Details

sample177.0ms

Algorithm

intervals

Results

106.0ms	69×	body	2560	valid
40.0ms	85×	body	1280	valid
13.0ms	53×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	9×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	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: 33.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin x)
0.1b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 1.0 (cos x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

2.0ms	(sin x)
7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series15.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(sin x)
9.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

simplify30.3s

Counts

68 → 68

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	9
1	12	9
2	14	9
done	14	9
0	7	8
1	15	8
2	20	8
3	23	8
done	23	8
0	7	8
1	12	8
2	18	8
3	22	8
4	25	8
5	31	8
6	35	8
7	51	8
8	55	8
9	62	8
10	71	8
11	91	8
12	112	8
13	126	8
14	133	8
15	139	8
16	143	8
done	143	8
0	10	23
1	21	23
2	69	11
3	204	9
4	563	9
5	2032	9
done	5000	9
0	8	17
1	13	17
2	16	17
3	18	17
done	18	17
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	8	23
1	20	23
2	51	9
3	177	9
4	572	9
5	1721	9
done	5000	9
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	5	5
1	7	5
2	11	5
3	13	5
4	14	4
done	14	4
0	3	3
done	3	3
0	4	4
done	4	4
0	4	5
done	4	5
0	10	19
1	18	19
2	28	19
3	34	19
done	34	19
0	8	9
1	10	9
2	11	9
done	11	9
0	9	15
1	13	15
2	16	15
3	17	15
done	17	15
0	8	9
1	10	9
2	11	9
done	11	9
0	8	13
1	14	11
2	21	11
3	26	11
done	26	11
0	7	8
1	9	8
2	10	8
done	10	8
0	9	13
1	13	13
2	14	13
done	14	13
0	8	9
1	10	9
2	11	9
done	11	9
0	8	9
1	10	9
2	11	9
done	11	9
0	8	9
1	10	9
2	11	9
done	11	9
0	7	7
1	11	5
2	14	5
done	14	5
0	7	8
1	9	8
2	10	8
done	10	8
0	6	9
1	10	9
done	10	9
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	5	5
1	7	5
done	7	5
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	2	3
1	4	1
done	4	1
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7
0	10	14
1	13	14
done	13	14
0	9	10
1	14	10
2	17	10
3	19	10
done	19	10
0	9	10
1	10	10
done	10	10
0	9	10
1	14	10
2	17	10
3	19	10
done	19	10
0	8	8
1	11	6
2	13	6
done	13	6
0	8	9
1	13	9
2	16	9
3	18	9
done	18	9
0	6	9
1	10	9
done	10	9
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	5	5
1	7	5
done	7	5
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	2	3
1	4	1
done	4	1
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	8	7
2	9	7
done	9	7
0	8	12
1	15	12
2	23	12
3	28	12
4	31	12
done	31	12
0	7	8
1	12	8
2	15	8
3	17	8
done	17	8
0	6	6
1	13	4
2	18	4
3	19	4
done	19	4
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	6	7
1	8	7
2	9	7
done	9	7
0	8	9
1	10	9
2	11	9
done	11	9
0	6	7
1	8	7
2	9	7
done	9	7
0	10	17
1	24	14
2	53	14
3	79	14
4	90	14
5	92	14
done	92	14
0	6	7
1	14	7
2	15	7
done	15	7
0	3	3
done	3	3
0	3	3
done	3	3
0	4	7
done	4	7
0	3	3
done	3	3
0	4	8
1	5	8
2	7	4
3	12	4
4	18	4
5	28	4
6	49	4
7	108	4
8	316	4
9	1236	4
done	5000	4
0	3	3
done	3	3
0	3	3
done	3	3
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	13	15
1	32	15
2	66	15
3	114	15
4	209	15
5	504	15
6	1563	15
done	5000	15
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	11	13
1	30	13
2	72	13
3	158	13
4	345	13
5	852	13
6	2834	13
done	5001	13
0	2	2
done	2	2
0	2	2
done	2	2

prune151.0ms

Filtered

51 candidates to 68 candidates (-33.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	54	14	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	14	69

Merged error: 0.2b

Counts

69 → 14

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`associate-r`
12×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-cbrt-cube`
4×	`cube-prod` `sqr-pow`
2×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
1×	`cube-mult` `unpow3`

Counts

2 → 56

Calls

2 calls:

6.0ms	(* 1/240 (pow x 5))
8.0ms	(* 1/24 (pow x 3))

series12.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* 1/240 (pow x 5))
7.0ms	(* 1/24 (pow x 3))

simplify4.6min

Counts

62 → 62

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	7	7
1	9	7
done	9	7
0	7	7
1	9	7
done	9	7
0	7	7
1	18	7
2	30	7
3	57	7
4	111	7
5	257	7
6	736	7
7	2804	7
done	5000	7
0	6	6
1	18	6
2	44	6
3	92	6
4	181	6
5	434	6
6	1321	6
done	5001	6
0	6	6
1	17	6
2	40	6
3	93	6
4	231	6
5	697	6
6	2747	6
done	5000	6
0	9	17
1	29	9
2	87	7
3	358	7
4	1597	7
done	5000	7
0	7	13
1	16	13
2	34	13
3	58	13
4	102	13
5	244	13
6	769	13
7	3060	13
done	5001	13
0	6	6
1	15	6
2	33	6
3	56	6
4	103	6
5	241	6
6	766	6
7	3067	6
done	5000	6
0	7	17
1	27	15
2	107	7
3	511	7
4	2469	7
done	5000	7
0	6	6
1	15	6
2	33	6
3	56	6
4	103	6
5	241	6
6	766	6
7	3067	6
done	5000	6
0	6	6
1	15	6
2	33	6
3	56	6
4	103	6
5	241	6
6	766	6
7	3067	6
done	5000	6
0	7	7
1	16	7
2	34	7
3	52	7
4	100	7
5	246	7
6	764	7
7	3053	7
done	5000	7
0	7	7
1	16	7
2	34	7
3	52	7
4	100	7
5	246	7
6	764	7
7	3053	7
done	5000	7
0	7	7
1	16	7
2	34	7
3	52	7
4	100	7
5	246	7
6	764	7
7	3053	7
done	5000	7
0	7	7
1	16	7
2	34	7
3	52	7
4	100	7
5	246	7
6	764	7
7	3053	7
done	5000	7
0	7	7
1	16	7
2	23	7
3	33	7
4	54	7
5	114	7
6	316	7
7	1251	7
done	5000	7
0	7	7
1	16	7
2	23	7
3	33	7
4	54	7
5	114	7
6	316	7
7	1251	7
done	5000	7
0	8	8
1	14	6
2	24	6
3	44	6
4	88	6
5	230	6
6	750	6
7	3051	6
done	5000	6
0	8	8
1	14	6
2	24	6
3	44	6
4	88	6
5	230	6
6	750	6
7	3051	6
done	5000	6
0	7	9
1	18	9
2	55	5
3	111	5
4	166	5
5	320	5
6	852	5
7	3190	5
done	5000	5
0	6	6
1	15	6
2	33	6
3	57	6
4	101	6
5	246	6
6	775	6
7	3072	6
done	5000	6
0	5	5
1	16	1
2	20	1
done	20	1
0	4	5
1	7	5
2	9	5
done	9	5
0	7	11
1	17	5
2	25	5
3	35	5
4	56	5
5	116	5
6	325	5
7	1246	5
done	5000	5
0	7	9
1	18	9
2	55	5
3	111	5
4	166	5
5	320	5
6	852	5
7	3190	5
done	5000	5
0	6	6
1	15	6
2	33	6
3	57	6
4	101	6
5	246	6
6	775	6
7	3072	6
done	5000	6
0	5	5
1	16	1
2	20	1
done	20	1
0	3	3
1	4	3
done	4	3
0	6	6
1	15	6
2	22	6
3	32	6
4	53	6
5	114	6
6	324	6
7	1259	6
done	5000	6
0	3	3
1	6	1
done	6	1
0	7	7
1	13	5
2	23	5
3	41	5
4	87	5
5	227	5
6	762	5
7	3059	5
done	5001	5
0	6	6
1	15	6
2	33	6
3	61	6
4	107	6
5	252	6
6	785	6
7	3076	6
done	5001	6
0	6	6
1	15	6
2	33	6
3	61	6
4	107	6
5	252	6
6	785	6
7	3076	6
done	5001	6
0	5	5
1	14	5
2	32	5
3	54	5
4	101	5
5	244	5
6	773	5
7	3060	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	24	7
3	42	7
4	91	7
5	241	7
6	737	7
7	2752	7
done	5000	7
0	6	6
1	15	6
2	30	6
3	60	6
4	144	6
5	405	6
6	1301	6
7	4933	6
done	5000	6
0	6	6
1	14	6
2	29	6
3	63	6
4	165	6
5	543	6
6	2400	6
done	5001	6
0	9	17
1	26	9
2	62	7
3	173	7
4	656	7
5	2869	7
done	5000	7
0	7	13
1	13	13
2	23	13
3	41	13
4	89	13
5	228	13
6	758	13
7	3065	13
done	5001	13
0	6	6
1	12	6
2	22	6
3	40	6
4	85	6
5	232	6
6	761	6
7	3051	6
done	5001	6
0	7	17
1	24	15
2	74	7
3	249	7
4	962	7
5	4036	7
done	5001	7
0	6	6
1	12	6
2	22	6
3	40	6
4	85	6
5	232	6
6	761	6
7	3051	6
done	5001	6
0	6	6
1	12	6
2	22	6
3	40	6
4	85	6
5	232	6
6	761	6
7	3051	6
done	5001	6
0	7	7
1	13	7
2	23	7
3	41	7
4	88	7
5	233	7
6	762	7
7	3059	7
done	5000	7
0	7	7
1	13	7
2	23	7
3	41	7
4	88	7
5	233	7
6	762	7
7	3059	7
done	5000	7
0	7	7
1	13	7
2	20	7
3	30	7
4	52	7
5	116	7
6	331	7
7	1268	7
done	5001	7
0	7	7
1	13	7
2	20	7
3	30	7
4	52	7
5	116	7
6	331	7
7	1268	7
done	5001	7
0	8	8
1	14	6
2	24	6
3	44	6
4	89	6
5	233	6
6	758	6
7	3055	6
done	5001	6
0	8	8
1	14	6
2	24	6
3	44	6
4	89	6
5	233	6
6	758	6
7	3055	6
done	5001	6
0	7	9
1	13	9
2	23	9
3	41	9
4	88	9
5	233	9
6	764	9
7	3068	9
done	5001	9
0	6	6
1	12	6
2	22	6
3	42	6
4	88	6
5	238	6
6	769	6
7	3058	6
done	5001	6
0	5	5
1	13	1
done	13	1
0	7	11
1	15	11
2	23	11
3	33	11
4	55	11
5	117	11
6	326	11
7	1255	11
done	5001	11
0	6	6
1	12	6
2	19	6
3	29	6
4	51	6
5	115	6
6	328	6
7	1249	6
done	5000	6
0	3	3
1	6	1
done	6	1
0	7	7
1	13	5
2	23	5
3	41	5
4	88	5
5	230	5
6	762	5
7	3072	5
done	5000	5
0	6	6
1	12	6
2	22	6
3	42	6
4	88	6
5	238	6
6	767	6
7	3058	6
done	5000	6
0	6	6
1	12	6
2	22	6
3	42	6
4	88	6
5	238	6
6	767	6
7	3058	6
done	5000	6
0	5	5
1	11	5
2	21	5
3	39	5
4	87	5
5	230	5
6	754	5
7	3051	5
done	5001	5
0	5	5
1	14	5
2	32	5
3	54	5
4	101	5
5	244	5
6	773	5
7	3060	5
done	5001	5
0	5	5
1	14	5
2	32	5
3	54	5
4	101	5
5	244	5
6	773	5
7	3060	5
done	5001	5
0	5	5
1	14	5
2	32	5
3	54	5
4	101	5
5	244	5
6	773	5
7	3060	5
done	5001	5
0	5	5
1	11	5
2	21	5
3	39	5
4	87	5
5	230	5
6	754	5
7	3051	5
done	5001	5
0	5	5
1	11	5
2	21	5
3	39	5
4	87	5
5	230	5
6	754	5
7	3051	5
done	5001	5
0	5	5
1	11	5
2	21	5
3	39	5
4	87	5
5	230	5
6	754	5
7	3051	5
done	5001	5

prune148.0ms

Filtered

44 candidates to 62 candidates (-40.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	62	14	76

Merged error: 0.2b

Counts

76 → 14

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin x)
0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
2.6b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-l`
4×	`div-exp` `prod-exp`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 94

Calls

4 calls:

2.0ms	(sin x)
5.0ms	(/ 1 (sin x))
11.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
4.0ms	(- 1.0 (cos x))

series20.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin x)
5.0ms	(/ 1 (sin x))
10.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

simplify1.3min

Counts

106 → 106

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	9
1	15	9
2	25	7
3	60	7
4	102	7
5	129	7
6	151	7
7	156	7
8	157	7
done	157	7
0	9	10
1	13	9
2	14	9
done	14	9
0	10	11
1	17	10
2	28	9
3	37	9
4	55	9
5	81	9
6	84	9
7	93	9
8	111	9
done	111	9
0	11	12
1	20	11
2	28	9
3	45	9
4	63	9
5	88	9
6	93	9
7	102	9
8	116	9
done	116	9
0	10	11
1	19	10
2	26	9
3	37	9
4	49	9
5	81	9
6	100	9
7	107	9
8	117	9
done	117	9
0	9	10
1	19	10
2	35	8
3	76	8
4	136	8
5	178	8
6	233	8
7	243	8
8	251	8
done	251	8
0	9	10
1	18	10
2	39	8
3	92	8
4	193	8
5	356	8
6	863	8
7	3112	8
done	5000	8
0	14	29
1	32	25
2	91	11
3	352	11
4	1235	11
5	4515	9
done	5001	9
0	12	29
1	29	29
2	91	13
3	304	13
4	1103	9
5	4248	9
done	5000	9
0	10	21
1	17	21
2	27	17
3	62	17
4	104	17
5	131	17
6	153	17
7	158	17
8	159	17
done	159	17
0	9	10
1	16	10
2	26	8
3	61	8
4	105	8
5	132	8
6	154	8
7	159	8
8	160	8
done	160	8
0	10	29
1	27	29
2	106	9
3	467	9
4	1616	9
5	4522	9
done	5000	9
0	9	10
1	16	10
2	26	8
3	61	8
4	105	8
5	132	8
6	154	8
7	159	8
8	160	8
done	160	8
0	9	10
1	16	10
2	26	8
3	61	8
4	105	8
5	132	8
6	154	8
7	159	8
8	160	8
done	160	8
0	9	10
1	27	8
2	58	8
3	143	8
4	377	8
5	997	8
6	3719	8
done	5001	8
0	10	17
1	18	14
2	40	14
3	74	14
4	89	14
5	91	14
done	91	14
0	8	11
1	16	9
2	36	9
3	93	9
4	183	9
5	240	9
6	340	9
7	565	9
8	2001	9
done	5000	9
0	6	7
1	8	7
2	16	7
done	16	7
0	10	11
1	15	11
2	16	11
done	16	11
0	10	11
1	15	11
2	16	11
done	16	11
0	11	12
1	18	11
2	22	11
3	26	9
4	37	9
done	37	9
0	11	12
1	18	11
2	22	11
3	26	9
4	37	9
done	37	9
0	10	11
1	17	11
2	21	9
3	36	9
4	39	9
done	39	9
0	10	11
1	17	11
2	21	9
3	36	9
4	39	9
done	39	9
0	10	16
1	17	16
2	26	16
3	43	16
4	57	16
5	67	16
done	67	16
0	9	10
1	14	10
2	21	10
3	26	10
4	30	10
done	30	10
0	12	18
1	25	16
2	61	14
3	142	12
4	253	12
5	323	12
6	412	12
7	435	12
8	451	12
done	451	12
0	11	14
1	20	12
2	37	10
3	78	8
4	144	8
5	184	8
6	208	8
7	213	8
8	214	8
done	214	8
0	9	12
1	18	8
2	40	6
3	58	4
4	73	4
5	82	4
6	91	4
7	105	4
8	106	4
done	106	4
0	11	15
1	20	14
2	38	14
3	86	12
4	194	12
5	282	12
6	365	12
7	386	12
8	393	12
done	393	12
0	10	11
1	17	10
2	27	10
3	51	8
4	99	8
5	126	8
6	148	8
7	153	8
8	154	8
done	154	8
0	8	9
1	15	6
2	27	4
3	45	4
4	56	4
5	65	4
6	74	4
7	88	4
8	89	4
done	89	4
0	10	14
1	19	14
2	36	12
3	101	12
4	206	12
5	281	12
6	363	12
7	385	12
8	392	12
done	392	12
0	9	10
1	16	10
2	26	8
3	61	8
4	105	8
5	132	8
6	154	8
7	159	8
8	160	8
done	160	8
0	7	8
1	14	6
2	26	4
3	44	4
4	55	4
5	64	4
6	73	4
7	87	4
8	88	4
done	88	4
0	6	6
1	11	4
2	21	4
3	32	4
4	41	4
5	47	4
done	47	4
0	6	6
1	11	4
2	21	4
3	32	4
4	41	4
5	47	4
done	47	4
0	9	10
1	16	10
2	20	8
3	35	8
4	38	8
done	38	8
0	9	10
1	16	10
2	20	8
3	35	8
4	38	8
done	38	8
0	8	9
1	15	9
2	25	7
3	60	7
4	102	7
5	129	7
6	151	7
7	156	7
8	157	7
done	157	7
0	10	11
1	17	11
2	27	9
3	62	9
4	104	9
5	132	9
6	154	9
7	159	9
8	160	9
done	160	9
0	8	9
1	15	9
2	25	7
3	60	7
4	102	7
5	129	7
6	151	7
7	156	7
8	157	7
done	157	7
0	6	6
1	11	4
2	21	4
3	32	4
4	41	4
5	47	4
done	47	4
0	11	13
1	31	13
2	62	11
3	179	11
4	540	11
5	1955	11
done	5001	11
0	10	14
1	20	14
2	42	12
3	144	12
4	370	12
5	756	12
6	1060	12
7	1593	12
8	4751	12
done	5000	12
0	2	2
1	5	1
done	5	1
0	4	4
done	4	4
0	5	5
1	7	4
2	11	4
3	13	4
4	19	4
5	24	4
done	24	4
0	6	6
1	10	5
2	11	4
3	17	4
4	23	4
5	28	4
done	28	4
0	5	5
1	11	4
2	12	4
3	16	4
4	18	4
5	24	4
6	29	4
done	29	4
0	5	5
1	7	5
done	7	5
0	8	14
1	18	10
2	30	6
3	53	6
4	80	6
5	106	6
6	177	6
7	393	6
8	1321	6
done	5000	6
0	6	11
1	8	11
done	8	11
0	5	5
1	7	5
done	7	5
0	6	14
1	15	14
2	31	6
3	68	6
4	84	6
5	114	6
6	177	6
7	338	6
8	826	6
9	2851	6
done	5000	6
0	5	5
1	7	5
done	7	5
0	5	5
1	7	5
done	7	5
0	2	2
1	5	1
done	5	1
0	3	3
done	3	3
0	8	13
1	16	11
2	25	9
3	31	9
done	31	9
0	6	6
1	8	5
done	8	5
0	7	9
1	11	7
2	13	5
3	14	5
done	14	5
0	6	6
1	8	5
done	8	5
0	4	7
1	8	3
2	12	1
done	12	1
0	5	5
1	7	4
done	7	4
0	7	10
1	11	9
done	11	9
0	6	6
1	8	5
done	8	5
0	6	6
1	8	5
done	8	5
0	6	6
1	8	5
done	8	5
0	3	4
1	5	1
done	5	1
0	5	5
1	7	4
done	7	4
0	6	9
1	10	9
done	10	9
0	5	5
1	7	5
done	7	5
0	5	5
1	7	5
done	7	5
0	5	5
1	7	5
done	7	5
0	2	3
1	4	1
done	4	1
0	4	4
1	6	4
done	6	4
0	4	4
1	6	4
done	6	4
0	4	4
1	6	2
2	8	2
done	8	2
0	6	9
1	10	9
done	10	9
0	5	5
1	7	5
done	7	5
0	2	3
1	4	1
done	4	1
0	5	5
1	7	4
done	7	4
0	5	5
1	7	4
done	7	4
0	4	4
1	6	2
2	8	2
done	8	2
0	3	3
done	3	3
0	3	3
done	3	3
0	4	7
done	4	7
0	3	3
done	3	3
0	4	8
1	5	8
2	7	4
3	12	4
4	18	4
5	28	4
6	49	4
7	108	4
8	316	4
9	1236	4
done	5000	4
0	3	3
done	3	3
0	3	3
done	3	3
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	13	15
1	32	15
2	66	15
3	114	15
4	209	15
5	504	15
6	1563	15
done	5000	15
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	11	13
1	27	13
2	51	13
3	78	13
4	129	13
5	277	13
6	807	13
7	3108	13
done	5000	13
0	4	4
1	6	4
done	6	4
0	4	4
1	6	4
done	6	4
0	11	13
1	30	13
2	72	13
3	158	13
4	345	13
5	852	13
6	2834	13
done	5001	13
0	2	2
done	2	2
0	2	2
done	2	2

prune134.0ms

Filtered

64 candidates to 106 candidates (-65.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	5	7	12
Picked	1	0	1
Done	0	1	1
Total	107	13	120

Merged error: 0.2b

Counts

120 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ (cos x) 1.0))
0.3b	(pow (cos x) 3)
0.3b	(+ (cos x) 1.0)
2.4b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

11.0ms	(* (cos x) (+ (cos x) 1.0))
3.0ms	(pow (cos x) 3)
5.0ms	(+ (cos x) 1.0)
13.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series22.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (cos x) (+ (cos x) 1.0))
6.0ms	(pow (cos x) 3)
2.0ms	(+ (cos x) 1.0)
9.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify4.5min

Counts

104 → 104

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	24	9
2	50	9
3	111	9
4	306	9
5	1069	9
done	5000	9
0	8	9
1	23	9
2	45	9
3	82	9
4	176	9
5	520	9
6	2326	9
done	5001	9
0	8	9
1	26	9
2	62	9
3	134	9
4	366	9
5	1490	9
done	5000	9
0	9	19
1	24	19
2	46	19
3	80	19
4	172	19
5	498	19
6	2272	19
done	5000	19
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	26
1	25	26
2	60	10
3	230	10
4	1413	10
done	5001	10
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	8	9
1	23	9
2	45	9
3	79	9
4	169	9
5	502	9
6	2259	9
done	5000	9
0	8	14
1	15	11
2	23	11
3	26	11
4	27	11
done	27	11
0	4	4
1	6	4
2	7	4
done	7	4
0	9	12
1	34	12
2	134	12
3	525	12
4	2010	12
done	5000	12
0	11	26
1	35	17
2	121	17
3	358	17
4	972	17
5	3415	15
done	5001	15
0	5	5
1	13	5
2	28	5
3	49	5
4	91	5
5	224	5
6	741	5
7	3056	5
done	5000	5
0	9	17
1	31	8
2	85	8
3	233	8
4	806	8
5	3520	8
done	5000	8
0	7	8
1	21	8
2	30	8
3	47	8
4	88	8
5	210	8
6	614	8
7	2450	8
done	5000	8
0	9	10
1	23	10
2	32	10
3	50	10
4	89	10
5	206	10
6	616	10
7	2429	10
done	5001	10
0	9	10
1	24	10
2	46	10
3	81	10
4	171	10
5	509	10
6	2263	10
done	5001	10
0	9	10
1	23	10
2	32	10
3	50	10
4	89	10
5	206	10
6	616	10
7	2429	10
done	5001	10
0	9	10
1	24	10
2	46	10
3	81	10
4	171	10
5	509	10
6	2263	10
done	5001	10
0	9	10
1	23	10
2	33	10
3	50	10
4	89	10
5	202	10
6	610	10
7	2426	10
done	5000	10
0	9	10
1	24	10
2	35	10
3	52	10
4	91	10
5	200	10
6	605	10
7	2448	10
done	5000	10
0	10	11
1	21	9
2	31	9
3	47	9
4	85	9
5	200	9
6	608	9
7	2435	9
done	5001	9
0	10	11
1	21	9
2	38	9
3	73	9
4	163	9
5	499	9
6	2281	9
done	5000	9
0	9	10
1	23	10
2	32	10
3	50	10
4	89	10
5	206	10
6	616	10
7	2429	10
done	5001	10
0	9	10
1	24	10
2	46	10
3	81	10
4	171	10
5	509	10
6	2263	10
done	5001	10
0	9	10
1	23	10
2	32	10
3	50	10
4	89	10
5	206	10
6	616	10
7	2429	10
done	5001	10
0	9	10
1	24	10
2	46	10
3	81	10
4	171	10
5	509	10
6	2263	10
done	5001	10
0	9	10
1	23	10
2	33	10
3	50	10
4	89	10
5	202	10
6	610	10
7	2426	10
done	5000	10
0	9	10
1	24	10
2	35	10
3	52	10
4	91	10
5	200	10
6	605	10
7	2448	10
done	5000	10
0	10	11
1	21	9
2	31	9
3	47	9
4	85	9
5	200	9
6	608	9
7	2435	9
done	5001	9
0	10	11
1	21	9
2	38	9
3	73	9
4	163	9
5	499	9
6	2281	9
done	5000	9
0	9	10
1	23	10
2	33	10
3	51	10
4	92	10
5	210	10
6	618	10
7	2456	10
done	5001	10
0	9	10
1	24	10
2	44	10
3	73	10
4	138	10
5	329	10
6	1059	10
7	4329	10
done	5001	10
0	9	10
1	23	10
2	33	10
3	51	10
4	92	10
5	210	10
6	618	10
7	2456	10
done	5001	10
0	9	10
1	24	10
2	44	10
3	73	10
4	138	10
5	329	10
6	1059	10
7	4329	10
done	5001	10
0	9	10
1	23	10
2	34	10
3	51	10
4	92	10
5	204	10
6	606	10
7	2443	10
done	5000	10
0	9	10
1	24	10
2	36	10
3	53	10
4	94	10
5	210	10
6	619	10
7	2445	10
done	5000	10
0	10	11
1	21	9
2	32	9
3	48	9
4	90	9
5	211	9
6	620	9
7	2426	9
done	5000	9
0	10	11
1	21	9
2	37	9
3	65	9
4	127	9
5	316	9
6	1033	9
7	4258	9
done	5000	9
0	10	11
1	21	9
2	31	9
3	48	9
4	88	9
5	203	9
6	611	9
7	2444	9
done	5001	9
0	10	11
1	21	9
2	45	9
3	79	9
4	164	9
5	496	9
6	2241	9
done	5001	9
0	10	11
1	21	9
2	31	9
3	48	9
4	88	9
5	203	9
6	611	9
7	2444	9
done	5001	9
0	10	11
1	21	9
2	45	9
3	79	9
4	164	9
5	496	9
6	2241	9
done	5001	9
0	10	11
1	21	9
2	32	9
3	48	9
4	86	9
5	200	9
6	609	9
7	2441	9
done	5000	9
0	10	11
1	21	9
2	34	9
3	50	9
4	90	9
5	198	9
6	603	9
7	2428	9
done	5001	9
0	9	12
1	16	8
2	25	8
3	43	8
4	84	8
5	195	8
6	611	8
7	2463	8
done	5001	8
0	9	12
1	18	8
2	34	8
3	64	8
4	151	8
5	482	8
6	2285	8
done	5000	8
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	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	500	8
6	2253	8
done	5001	8
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	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	500	8
6	2253	8
done	5001	8
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	5	5
1	13	5
2	28	5
3	49	5
4	91	5
5	224	5
6	741	5
7	3056	5
done	5000	5
0	6	6
1	9	5
2	10	5
done	10	5
0	5	5
1	6	5
done	6	5
0	5	5
1	9	5
2	10	5
done	10	5
0	6	11
1	7	11
done	7	11
0	5	5
1	6	5
done	6	5
0	6	14
1	20	14
2	52	6
3	117	6
4	276	6
5	847	6
6	1937	6
7	2715	6
8	3202	6
9	4284	6
done	5001	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	7	8
1	21	8
2	30	8
3	47	8
4	88	8
5	201	8
6	602	8
7	2456	8
done	5000	8
0	8	14
1	16	12
2	31	12
3	44	11
4	64	11
5	85	11
6	102	11
7	135	11
8	190	11
9	222	11
done	222	11
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	1627	9
done	5000	9
0	4	4
1	6	4
2	7	4
done	7	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	3	3
1	6	1
done	6	1
0	6	8
1	10	8
2	17	8
3	41	8
4	97	8
5	255	8
6	872	8
7	3300	8
done	5000	8
0	5	5
1	9	5
2	14	5
3	32	5
4	71	5
5	175	5
6	548	5
7	2169	5
done	5000	5
0	4	4
1	11	2
2	18	2
3	29	2
4	51	2
5	112	2
6	321	2
7	1250	2
done	5000	2
0	6	9
1	16	9
2	37	5
3	70	5
4	145	5
5	372	5
6	1199	5
done	5000	5
0	5	5
1	13	2
2	19	2
3	29	2
4	50	2
5	108	2
6	312	2
7	1238	2
done	5000	2
0	5	5
1	13	5
2	19	5
3	30	5
4	51	5
5	112	5
6	322	5
7	1253	5
done	5000	5
0	5	5
1	13	5
2	19	5
3	30	5
4	51	5
5	112	5
6	322	5
7	1253	5
done	5000	5
0	3	3
1	13	1
done	13	1
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	3	5
done	3	5
0	5	5
1	15	5
2	27	5
3	42	5
4	82	5
5	194	5
6	565	5
7	2161	5
done	5000	5
0	5	5
1	13	5
2	25	5
3	47	5
4	97	5
5	255	5
6	808	5
7	3372	5
done	5000	5
0	6	11
1	13	5
2	19	5
3	29	5
4	50	5
5	110	5
6	319	5
7	1251	5
done	5001	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	6	14
1	18	9
2	57	6
3	165	6
4	517	6
5	1868	4
done	5001	4
0	6	9
1	16	9
2	37	5
3	70	5
4	145	5
5	372	5
6	1199	5
done	5000	5
0	5	5
1	13	2
2	19	2
3	29	2
4	50	2
5	108	2
6	312	2
7	1238	2
done	5000	2
0	5	5
1	13	5
2	19	5
3	30	5
4	51	5
5	112	5
6	322	5
7	1253	5
done	5000	5
0	5	5
1	13	5
2	19	5
3	30	5
4	51	5
5	112	5
6	322	5
7	1253	5
done	5000	5
0	3	3
1	13	1
done	13	1
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	3	5
done	3	5
0	5	5
1	13	5
2	20	5
3	30	5
4	51	5
5	113	5
6	323	5
7	1246	5
done	5000	5
0	5	5
1	13	5
2	20	5
3	30	5
4	51	5
5	113	5
6	323	5
7	1246	5
done	5000	5
0	6	6
1	11	4
2	17	4
3	27	4
4	50	4
5	112	4
6	329	4
7	1255	4
done	5001	4
0	6	6
1	11	4
2	17	4
3	27	4
4	50	4
5	112	4
6	329	4
7	1255	4
done	5001	4
0	5	7
1	12	7
2	13	7
done	13	7
0	7	9
1	9	9
done	9	9
0	6	8
1	16	8
2	18	8
done	18	8
0	6	8
1	15	8
2	25	8
3	40	8
4	70	8
5	164	8
6	405	8
7	1281	8
done	5000	8
0	9	23
1	29	23
2	107	11
3	319	11
4	1028	9
5	3569	9
done	5000	9
0	7	17
1	14	17
2	15	17
done	15	17
0	6	8
1	13	8
2	14	8
done	14	8
0	7	23
1	23	23
2	90	9
3	287	9
4	735	9
5	2081	9
done	5000	9
0	6	8
1	13	8
2	14	8
done	14	8
0	6	8
1	13	8
2	14	8
done	14	8
0	7	9
1	9	9
done	9	9
0	7	9
1	9	9
done	9	9
0	3	5
done	3	5
0	4	4
1	5	4
done	5	4
0	3	5
done	3	5
0	4	4
1	5	4
done	5	4
0	7	14
1	11	14
2	13	14
done	13	14
0	6	8
1	8	8
done	8	8
0	4	4
1	7	2
2	10	2
done	10	2
0	4	4
1	7	2
2	10	2
done	10	2
0	6	8
1	14	8
2	15	8
done	15	8
0	6	8
1	14	8
2	15	8
done	15	8
0	5	7
1	12	7
2	13	7
done	13	7
0	8	11
1	29	11
2	60	11
3	104	11
4	203	11
5	530	11
6	1809	11
done	5000	11
0	7	12
1	13	12
2	30	12
3	70	12
4	142	11
5	238	11
6	435	11
7	1135	11
done	5000	11
0	15	17
1	35	17
2	92	17
3	193	17
4	496	17
5	1268	17
6	3918	17
done	5000	17
0	6	6
1	16	6
2	32	6
3	53	6
4	95	6
5	229	6
6	746	6
7	3067	6
done	5000	6
0	6	6
1	16	6
2	32	6
3	53	6
4	95	6
5	229	6
6	746	6
7	3067	6
done	5000	6
0	12	13
1	27	13
2	74	13
3	119	13
4	163	13
5	209	13
6	331	13
7	786	13
8	2600	13
done	5000	13
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	12	13
1	28	13
2	74	13
3	187	13
4	552	13
5	1273	13
6	4407	13
done	5001	13
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	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	12	13
1	27	13
2	74	13
3	119	13
4	163	13
5	209	13
6	330	13
7	779	13
8	2603	13
done	5000	13
0	5	7
1	12	7
2	13	7
done	13	7
0	5	7
1	12	7
2	13	7
done	13	7

prune174.0ms

Filtered

69 candidates to 104 candidates (-50.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	103	14	117

Merged error: 0.1b

Counts

117 → 14

regimes199.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.9b

bsearch42.0ms

Steps

Iters	Range		Point
9	2.685778245287387e-07	280.39199233801065	0.023225148427654944
8	-1.1417122487016937	-0.00029558442529086166	-0.023111695854390213

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	59
1	50	59
done	50	59

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.3s	1608×	body	2560	valid
1.4s	2794×	body	1280	valid
507.0ms	1860×	body	640	valid
172.0ms	912×	body	320	valid
69.0ms	467×	body	160	valid
26.0ms	354×	body	80	valid
13.0ms	5×	body	5120	valid

Details

sample177.0ms

simplify6.0ms

prune3.0ms

localize7.0ms

rewrite15.0ms

series15.0ms

simplify30.3s

prune151.0ms

localize10.0ms

rewrite15.0ms

series12.0ms

simplify4.6min

prune148.0ms

localize9.0ms

rewrite25.0ms

series20.0ms

simplify1.3min

prune134.0ms

localize16.0ms

rewrite35.0ms

series22.0ms

simplify4.5min

prune174.0ms

regimes199.0ms

bsearch42.0ms

simplify4.0ms

end0.0ms

sample4.7s

Profiling