Details

sample105.0ms

Algorithm

intervals

Results

51.0ms	107×	body	1280	valid
17.0ms	56×	body	640	valid
5.0ms	68×	body	80	valid
5.0ms	21×	body	320	valid
2.0ms	6×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	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)
0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

2.0ms	(sin b)
5.0ms	(* r (sin b))
6.0ms	(/ (* r (sin b)) (cos (+ a b)))
5.0ms	(cos (+ a b))

series52.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
9.0ms	(* r (sin b))
34.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

simplify52.8s

Counts

66 → 66

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	11	12
1	17	12
2	24	12
3	30	12
4	36	12
5	45	12
6	58	12
7	76	12
8	92	12
9	99	12
10	116	12
11	118	12
done	118	12
0	10	11
1	17	11
2	23	11
3	32	11
4	35	11
5	41	11
6	50	11
7	63	11
8	81	11
9	97	11
10	104	11
11	121	11
12	123	11
done	123	11
0	9	10
1	16	10
2	28	10
3	47	10
4	63	10
5	71	10
6	83	10
7	101	10
8	117	10
9	124	10
10	141	10
11	143	10
done	143	10
0	9	10
1	13	10
2	17	10
3	22	10
4	31	10
5	44	10
6	77	10
7	162	10
8	379	10
9	1039	10
10	4640	10
done	5001	10
0	14	29
1	30	29
2	126	15
3	561	15
4	2285	13
done	5001	13
0	12	29
1	32	29
2	133	13
3	695	11
4	2613	11
5	4870	11
done	5000	11
0	10	21
1	14	21
2	18	21
3	21	21
4	22	21
done	22	21
0	9	10
1	13	10
2	17	10
3	20	10
4	21	10
done	21	10
0	10	29
1	21	29
2	62	11
3	241	11
4	1000	11
5	2989	11
done	5001	11
0	9	10
1	13	10
2	17	10
3	20	10
4	21	10
done	21	10
0	9	10
1	13	10
2	17	10
3	20	10
4	21	10
done	21	10
0	5	5
1	10	5
2	12	5
done	12	5
0	5	5
1	6	5
done	6	5
0	8	13
1	11	13
done	11	13
0	7	8
1	8	8
done	8	8
0	7	7
1	8	7
done	8	7
0	7	8
1	8	8
done	8	8
0	3	3
1	5	1
done	5	1
0	6	7
1	7	7
done	7	7
0	6	6
1	9	6
done	9	6
0	8	9
1	12	9
2	14	9
done	14	9
0	10	16
1	19	16
2	33	16
3	46	16
4	50	16
done	50	16
0	9	10
1	13	10
2	17	10
3	20	10
4	21	10
done	21	10
0	6	6
1	11	4
2	19	4
3	28	4
4	33	4
done	33	4
0	6	7
1	7	7
done	7	7
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	5	5
1	9	5
2	10	5
done	10	5
0	5	5
1	8	5
2	14	5
3	22	5
4	45	5
5	101	5
6	240	5
7	694	5
8	2697	5
done	5001	5
0	8	14
1	15	14
2	40	8
3	79	8
4	137	6
5	259	6
6	654	6
7	2457	6
done	5001	6
0	6	11
1	7	11
done	7	11
0	5	5
1	6	5
done	6	5
0	6	14
1	17	14
2	46	6
3	89	6
4	105	6
5	151	6
6	283	6
7	735	6
8	2697	6
done	5000	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	6	9
1	9	9
2	11	9
done	11	9
0	5	5
1	6	5
done	6	5
0	3	3
1	6	1
done	6	1
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
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	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	3	3
1	4	3
done	4	3
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
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

prune117.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 0.2b

Counts

67 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

6.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
11.0ms	(* (sin a) (sin b))
64.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7min

Counts

88 → 88

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	15	19
1	24	19
2	38	19
3	44	19
4	50	19
5	59	19
6	72	19
7	90	19
8	106	19
9	113	19
10	130	19
11	132	19
done	132	19
0	14	18
1	24	18
2	37	18
3	46	18
4	51	18
5	57	18
6	66	18
7	79	18
8	97	18
9	113	18
10	120	18
11	137	18
12	139	18
done	139	18
0	13	17
1	23	17
2	45	17
3	77	17
4	115	16
5	154	14
6	401	14
7	2118	14
done	5000	14
0	13	17
1	20	17
2	34	17
3	52	17
4	83	16
5	127	14
6	395	14
7	2180	14
done	5001	14
0	18	50
1	37	50
2	152	22
3	681	22
4	2976	20
done	5000	20
0	16	50
1	39	50
2	159	20
3	815	18
4	3361	18
done	5000	18
0	14	35
1	21	35
2	35	35
3	51	35
4	74	33
5	105	29
6	340	29
7	2049	29
done	5000	29
0	13	17
1	20	17
2	34	17
3	50	17
4	73	16
5	104	14
6	339	14
7	2050	14
done	5000	14
0	14	50
1	28	50
2	79	18
3	275	18
4	1187	17
5	4934	15
done	5000	15
0	13	17
1	20	17
2	34	17
3	50	17
4	73	16
5	104	14
6	339	14
7	2050	14
done	5000	14
0	13	17
1	20	17
2	34	17
3	50	17
4	73	16
5	104	14
6	339	14
7	2050	14
done	5000	14
0	5	5
1	10	5
2	12	5
done	12	5
0	10	12
1	14	12
2	24	12
3	40	12
4	51	11
done	51	11
0	13	27
1	19	27
2	26	27
done	26	27
0	11	15
1	15	15
2	22	15
done	22	15
0	12	14
1	16	14
2	23	14
done	23	14
0	11	15
1	15	15
2	22	15
done	22	15
0	3	3
1	5	1
done	5	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	12	16
1	22	16
2	66	16
3	153	15
4	243	13
5	778	13
6	3906	13
done	5000	13
0	14	30
1	26	30
2	47	30
3	60	30
4	64	30
done	64	30
0	13	17
1	20	17
2	31	17
3	34	17
4	35	17
done	35	17
0	6	6
1	11	4
2	19	4
3	28	4
4	33	4
done	33	4
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	13	24
1	28	24
2	56	24
3	111	16
4	179	11
5	640	11
6	3419	11
done	5000	11
0	16	28
1	29	28
2	60	26
3	129	26
4	293	26
5	578	13
6	1029	11
done	5001	11
0	15	20
1	41	20
2	132	20
3	450	20
4	1432	20
5	4887	20
done	5000	20
0	14	28
1	38	28
2	95	28
3	212	28
4	425	27
5	935	25
6	2489	25
done	5001	25
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	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	5	5
1	9	5
2	10	5
done	10	5
0	5	5
1	8	5
2	14	5
3	22	5
4	45	5
5	101	5
6	240	5
7	694	5
8	2697	5
done	5001	5
0	8	14
1	15	14
2	40	8
3	79	8
4	137	6
5	259	6
6	654	6
7	2457	6
done	5001	6
0	6	11
1	7	11
done	7	11
0	5	5
1	6	5
done	6	5
0	6	14
1	17	14
2	46	6
3	89	6
4	105	6
5	151	6
6	283	6
7	735	6
8	2697	6
done	5000	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	6	9
1	9	9
2	11	9
done	11	9
0	5	5
1	6	5
done	6	5
0	3	3
1	6	1
done	6	1
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
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	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	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	3	3
1	4	3
done	4	3
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
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

prune155.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.0b

Counts

96 → 10

localize16.0ms

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))

rewrite43.0ms

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:

7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* 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))

series128.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
64.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms	(/ (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

prune169.0ms

Filtered

92 candidates to 112 candidates (-21.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	109	13	122

Merged error: 0.0b

Counts

122 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `flip--` `div-inv` `sub-div` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 114

Calls

4 calls:

5.0ms	(* r (sin b))
9.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
14.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* r (sin b))
28.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
63.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify2.1min

Counts

126 → 126

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	26	18
2	47	16
3	101	16
4	152	16
5	349	16
6	1126	13
7	2391	13
done	5001	13
0	14	18
1	26	18
2	47	16
3	101	16
4	152	16
5	349	16
6	1126	13
7	2391	13
done	5001	13
0	16	20
1	25	19
2	41	19
3	46	19
4	52	19
5	61	19
6	74	19
7	92	19
8	108	19
9	115	19
10	132	19
11	134	19
done	134	19
0	17	21
1	29	20
2	59	19
3	105	19
4	147	19
5	234	19
6	389	19
7	425	19
8	467	19
done	467	19
0	18	22
1	32	21
2	58	19
3	112	19
4	152	19
5	238	19
6	391	19
7	428	19
8	466	19
done	466	19
0	17	21
1	31	20
2	53	19
3	83	19
4	132	19
5	216	19
6	383	19
7	418	19
8	452	19
done	452	19
0	15	19
1	25	18
2	39	18
3	46	18
4	49	18
5	55	18
6	64	18
7	77	18
8	95	18
9	111	18
10	118	18
11	135	18
12	137	18
done	137	18
0	16	20
1	29	19
2	53	18
3	93	18
4	162	18
5	254	18
6	393	18
7	424	18
8	473	18
done	473	18
0	17	21
1	32	20
2	53	18
3	101	18
4	170	18
5	262	18
6	403	18
7	436	18
8	492	18
done	492	18
0	16	20
1	31	19
2	49	18
3	79	18
4	137	18
5	217	18
6	369	18
7	406	18
8	450	18
done	450	18
0	15	19
1	30	19
2	63	17
3	137	17
4	232	17
5	495	17
6	1411	14
7	2859	14
done	5000	14
0	15	19
1	29	19
2	61	17
3	140	17
4	280	17
5	742	17
6	2294	14
done	5000	14
0	22	56
1	48	52
2	153	22
3	803	22
4	3969	20
done	5000	20
0	20	56
1	45	56
2	141	24
3	517	24
4	2150	20
done	5000	20
0	20	56
1	50	52
2	157	20
3	810	20
4	4086	20
done	5001	20
0	18	56
1	47	56
2	145	22
3	544	22
4	2343	18
done	5001	18
0	16	39
1	28	39
2	49	35
3	103	35
4	156	35
5	351	35
6	1139	29
7	2394	29
done	5000	29
0	15	19
1	27	19
2	48	17
3	102	17
4	155	17
5	350	17
6	1124	14
7	2397	14
done	5000	14
0	16	56
1	38	56
2	145	18
3	720	18
4	2474	18
done	5000	18
0	15	19
1	27	19
2	48	17
3	102	17
4	155	17
5	350	17
6	1124	14
7	2397	14
done	5000	14
0	15	19
1	27	19
2	48	17
3	102	17
4	155	17
5	350	17
6	1124	14
7	2397	14
done	5000	14
0	16	34
1	28	34
2	48	34
3	58	34
done	58	34
0	15	19
1	25	19
2	38	19
done	38	19
0	18	36
1	36	34
2	89	32
3	187	30
4	292	30
5	327	30
6	334	30
done	334	30
0	17	23
1	31	21
2	61	19
3	104	17
4	167	17
5	194	17
6	197	17
done	197	17
0	9	12
1	19	8
2	46	6
3	75	4
4	103	4
5	122	4
done	122	4
0	17	33
1	31	32
2	62	32
3	116	30
4	236	30
5	293	30
6	307	30
done	307	30
0	16	20
1	28	19
2	49	19
3	69	17
4	113	17
5	146	17
6	154	17
done	154	17
0	8	9
1	16	6
2	29	4
3	54	4
4	86	4
5	107	4
done	107	4
0	16	32
1	30	32
2	60	30
3	154	30
4	256	30
5	302	30
6	315	30
done	315	30
0	15	19
1	27	19
2	48	17
3	97	17
4	129	17
5	158	17
6	162	17
done	162	17
0	7	8
1	15	6
2	28	4
3	53	4
4	85	4
5	100	4
done	100	4
0	6	6
1	12	4
2	24	4
3	32	4
done	32	4
0	6	6
1	12	4
2	24	4
3	32	4
done	32	4
0	15	26
1	35	26
2	70	24
3	164	16
4	271	11
5	947	11
6	4044	11
done	5000	11
0	18	30
1	36	30
2	74	26
3	188	26
4	459	26
5	1016	13
6	2275	11
done	5000	11
0	17	22
1	48	22
2	146	20
3	473	20
4	1362	20
done	5000	20
0	16	30
1	45	30
2	106	28
3	265	28
4	593	28
5	1629	28
done	5000	28
0	12	16
1	21	16
2	31	14
3	67	14
4	117	14
5	199	14
6	468	13
7	879	13
8	2480	13
done	5001	13
0	6	6
1	12	4
2	24	4
3	32	4
done	32	4
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	2	2
1	5	1
done	5	1
0	11	13
1	15	13
2	22	13
done	22	13
0	12	14
1	18	13
2	29	13
3	31	13
4	37	13
5	42	13
done	42	13
0	13	15
1	21	14
2	29	13
3	35	13
4	41	13
5	46	13
done	46	13
0	12	14
1	22	13
2	30	13
3	34	13
4	36	13
5	42	13
6	47	13
done	47	13
0	12	14
1	18	14
2	25	14
done	25	14
0	15	41
1	29	37
2	60	15
3	174	15
4	623	15
5	2331	15
done	5000	15
0	13	29
1	19	29
2	26	29
done	26	29
0	12	14
1	18	14
2	25	14
done	25	14
0	13	41
1	26	41
2	49	15
3	92	15
4	161	15
5	409	15
6	1055	15
7	2933	15
done	5000	15
0	12	14
1	18	14
2	25	14
done	25	14
0	12	14
1	18	14
2	25	14
done	25	14
0	2	2
1	5	1
done	5	1
0	10	12
1	14	12
2	24	12
3	40	12
4	51	11
done	51	11
0	15	31
1	27	29
2	43	27
3	49	27
done	49	27
0	13	15
1	19	14
2	26	14
done	26	14
0	14	18
1	22	16
2	31	14
3	32	14
done	32	14
0	13	15
1	19	14
2	26	14
done	26	14
0	4	7
1	8	3
2	12	1
done	12	1
0	12	14
1	18	13
2	25	13
done	25	13
0	14	28
1	22	27
2	29	27
done	29	27
0	13	15
1	19	14
2	26	14
done	26	14
0	13	15
1	19	14
2	26	14
done	26	14
0	13	15
1	19	14
2	26	14
done	26	14
0	3	4
1	5	1
done	5	1
0	12	14
1	18	13
2	25	13
done	25	13
0	13	27
1	21	27
2	28	27
done	28	27
0	12	14
1	18	14
2	25	14
done	25	14
0	12	14
1	18	14
2	25	14
done	25	14
0	12	14
1	18	14
2	25	14
done	25	14
0	2	3
1	4	1
done	4	1
0	11	13
1	17	13
2	24	13
done	24	13
0	11	13
1	17	13
2	24	13
done	24	13
0	11	13
1	20	11
2	39	11
3	58	11
4	94	11
5	106	11
6	114	11
done	114	11
0	13	27
1	21	27
2	28	27
done	28	27
0	12	14
1	18	14
2	25	14
done	25	14
0	2	3
1	4	1
done	4	1
0	12	14
1	21	13
2	38	13
3	50	11
4	70	11
5	100	11
6	108	11
done	108	11
0	12	14
1	21	13
2	38	13
3	50	11
4	70	11
5	100	11
6	108	11
done	108	11
0	11	13
1	20	11
2	39	11
3	58	11
4	94	11
5	106	11
6	114	11
done	114	11
0	11	21
1	25	21
2	46	21
3	83	13
4	115	8
5	488	6
6	2742	6
done	5000	6
0	14	25
1	26	25
2	50	23
3	97	21
4	210	21
5	311	10
6	421	8
7	2198	6
done	5001	6
0	14	17
1	39	17
2	123	17
3	382	17
4	910	17
5	2382	17
done	5001	17
0	13	25
1	36	25
2	79	25
3	139	25
4	204	25
5	333	25
6	511	25
7	881	25
8	2679	25
done	5001	25
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	5	5
1	9	5
2	10	5
done	10	5
0	5	5
1	8	5
2	14	5
3	22	5
4	45	5
5	101	5
6	240	5
7	694	5
8	2697	5
done	5001	5
0	8	14
1	15	14
2	40	8
3	79	8
4	137	6
5	259	6
6	654	6
7	2457	6
done	5001	6
0	6	11
1	7	11
done	7	11
0	5	5
1	6	5
done	6	5
0	6	14
1	17	14
2	46	6
3	89	6
4	105	6
5	151	6
6	283	6
7	735	6
8	2697	6
done	5000	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	6	9
1	9	9
2	11	9
done	11	9
0	5	5
1	6	5
done	6	5
0	3	3
1	6	1
done	6	1
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	4	4
1	5	4
done	5	4
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	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	10	11
1	22	11
2	41	11
3	66	9
4	113	9
5	252	9
6	775	9
7	3219	9
done	5000	9
0	11	13
1	17	13
2	24	13
done	24	13
0	11	13
1	17	13
2	24	13
done	24	13
0	3	3
1	4	3
done	4	3
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4

prune106.0ms

Filtered

83 candidates to 126 candidates (-51.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	125	14	139

Merged error: 0.0b

Counts

139 → 14

regimes302.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	2997×	body	1280	valid
548.0ms	1845×	body	640	valid
161.0ms	2116×	body	80	valid
157.0ms	720×	body	320	valid
51.0ms	327×	body	160	valid

Details

sample105.0ms

simplify10.0ms

prune4.0ms

localize11.0ms

rewrite19.0ms

series52.0ms

simplify52.8s

prune117.0ms

localize17.0ms

rewrite29.0ms

series104.0ms

simplify1.7min

prune155.0ms

localize16.0ms

rewrite43.0ms

series128.0ms

simplify2.1min

prune169.0ms

localize17.0ms

rewrite37.0ms

series110.0ms

simplify2.1min

prune106.0ms

regimes302.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling