Details

sample103.0ms

Algorithm

intervals

Results

58.0ms	107×	body	1280	valid
16.0ms	56×	body	640	valid
5.0ms	68×	body	80	valid
5.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

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: 17.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin b)
0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 74

Calls

4 calls:

2.0ms	(sin b)
8.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
5.0ms	(cos (+ a b))

series56.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
34.0ms	(* r (/ (sin b) (cos (+ a b))))
13.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify47.8s

Counts

86 → 86

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
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	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	9
2	12	9
done	12	9
0	7	8
1	11	8
2	13	8
3	14	8
done	14	8
0	7	8
1	8	8
done	8	8
0	10	23
1	20	23
2	52	11
3	119	9
4	198	9
5	316	9
6	777	9
7	3364	9
done	5000	9
0	8	17
1	9	17
done	9	17
0	7	8
1	8	8
done	8	8
0	8	23
1	16	23
2	32	9
3	70	9
4	137	9
5	201	9
6	327	9
7	828	9
8	3580	9
done	5000	9
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	3	3
done	3	3
0	5	5
1	6	5
done	6	5
0	10	19
1	17	19
2	26	19
3	32	19
done	32	19
0	8	9
1	9	9
done	9	9
0	9	13
1	12	13
2	14	13
3	15	13
done	15	13
0	8	9
1	9	9
done	9	9
0	6	9
1	10	7
2	16	7
3	21	7
done	21	7
0	7	8
1	8	8
done	8	8
0	9	15
1	12	15
done	12	15
0	8	9
1	9	9
done	9	9
0	8	9
1	9	9
done	9	9
0	8	9
1	9	9
done	9	9
0	5	5
1	7	3
2	9	3
done	9	3
0	7	8
1	8	8
done	8	8
0	8	13
1	13	13
done	13	13
0	7	8
1	8	8
done	8	8
0	7	7
1	10	7
done	10	7
0	7	8
1	8	8
done	8	8
0	2	3
1	4	1
done	4	1
0	6	7
1	7	7
done	7	7
0	6	6
1	9	6
done	9	6
0	6	7
1	7	7
done	7	7
0	8	14
1	11	14
done	11	14
0	7	8
1	8	8
done	8	8
0	4	4
1	6	2
2	8	2
done	8	2
0	7	8
1	8	8
done	8	8
0	7	8
1	8	8
done	8	8
0	6	7
1	7	7
done	7	7
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9
0	11	12
1	17	12
2	24	12
3	33	12
4	39	12
5	49	12
6	56	12
7	68	12
8	91	12
9	105	12
10	111	12
done	111	12
0	10	11
1	15	11
2	21	11
3	30	11
4	40	11
5	49	11
6	54	11
7	63	11
8	80	11
9	99	11
10	107	11
done	107	11
0	9	10
1	16	10
2	25	10
3	39	10
4	59	10
5	72	10
6	84	10
7	102	10
8	118	10
9	125	10
10	142	10
11	144	10
done	144	10
0	9	10
1	15	10
2	24	10
3	38	10
4	71	10
5	154	10
6	364	10
7	1385	10
done	5000	10
0	14	29
1	30	29
2	108	15
3	453	13
4	1720	13
done	5000	13
0	12	29
1	26	29
2	75	13
3	229	13
4	780	11
5	2445	11
done	5000	11
0	10	21
1	14	21
2	17	21
3	21	21
4	22	21
done	22	21
0	9	10
1	13	10
2	16	10
3	20	10
4	21	10
done	21	10
0	10	29
1	24	29
2	78	11
3	281	11
4	852	11
5	2536	11
done	5000	11
0	9	10
1	13	10
2	16	10
3	20	10
4	21	10
done	21	10
0	9	10
1	13	10
2	16	10
3	20	10
4	21	10
done	21	10
0	10	11
1	12	11
done	12	11
0	10	11
1	12	11
done	12	11
0	11	12
1	15	12
2	18	12
3	22	12
4	23	12
done	23	12
0	11	12
1	15	12
2	18	12
3	22	12
4	23	12
done	23	12
0	10	19
1	14	19
2	16	19
done	16	19
0	9	10
1	11	10
done	11	10
0	12	21
1	22	21
2	51	21
3	90	21
4	146	21
5	160	21
done	160	21
0	11	15
1	17	15
2	27	15
3	42	15
4	55	15
5	57	15
done	57	15
0	8	11
1	15	9
2	32	9
3	69	9
4	103	9
done	103	9
0	11	17
1	17	17
2	28	17
3	41	17
4	53	17
done	53	17
0	10	11
1	14	11
2	17	11
3	21	11
4	22	11
done	22	11
0	7	7
1	12	5
2	19	5
3	28	5
4	34	5
done	34	5
0	10	15
1	18	15
2	28	13
3	36	13
4	56	13
5	87	13
6	92	13
done	92	13
0	9	9
1	15	9
2	18	7
3	19	7
4	24	7
5	25	7
done	25	7
0	4	5
1	9	3
2	14	1
done	14	1
0	3	3
1	6	1
done	6	1
0	4	4
1	5	4
done	5	4
0	9	10
1	13	10
2	16	10
3	20	10
4	21	10
done	21	10
0	9	10
1	13	10
2	16	10
3	20	10
4	21	10
done	21	10
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9
0	4	4
1	5	4
done	5	4
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	10	11
1	23	11
2	45	11
3	104	9
4	240	9
5	627	9
6	2147	9
done	5001	9
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	11	13
1	28	13
2	74	13
3	106	11
4	174	11
5	342	11
6	897	11
7	3244	11
done	5000	11
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	15	19
1	39	19
2	101	19
3	205	17
4	379	13
5	788	13
6	2136	13
done	5001	13
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9
0	11	13
1	30	13
2	72	13
3	158	13
4	346	13
5	880	13
6	3259	13
done	5000	13
0	2	2
done	2	2
0	2	2
done	2	2

prune147.0ms

Filtered

70 candidates to 86 candidates (-22.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	11	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	11	87

Merged error: 0.2b

Counts

87 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

6.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
10.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
6.0ms	(* (sin a) (sin b))

series126.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))

simplify2.1min

Counts

112 → 112

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
2	14	9
done	14	9
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	12	16
1	18	16
2	26	16
done	26	16
0	11	15
1	18	15
2	27	15
3	28	15
done	28	15
0	11	15
1	15	15
2	22	15
done	22	15
0	14	44
1	27	44
2	78	18
3	234	16
4	735	16
5	2710	16
done	5000	16
0	12	31
1	16	31
2	23	31
done	23	31
0	11	15
1	15	15
2	22	15
done	22	15
0	12	44
1	23	44
2	46	16
3	90	16
4	202	16
5	571	16
6	2032	16
done	5001	15
0	11	15
1	15	15
2	22	15
done	22	15
0	11	15
1	15	15
2	22	15
done	22	15
0	3	3
done	3	3
0	10	12
1	14	12
2	24	12
3	40	12
4	51	11
done	51	11
0	14	33
1	24	33
2	40	33
3	46	33
done	46	33
0	12	16
1	16	16
2	23	16
done	23	16
0	13	20
1	19	20
2	28	20
3	29	20
done	29	20
0	12	16
1	16	16
2	23	16
done	23	16
0	6	9
1	10	7
2	16	7
3	21	7
done	21	7
0	11	15
1	15	15
2	22	15
done	22	15
0	13	29
1	19	29
2	26	29
done	26	29
0	12	16
1	16	16
2	23	16
done	23	16
0	12	16
1	16	16
2	23	16
done	23	16
0	12	16
1	16	16
2	23	16
done	23	16
0	5	5
1	7	3
2	9	3
done	9	3
0	11	15
1	15	15
2	22	15
done	22	15
0	13	27
1	21	27
2	28	27
done	28	27
0	11	15
1	15	15
2	22	15
done	22	15
0	12	14
1	18	14
2	25	14
done	25	14
0	11	15
1	15	15
2	22	15
done	22	15
0	2	3
1	4	1
done	4	1
0	10	14
1	14	14
2	21	14
done	21	14
0	11	13
1	17	13
2	24	13
done	24	13
0	10	14
1	17	14
2	34	14
3	46	13
4	65	11
5	226	11
6	1166	11
7	4142	11
done	5000	11
0	12	28
1	18	28
2	25	28
done	25	28
0	11	15
1	15	15
2	22	15
done	22	15
0	4	4
1	6	2
2	8	2
done	8	2
0	11	15
1	18	15
2	35	15
3	47	15
4	65	15
5	71	15
done	71	15
0	11	15
1	18	15
2	35	15
3	47	15
4	65	15
5	71	15
done	71	15
0	10	14
1	17	14
2	34	14
3	46	13
4	65	11
5	226	11
6	1166	11
7	4142	11
done	5000	11
0	11	22
1	23	22
2	44	22
3	82	14
4	114	9
5	483	9
6	2729	9
done	5000	9
0	14	26
1	24	26
2	48	24
3	94	24
4	209	24
5	309	11
6	419	9
7	2195	9
done	5000	9
0	13	18
1	36	18
2	120	18
3	382	18
4	910	18
5	2378	18
done	5001	18
0	12	26
1	33	26
2	76	26
3	138	26
4	205	26
5	332	26
6	512	26
7	874	26
8	2671	26
done	5000	26
0	12	16
1	19	16
2	29	16
3	36	16
4	50	16
5	72	15
6	103	13
7	338	13
8	2037	13
done	5000	13
0	15	19
1	24	19
2	38	19
3	47	19
4	53	19
5	63	19
6	70	19
7	82	19
8	105	19
9	119	19
10	125	19
done	125	19
0	14	18
1	22	18
2	35	18
3	44	18
4	54	18
5	63	18
6	68	18
7	77	18
8	94	18
9	113	18
10	121	18
done	121	18
0	13	17
1	23	17
2	39	17
3	56	17
4	89	17
5	124	16
6	167	14
7	420	14
8	2126	14
done	5000	14
0	13	17
1	22	17
2	38	17
3	55	17
4	109	17
5	245	16
6	547	14
7	1867	14
done	5000	14
0	18	50
1	37	50
2	134	22
3	562	20
4	2258	20
done	5000	20
0	16	50
1	33	50
2	89	20
3	250	20
4	855	18
5	3066	17
done	5000	17
0	14	35
1	21	35
2	31	35
3	38	35
4	52	35
5	74	33
6	105	29
7	340	29
8	2043	29
done	5001	29
0	13	17
1	20	17
2	30	17
3	37	17
4	51	17
5	73	16
6	104	14
7	339	14
8	2047	14
done	5000	14
0	14	50
1	31	50
2	92	18
3	293	18
4	885	18
5	3101	17
done	5001	17
0	13	17
1	20	17
2	30	17
3	37	17
4	51	17
5	73	16
6	104	14
7	339	14
8	2047	14
done	5000	14
0	13	17
1	20	17
2	30	17
3	37	17
4	51	17
5	73	16
6	104	14
7	339	14
8	2047	14
done	5000	14
0	14	18
1	19	18
2	26	18
done	26	18
0	14	18
1	19	18
2	26	18
done	26	18
0	15	19
1	22	19
2	32	19
3	36	19
4	37	19
done	37	19
0	15	19
1	22	19
2	32	19
3	36	19
4	37	19
done	37	19
0	14	33
1	21	33
2	30	33
done	30	33
0	13	17
1	18	17
2	25	17
done	25	17
0	16	35
1	29	35
2	65	35
3	106	35
4	162	35
5	176	35
done	176	35
0	15	22
1	24	22
2	41	22
3	56	22
4	69	22
5	71	22
done	71	22
0	8	11
1	15	9
2	32	9
3	69	9
4	103	9
done	103	9
0	15	31
1	24	31
2	42	31
3	55	31
4	67	31
done	67	31
0	14	18
1	21	18
2	31	18
3	35	18
4	36	18
done	36	18
0	7	7
1	12	5
2	19	5
3	28	5
4	34	5
done	34	5
0	15	29
1	26	29
2	43	27
3	50	27
4	68	27
5	101	27
6	104	27
done	104	27
0	14	16
1	23	16
2	33	14
3	34	14
4	39	14
5	40	14
done	40	14
0	4	5
1	9	3
2	14	1
done	14	1
0	3	3
1	6	1
done	6	1
0	4	4
1	5	4
done	5	4
0	13	24
1	28	24
2	52	24
3	100	16
4	164	11
5	606	11
6	3287	11
done	5001	11
0	16	28
1	29	28
2	56	26
3	117	26
4	271	26
5	489	13
6	900	11
7	4549	11
done	5000	11
0	15	20
1	41	20
2	128	20
3	404	20
4	1077	20
5	3467	20
done	5001	20
0	14	28
1	38	28
2	89	28
3	175	28
4	299	28
5	592	27
6	1180	25
7	2984	25
done	5000	25
0	13	17
1	20	17
2	30	17
3	37	17
4	51	17
5	73	16
6	104	14
7	339	14
8	2039	14
done	5001	14
0	13	17
1	20	17
2	30	17
3	37	17
4	51	17
5	73	16
6	104	14
7	339	14
8	2039	14
done	5001	14
0	12	16
1	19	16
2	29	16
3	36	16
4	50	16
5	72	15
6	103	13
7	338	13
8	2037	13
done	5000	13
0	4	4
1	5	4
done	5	4
0	11	13
1	19	12
2	32	12
3	63	12
4	162	12
5	608	12
6	3916	12
done	5000	12
0	10	12
1	14	12
2	21	12
done	21	12
0	10	12
1	17	12
2	34	12
3	56	12
4	122	12
5	458	12
6	2445	12
done	5000	12
0	11	25
1	15	25
2	22	25
done	22	25
0	10	12
1	14	12
2	21	12
done	21	12
0	11	35
1	16	35
2	37	13
3	128	13
4	513	13
5	1944	13
done	5000	13
0	10	12
1	14	12
2	21	12
done	21	12
0	10	12
1	14	12
2	21	12
done	21	12
0	9	19
1	21	19
2	42	19
3	80	11
4	112	6
5	481	6
6	2716	6
done	5001	6
0	12	23
1	22	23
2	46	21
3	90	21
4	201	21
5	307	8
6	416	6
7	2172	6
done	5000	6
0	2	3
1	3	1
done	3	1
0	12	15
1	35	15
2	119	15
3	380	15
4	897	15
5	2392	15
done	5000	15
0	13	35
1	40	29
2	97	29
3	141	29
4	153	29
5	155	29
done	155	29
0	6	6
1	11	6
2	13	6
done	13	6
0	11	23
1	32	23
2	73	23
3	133	23
4	198	23
5	331	23
6	501	23
7	871	23
8	2634	23
done	5000	23
0	9	11
1	12	11
done	12	11
0	6	6
1	11	6
2	13	6
done	13	6
0	3	3
1	4	3
done	4	3
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	11	13
1	28	13
2	74	13
3	106	11
4	174	11
5	342	11
6	897	11
7	3244	11
done	5000	11
0	10	14
1	14	14
2	21	14
done	21	14
0	10	14
1	14	14
2	21	14
done	21	14
0	15	19
1	39	19
2	101	19
3	205	17
4	379	13
5	788	13
6	2136	13
done	5001	13
0	12	16
1	19	16
2	33	16
3	49	16
4	72	15
5	103	13
6	338	13
7	2023	13
done	5000	13
0	12	16
1	19	16
2	33	16
3	49	16
4	72	15
5	103	13
6	338	13
7	2023	13
done	5000	13
0	10	11
1	23	11
2	45	11
3	104	9
4	240	9
5	627	9
6	2147	9
done	5001	9
0	9	11
1	13	11
2	20	11
done	20	11
0	9	11
1	13	11
2	20	11
done	20	11

prune215.0ms

Filtered

95 candidates to 112 candidates (-17.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos b) (cos a))
0.1b	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
0.2b	(/ (* (cos b) (cos a)) (sin b))
0.2b	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

5.0ms	(* (cos b) (cos a))
8.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
9.0ms	(/ (* (cos b) (cos a)) (sin b))
10.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cos b) (cos a))
25.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
17.0ms	(/ (* (cos b) (cos a)) (sin b))
52.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify1.3min

Counts

104 → 104

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	26	15
3	29	15
4	30	15
done	30	15
0	12	14
1	20	14
2	27	14
3	31	14
4	32	14
done	32	14
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	15	41
1	29	41
2	78	17
3	219	15
4	667	15
5	2549	15
done	5000	15
0	13	29
1	18	29
2	23	29
3	26	29
4	27	29
done	27	29
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	13	41
1	25	41
2	46	15
3	93	15
4	216	15
5	635	15
6	2312	15
done	5000	15
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	2	2
done	2	2
0	10	12
1	15	12
2	23	12
3	37	12
4	53	11
5	60	11
done	60	11
0	15	31
1	26	31
2	40	31
3	49	31
4	50	31
done	50	31
0	13	15
1	18	15
2	23	15
3	26	15
4	27	15
done	27	15
0	14	18
1	21	18
2	28	18
3	32	18
4	33	18
done	33	18
0	13	15
1	18	15
2	23	15
3	26	15
4	27	15
done	27	15
0	5	7
1	9	5
2	15	5
3	20	5
done	20	5
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	15	19
1	21	19
2	27	19
3	31	19
4	32	19
done	32	19
0	14	16
1	19	16
2	24	16
3	27	16
4	28	16
done	28	16
0	5	7
1	9	5
2	15	5
3	20	5
done	20	5
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	14	28
1	21	28
2	26	28
3	29	28
4	30	28
done	30	28
0	13	15
1	18	15
2	23	15
3	26	15
4	27	15
done	27	15
0	13	15
1	18	15
2	23	15
3	26	15
4	27	15
done	27	15
0	13	15
1	18	15
2	23	15
3	26	15
4	27	15
done	27	15
0	4	4
1	6	2
2	8	2
done	8	2
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	14	16
1	18	16
2	22	16
3	25	16
4	26	16
done	26	16
0	14	16
1	19	16
2	24	16
3	27	16
4	28	16
done	28	16
0	4	4
1	6	2
2	8	2
done	8	2
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	13	27
1	22	27
2	27	27
3	30	27
4	31	27
done	31	27
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	12	14
1	19	14
2	24	14
3	27	14
4	28	14
done	28	14
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	2	3
1	4	1
done	4	1
0	11	13
1	16	13
2	21	13
3	24	13
4	25	13
done	25	13
0	13	15
1	19	15
2	23	15
3	26	15
4	27	15
done	27	15
0	13	15
1	18	15
2	23	15
3	26	15
4	27	15
done	27	15
0	2	3
1	4	1
done	4	1
0	11	13
1	16	13
2	21	13
3	24	13
4	25	13
done	25	13
0	11	13
1	18	13
2	23	13
3	26	13
4	27	13
done	27	13
0	11	13
1	19	13
2	30	13
3	52	13
4	80	13
5	95	13
done	95	13
0	13	27
1	20	27
2	25	27
3	28	27
4	29	27
done	29	27
0	12	14
1	17	14
2	22	14
3	25	14
4	26	14
done	26	14
0	3	3
1	5	1
done	5	1
0	13	15
1	17	15
2	21	15
3	24	15
4	25	15
done	25	15
0	3	3
1	5	1
done	5	1
0	12	14
1	20	14
2	31	14
3	53	14
4	81	14
5	96	14
done	96	14
0	12	14
1	20	14
2	31	14
3	53	14
4	81	14
5	96	14
done	96	14
0	11	13
1	19	13
2	30	13
3	52	13
4	80	13
5	95	13
done	95	13
0	14	17
1	35	17
2	93	17
3	298	17
4	1284	17
done	5001	17
0	13	25
1	25	25
2	58	25
3	150	25
4	381	25
5	683	25
6	906	25
7	1267	25
8	3093	25
done	5000	25
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	6	10
1	8	10
done	8	10
0	6	6
done	6	6
0	5	6
done	5	6
0	6	6
done	6	6
0	4	4
1	6	2
2	8	2
done	8	2
0	5	5
done	5	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	5	5
done	5	5
0	4	4
1	5	4
done	5	4
0	11	13
1	16	12
2	22	12
3	30	12
4	42	12
5	67	12
6	144	12
7	440	12
8	1175	12
9	3393	12
done	5001	12
0	10	12
1	15	12
2	20	12
3	23	12
4	24	12
done	24	12
0	10	12
1	18	12
2	25	12
3	33	12
4	48	12
5	75	12
6	197	12
7	486	12
8	1235	12
9	3316	12
done	5001	12
0	11	25
1	16	25
2	21	25
3	24	25
4	25	25
done	25	25
0	10	12
1	15	12
2	20	12
3	23	12
4	24	12
done	24	12
0	11	35
1	17	35
2	36	13
3	112	13
4	437	13
5	1736	13
done	5000	13
0	10	12
1	15	12
2	20	12
3	23	12
4	24	12
done	24	12
0	10	12
1	15	12
2	20	12
3	23	12
4	24	12
done	24	12
0	12	15
1	33	15
2	91	15
3	294	15
4	1303	15
done	5001	15
0	13	35
1	29	32
2	71	32
3	170	26
4	375	26
5	578	26
6	625	26
7	634	26
8	637	26
done	637	26
0	3	3
done	3	3
0	11	23
1	23	23
2	54	23
3	144	23
4	375	23
5	690	23
6	895	23
7	1257	23
8	3117	23
done	5000	23
0	9	11
1	13	11
2	17	11
3	20	11
4	21	11
done	21	11
0	11	13
1	15	13
2	19	13
3	22	13
4	23	13
done	23	13
0	11	13
1	16	13
2	21	13
3	24	13
4	25	13
done	25	13
0	9	11
1	14	11
2	19	11
3	22	11
4	23	11
done	23	11
0	3	3
done	3	3
0	7	9
1	11	9
2	12	9
done	12	9
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	15	19
1	39	19
2	101	19
3	205	17
4	379	13
5	788	13
6	2136	13
done	5001	13
0	11	13
1	16	13
2	21	13
3	24	13
4	25	13
done	25	13
0	11	13
1	16	13
2	21	13
3	24	13
4	25	13
done	25	13
0	13	15
1	28	15
2	53	15
3	115	15
4	296	15
5	840	15
6	3535	15
done	5000	15
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	8	9
1	16	9
2	25	9
3	42	9
4	52	9
5	76	9
6	103	9
7	118	9
8	125	9
9	131	9
10	132	9
done	132	9
0	9	11
1	14	11
2	19	11
3	22	11
4	23	11
done	23	11
0	9	11
1	14	11
2	19	11
3	22	11
4	23	11
done	23	11
0	11	13
1	29	11
2	69	11
3	160	11
4	394	11
5	1081	11
6	4173	11
done	5001	11
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5

prune161.0ms

Filtered

79 candidates to 104 candidates (-31.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
0.2b	(* (cos b) (/ (cos a) (sin b)))
0.2b	(/ (cos a) (sin b))
0.2b	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-r` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 100

Calls

4 calls:

7.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
8.0ms	(* (cos b) (/ (cos a) (sin b)))
5.0ms	(/ (cos a) (sin b))
9.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
17.0ms	(* (cos b) (/ (cos a) (sin b)))
12.0ms	(/ (cos a) (sin b))
56.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))

simplify1.1min

Counts

112 → 112

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	25	15
3	29	15
4	30	15
done	30	15
0	12	14
1	20	14
2	26	14
3	31	14
4	32	14
done	32	14
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	15	41
1	29	41
2	77	17
3	217	15
4	664	15
5	2556	15
done	5001	15
0	13	29
1	18	29
2	22	29
3	26	29
4	27	29
done	27	29
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	13	41
1	25	41
2	45	15
3	93	15
4	214	15
5	633	15
6	2305	15
done	5000	15
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	2	2
done	2	2
0	10	12
1	15	12
2	22	12
3	37	12
4	53	11
5	60	11
done	60	11
0	15	31
1	26	31
2	39	31
3	49	31
4	50	31
done	50	31
0	13	15
1	18	15
2	22	15
3	26	15
4	27	15
done	27	15
0	14	18
1	21	18
2	27	18
3	32	18
4	33	18
done	33	18
0	13	15
1	18	15
2	22	15
3	26	15
4	27	15
done	27	15
0	5	7
1	9	5
2	15	5
3	20	5
done	20	5
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	14	28
1	21	28
2	25	28
3	29	28
4	30	28
done	30	28
0	13	15
1	18	15
2	22	15
3	26	15
4	27	15
done	27	15
0	13	15
1	18	15
2	22	15
3	26	15
4	27	15
done	27	15
0	13	15
1	18	15
2	22	15
3	26	15
4	27	15
done	27	15
0	4	4
1	6	2
2	8	2
done	8	2
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	13	27
1	22	27
2	26	27
3	30	27
4	31	27
done	31	27
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	12	14
1	19	14
2	23	14
3	27	14
4	28	14
done	28	14
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	2	3
1	4	1
done	4	1
0	11	13
1	16	13
2	20	13
3	24	13
4	25	13
done	25	13
0	11	13
1	18	13
2	22	13
3	26	13
4	27	13
done	27	13
0	11	13
1	19	13
2	31	13
3	56	13
4	79	13
5	89	13
done	89	13
0	13	27
1	20	27
2	24	27
3	28	27
4	29	27
done	29	27
0	12	14
1	17	14
2	21	14
3	25	14
4	26	14
done	26	14
0	3	3
1	5	1
done	5	1
0	12	14
1	20	14
2	32	14
3	57	14
4	80	14
5	90	14
done	90	14
0	12	14
1	20	14
2	32	14
3	57	14
4	80	14
5	90	14
done	90	14
0	11	13
1	19	13
2	31	13
3	56	13
4	79	13
5	89	13
done	89	13
0	14	17
1	35	17
2	102	17
3	318	17
4	1073	17
5	4029	17
done	5000	17
0	13	25
1	28	25
2	67	25
3	140	25
4	330	25
5	644	25
6	885	25
7	1255	25
8	3062	25
done	5000	25
0	7	7
1	9	7
2	10	7
done	10	7
0	6	6
1	9	6
2	11	6
3	12	6
done	12	6
0	6	6
done	6	6
0	9	17
1	18	17
2	50	9
3	117	7
4	196	7
5	312	7
6	773	7
7	3362	7
done	5000	7
0	7	13
done	7	13
0	6	6
done	6	6
0	7	17
1	14	17
2	30	7
3	68	7
4	133	7
5	197	7
6	323	7
7	822	7
8	3529	7
done	5000	7
0	6	6
done	6	6
0	6	6
done	6	6
0	3	3
done	3	3
0	3	3
done	3	3
0	9	15
1	15	15
2	24	15
3	30	15
done	30	15
0	7	7
done	7	7
0	8	11
1	10	11
2	12	11
3	13	11
done	13	11
0	7	7
done	7	7
0	6	9
1	10	7
2	16	7
3	21	7
done	21	7
0	6	6
done	6	6
0	8	11
1	10	11
done	10	11
0	7	7
done	7	7
0	7	7
done	7	7
0	7	7
done	7	7
0	5	5
1	7	3
2	9	3
done	9	3
0	6	6
done	6	6
0	6	9
1	10	9
done	10	9
0	6	6
done	6	6
0	5	5
1	7	5
done	7	5
0	6	6
done	6	6
0	2	3
1	4	1
done	4	1
0	5	5
done	5	5
0	4	4
1	6	4
done	6	4
0	5	5
done	5	5
0	7	10
1	9	10
done	9	10
0	6	6
done	6	6
0	4	4
1	6	2
2	8	2
done	8	2
0	6	6
done	6	6
0	6	6
done	6	6
0	5	5
done	5	5
0	7	8
1	10	8
2	13	8
3	17	8
4	18	8
done	18	8
0	10	11
1	15	11
2	22	11
3	31	11
4	37	11
5	47	11
6	54	11
7	66	11
8	89	11
9	103	11
10	109	11
done	109	11
0	9	10
1	13	10
2	19	10
3	28	10
4	38	10
5	47	10
6	52	10
7	61	10
8	78	10
9	97	10
10	105	10
done	105	10
0	8	9
1	14	9
2	23	9
3	37	9
4	57	9
5	70	9
6	82	9
7	100	9
8	116	9
9	123	9
10	140	9
11	142	9
done	142	9
0	8	9
1	13	9
2	22	9
3	36	9
4	69	9
5	150	9
6	361	9
7	1385	9
done	5001	9
0	13	26
1	28	26
2	106	14
3	447	12
4	1693	12
done	5000	12
0	11	26
1	24	26
2	73	12
3	226	12
4	780	10
5	2445	10
done	5000	10
0	9	19
1	12	19
2	15	19
3	19	19
4	20	19
done	20	19
0	8	9
1	11	9
2	14	9
3	18	9
4	19	9
done	19	9
0	9	26
1	22	26
2	76	10
3	275	10
4	835	10
5	2533	10
done	5001	10
0	8	9
1	11	9
2	14	9
3	18	9
4	19	9
done	19	9
0	8	9
1	11	9
2	14	9
3	18	9
4	19	9
done	19	9
0	9	10
1	10	10
done	10	10
0	9	10
1	10	10
done	10	10
0	10	11
1	13	11
2	16	11
3	20	11
4	21	11
done	21	11
0	10	11
1	13	11
2	16	11
3	20	11
4	21	11
done	21	11
0	9	16
1	12	16
2	14	16
done	14	16
0	8	9
1	9	9
done	9	9
0	11	18
1	20	18
2	49	18
3	88	18
4	144	18
5	156	18
done	156	18
0	10	14
1	15	14
2	25	14
3	40	14
4	53	14
5	55	14
done	55	14
0	9	12
1	16	10
2	33	10
3	70	10
4	108	10
done	108	10
0	10	14
1	15	14
2	26	14
3	40	14
4	52	14
done	52	14
0	9	10
1	12	10
2	15	10
3	19	10
4	20	10
done	20	10
0	8	8
1	13	6
2	20	6
3	29	6
4	35	6
done	35	6
0	8	12
1	15	12
2	25	10
3	55	10
4	76	10
5	78	10
done	78	10
0	7	8
1	12	8
2	15	6
3	30	6
4	31	6
done	31	6
0	5	6
1	10	4
2	15	2
3	19	2
done	19	2
0	4	4
1	7	2
2	10	2
done	10	2
0	5	5
1	6	5
done	6	5
0	8	9
1	11	9
2	14	9
3	18	9
4	19	9
done	19	9
0	8	9
1	11	9
2	14	9
3	18	9
4	19	9
done	19	9
0	7	8
1	10	8
2	13	8
3	17	8
4	18	8
done	18	8
0	5	5
1	6	5
done	6	5
0	11	13
1	18	12
2	29	12
3	48	12
4	96	12
5	232	12
6	687	12
7	2735	12
done	5000	12
0	10	12
1	15	12
2	19	12
3	23	12
4	24	12
done	24	12
0	10	12
1	18	12
2	28	12
3	42	12
4	75	12
5	168	12
6	497	12
7	1402	12
8	4442	12
done	5000	12
0	11	25
1	16	25
2	20	25
3	24	25
4	25	25
done	25	25
0	10	12
1	15	12
2	19	12
3	23	12
4	24	12
done	24	12
0	11	35
1	17	35
2	35	13
3	110	13
4	433	13
5	1735	13
done	5000	13
0	10	12
1	15	12
2	19	12
3	23	12
4	24	12
done	24	12
0	10	12
1	15	12
2	19	12
3	23	12
4	24	12
done	24	12
0	12	15
1	33	15
2	100	15
3	320	15
4	1078	15
5	4054	15
done	5000	15
0	13	35
1	32	32
2	82	32
3	162	26
4	323	26
5	527	26
6	591	26
7	609	26
8	612	26
done	612	26
0	3	3
done	3	3
0	11	23
1	26	23
2	63	23
3	134	23
4	325	23
5	649	23
6	874	23
7	1244	23
8	3083	23
done	5001	23
0	9	11
1	13	11
2	16	11
3	20	11
4	21	11
done	21	11
0	3	3
done	3	3
0	15	19
1	39	19
2	101	19
3	205	17
4	379	13
5	788	13
6	2136	13
done	5001	13
0	11	13
1	16	13
2	21	13
3	24	13
4	25	13
done	25	13
0	11	13
1	16	13
2	21	13
3	24	13
4	25	13
done	25	13
0	13	15
1	28	15
2	60	15
3	128	15
4	345	15
5	1002	15
6	3980	15
done	5000	15
0	5	5
done	5	5
0	5	5
done	5	5
0	13	15
1	28	15
2	53	15
3	115	15
4	296	15
5	840	15
6	3535	15
done	5000	15
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	8	9
1	16	9
2	25	9
3	42	9
4	52	9
5	76	9
6	103	9
7	118	9
8	125	9
9	131	9
10	132	9
done	132	9
0	9	11
1	14	11
2	19	11
3	22	11
4	23	11
done	23	11
0	9	11
1	14	11
2	19	11
3	22	11
4	23	11
done	23	11

prune109.0ms

Filtered

89 candidates to 112 candidates (-25.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	112	10	122

Merged error: 0.0b

Counts

122 → 10

regimes256.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	12	13
done	12	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	2997×	body	1280	valid
568.0ms	1845×	body	640	valid
168.0ms	720×	body	320	valid
164.0ms	2116×	body	80	valid
53.0ms	327×	body	160	valid

Details

sample103.0ms

simplify9.0ms

prune4.0ms

localize11.0ms

rewrite23.0ms

series56.0ms

simplify47.8s

prune147.0ms

localize17.0ms

rewrite39.0ms

series126.0ms

simplify2.1min

prune215.0ms

localize15.0ms

rewrite35.0ms

series104.0ms

simplify1.3min

prune161.0ms

localize16.0ms

rewrite33.0ms

series107.0ms

simplify1.1min

prune109.0ms

regimes256.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling