1084×	body	80	valid
38.0ms	331×	body	160	valid

Details

sample94.0ms

simplify3.0ms

prune3.0ms

localize9.0ms

rewrite13.0ms

series55.0ms

simplify28.8s

prune69.0ms

localize12.0ms

rewrite38.0ms

series250.0ms

simplify1.6min

prune180.0ms

localize17.0ms

rewrite41.0ms

series197.0ms

simplify1.8min

prune140.0ms

localize18.0ms

rewrite44.0ms

series249.0ms

simplify4.5min

prune134.0ms

regimes147.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.7s

Profiling