Details

sample312.0ms

Algorithm

intervals

Results

216.0ms	150×	body	1280	valid
53.0ms	62×	body	640	valid
12.0ms	21×	body	320	valid
3.0ms	19×	body	80	valid
1.0ms	4×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	45	24
3	70	24
4	74	24
done	74	24

prune6.0ms

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: 13.1b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.8b	(sin (- lambda1 lambda2))
5.0b	(cos (- lambda1 lambda2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

8.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series59.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
28.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

simplify45.2s

Counts

72 → 72

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	8	5
done	8	5
0	6	6
1	9	6
2	13	6
3	16	6
done	16	6
0	6	6
1	8	5
done	8	5
0	6	6
1	9	6
2	13	6
3	16	6
done	16	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
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	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	12	6
3	17	6
4	23	6
5	33	6
6	56	6
7	116	6
8	332	6
9	1267	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	6	6
1	8	5
done	8	5
0	6	6
1	9	6
2	13	6
3	16	6
done	16	6
0	6	6
1	8	5
done	8	5
0	6	6
1	9	6
2	13	6
3	16	6
done	16	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
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	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	12	6
3	17	6
4	23	6
5	33	6
6	56	6
7	116	6
8	332	6
9	1267	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	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	13	13
1	19	13
2	26	13
done	26	13
0	12	12
1	19	12
2	25	12
3	29	12
done	29	12
0	11	11
1	20	11
2	34	11
3	48	11
done	48	11
0	11	11
1	19	11
2	37	11
3	61	11
4	117	11
5	256	11
6	598	11
7	1562	11
done	5001	11
0	16	32
1	31	32
2	97	16
3	347	16
4	1076	14
5	3033	14
done	5000	14
0	14	32
1	33	32
2	101	14
3	387	14
4	1191	12
5	2197	12
done	5000	12
0	12	23
1	18	23
2	25	23
3	27	23
done	27	23
0	11	11
1	17	11
2	24	11
3	26	11
done	26	11
0	12	32
1	28	32
2	99	12
3	435	12
4	1202	12
5	1698	12
6	3285	12
done	5000	12
0	11	11
1	17	11
2	24	11
3	26	11
done	26	11
0	11	11
1	17	11
2	24	11
3	26	11
done	26	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	12	17
1	20	17
2	34	17
3	44	17
done	44	17
0	11	11
1	17	11
2	24	11
done	24	11
0	7	7
1	13	5
2	25	5
3	31	5
done	31	5
0	7	7
1	10	7
2	11	7
done	11	7
0	12	14
1	19	14
2	29	14
done	29	14
0	9	13
1	19	13
2	38	13
3	62	13
4	80	13
5	92	13
6	112	13
7	148	13
8	166	13
9	185	13
10	192	13
11	196	13
12	199	13
13	201	13
14	203	13
done	203	13
0	7	7
1	10	7
2	11	7
done	11	7
0	9	9
1	12	9
2	13	9
done	13	9
0	8	8
1	14	8
2	16	8
done	16	8
0	8	8
1	13	8
2	20	8
3	28	8
4	51	8
5	107	8
6	252	8
7	714	8
8	2716	8
done	5000	8
0	11	23
1	20	23
2	46	11
3	84	11
4	140	9
5	257	9
6	656	9
7	2460	9
done	5000	9
0	9	17
1	12	17
2	13	17
done	13	17
0	8	8
1	11	8
2	12	8
done	12	8
0	9	23
1	22	23
2	52	9
3	96	9
4	112	9
5	158	9
6	297	9
7	749	9
8	2750	9
done	5000	9
0	8	8
1	11	8
2	12	8
done	12	8
0	8	8
1	11	8
2	12	8
done	12	8
0	9	9
1	12	9
2	13	9
done	13	9
0	9	9
1	12	9
2	13	9
done	13	9
0	9	12
1	14	12
2	17	12
done	17	12
0	8	8
1	11	8
2	12	8
done	12	8
0	6	6
1	11	4
2	15	4
done	15	4
0	8	8
1	11	8
2	12	8
done	12	8
0	8	8
1	11	8
2	12	8
done	12	8
0	7	7
1	10	7
2	11	7
done	11	7
0	10	11
1	23	11
2	50	11
3	103	9
4	229	9
5	569	9
6	1981	9
done	5000	9
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	8	9
1	22	9
2	49	9
3	112	9
4	257	9
5	676	9
6	2755	9
done	5000	9
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	1	1
done	1	1
0	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	3	3
1	5	3
2	6	3
done	6	3
0	7	7
1	10	7
2	11	7
done	11	7
0	7	7
1	10	7
2	11	7
done	11	7

prune211.0ms

Filtered

54 candidates to 72 candidates (-33.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	57	15	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	15	73

Merged error: 6.7b

Counts

73 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0b	(cos (- lambda1 lambda2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series85.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cos lambda1) (sin lambda2))
39.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

simplify54.8s

Counts

81 → 81

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	8	5
done	8	5
0	6	6
1	9	6
2	13	6
3	16	6
done	16	6
0	6	6
1	8	5
done	8	5
0	6	6
1	9	6
2	13	6
3	16	6
done	16	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
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	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	12	6
3	17	6
4	23	6
5	33	6
6	56	6
7	116	6
8	332	6
9	1267	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	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	13	13
1	19	13
2	26	13
done	26	13
0	12	12
1	19	12
2	25	12
3	29	12
done	29	12
0	11	11
1	20	11
2	34	11
3	48	11
done	48	11
0	11	11
1	19	11
2	37	11
3	61	11
4	117	11
5	256	11
6	598	11
7	1562	11
done	5001	11
0	16	32
1	31	32
2	97	16
3	347	16
4	1076	14
5	3033	14
done	5000	14
0	14	32
1	33	32
2	101	14
3	387	14
4	1191	12
5	2197	12
done	5000	12
0	12	23
1	18	23
2	25	23
3	27	23
done	27	23
0	11	11
1	17	11
2	24	11
3	26	11
done	26	11
0	12	32
1	28	32
2	99	12
3	435	12
4	1202	12
5	1698	12
6	3285	12
done	5000	12
0	11	11
1	17	11
2	24	11
3	26	11
done	26	11
0	11	11
1	17	11
2	24	11
3	26	11
done	26	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	12	17
1	20	17
2	34	17
3	44	17
done	44	17
0	11	11
1	17	11
2	24	11
done	24	11
0	7	7
1	13	5
2	25	5
3	31	5
done	31	5
0	7	7
1	10	7
2	11	7
done	11	7
0	12	14
1	19	14
2	29	14
done	29	14
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	14	16
1	19	16
2	26	16
done	26	16
0	13	15
1	21	15
2	35	15
3	64	15
4	80	15
5	88	15
done	88	15
0	13	15
1	20	15
2	44	15
3	101	15
4	200	15
5	477	15
6	1789	15
done	5000	15
0	16	44
1	27	44
2	71	18
3	243	18
4	1215	16
done	5001	16
0	14	31
1	19	31
2	32	31
3	61	31
4	77	31
5	85	31
done	85	31
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	14	44
1	29	44
2	89	16
3	392	16
4	1845	16
done	5001	16
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	14	16
1	19	16
2	26	16
done	26	16
0	14	16
1	19	16
2	26	16
done	26	16
0	14	19
1	21	19
2	36	19
3	77	19
4	135	19
5	183	19
6	207	19
done	207	19
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	11	13
1	18	11
2	34	11
3	69	11
4	116	11
5	130	11
done	130	11
0	13	15
1	18	15
2	25	15
done	25	15
0	13	15
1	18	15
2	25	15
done	25	15
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	15	18
1	39	18
2	129	18
3	460	18
4	1659	18
5	4742	18
done	5000	18
0	14	26
1	36	26
2	87	26
3	226	26
4	549	26
5	961	26
6	1473	26
7	2540	26
done	5000	26
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	10	11
1	23	11
2	50	11
3	103	9
4	229	9
5	569	9
6	1981	9
done	5000	9
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	1	1
done	1	1
0	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	10	10
1	16	10
2	23	10
3	25	10
done	25	10
0	3	3
1	5	3
2	6	3
done	6	3
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	13	15
1	35	15
2	87	15
3	185	15
4	428	15
5	905	15
6	2998	15
done	5000	15
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5

prune199.0ms

Filtered

61 candidates to 81 candidates (-32.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.1b

Counts

96 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 84

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
6.0ms	(* (sin lambda1) (sin lambda2))

series110.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
33.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
55.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(* (sin lambda1) (sin lambda2))

simplify1.2min

Counts

96 → 96

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	15	17
1	28	17
2	71	17
3	127	17
4	157	17
done	157	17
0	15	17
1	28	17
2	71	17
3	127	17
4	157	17
done	157	17
0	18	20
1	25	20
2	31	20
done	31	20
0	17	19
1	25	19
2	30	19
3	34	19
done	34	19
0	16	18
1	32	18
2	82	18
3	158	18
4	176	18
done	176	18
0	16	18
1	31	18
2	88	18
3	207	18
4	405	18
5	1325	18
done	5000	18
0	21	53
1	49	53
2	202	23
3	1128	23
done	5000	23
0	19	53
1	51	53
2	206	21
3	1152	21
done	5000	21
0	17	37
1	30	37
2	73	37
3	131	37
4	161	37
done	161	37
0	16	18
1	29	18
2	72	18
3	130	18
4	150	18
done	150	18
0	17	53
1	40	53
2	189	19
3	1113	19
done	5000	19
0	16	18
1	29	18
2	72	18
3	130	18
4	150	18
done	150	18
0	16	18
1	29	18
2	72	18
3	130	18
4	150	18
done	150	18
0	20	33
1	40	33
2	98	31
3	276	31
4	758	31
5	2533	18
done	5000	18
0	3	5
1	8	1
done	8	1
0	20	25
1	53	25
2	178	25
3	730	25
4	2406	25
done	5000	25
0	15	37
1	50	31
2	147	31
3	394	31
4	913	31
5	1545	31
6	1930	31
7	2432	31
8	3437	31
done	5000	31
0	19	33
1	45	33
2	105	33
3	286	33
4	959	33
5	2364	33
done	5000	33
0	11	13
1	16	13
2	29	13
3	58	13
4	69	13
5	77	13
done	77	13
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	11	11
1	18	11
2	37	11
3	58	11
4	63	11
done	63	11
0	17	31
1	26	31
2	39	31
3	51	31
done	51	31
0	16	18
1	23	18
2	29	18
done	29	18
0	7	7
1	13	5
2	25	5
3	31	5
done	31	5
0	12	14
1	22	14
2	39	14
3	43	14
done	43	14
0	18	29
1	37	29
2	96	27
3	268	27
4	642	27
5	1150	14
6	2117	12
done	5000	12
0	18	21
1	50	21
2	176	21
3	723	21
4	2592	21
done	5001	21
0	17	29
1	42	29
2	107	29
3	356	29
4	1212	29
5	2659	29
6	4616	29
done	5001	29
0	17	21
1	31	21
2	73	21
3	141	21
4	173	21
5	177	21
done	177	21
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	14	16
1	19	16
2	26	16
done	26	16
0	13	15
1	21	15
2	35	15
3	64	15
4	80	15
5	88	15
done	88	15
0	13	15
1	20	15
2	44	15
3	101	15
4	200	15
5	477	15
6	1789	15
done	5000	15
0	16	44
1	27	44
2	71	18
3	243	18
4	1215	16
done	5001	16
0	14	31
1	19	31
2	32	31
3	61	31
4	77	31
5	85	31
done	85	31
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	14	44
1	29	44
2	89	16
3	392	16
4	1845	16
done	5001	16
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	14	16
1	19	16
2	26	16
done	26	16
0	14	16
1	19	16
2	26	16
done	26	16
0	14	19
1	21	19
2	36	19
3	77	19
4	135	19
5	183	19
6	207	19
done	207	19
0	13	15
1	18	15
2	31	15
3	60	15
4	72	15
5	80	15
done	80	15
0	11	13
1	18	11
2	34	11
3	69	11
4	116	11
5	130	11
done	130	11
0	13	15
1	18	15
2	25	15
done	25	15
0	13	15
1	18	15
2	25	15
done	25	15
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	15	18
1	39	18
2	129	18
3	460	18
4	1659	18
5	4742	18
done	5000	18
0	14	26
1	36	26
2	87	26
3	226	26
4	549	26
5	961	26
6	1473	26
7	2540	26
done	5000	26
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	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	1	1
done	1	1
0	15	17
1	28	17
2	65	17
3	132	17
4	183	17
done	183	17
0	15	17
1	28	17
2	65	17
3	132	17
4	183	17
done	183	17
0	3	3
1	5	3
2	6	3
done	6	3
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	12	14
1	17	14
2	30	14
3	59	14
4	73	14
5	81	14
done	81	14
0	13	15
1	35	15
2	87	15
3	185	15
4	428	15
5	905	15
6	2998	15
done	5000	15
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5

prune261.0ms

Filtered

75 candidates to 96 candidates (-28.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 0.0b

Counts

108 → 14

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.4b	(pow (* (sin phi1) (cos phi2)) 3)
0.5b	(pow (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) 3)
19.1b	(cbrt (* (pow (* (sin phi1) (cos phi2)) 3) (pow (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) 3)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cube-div`
12×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`cbrt-div`
6×	`pow-unpow`
5×	`sin-cos-mult`
4×	`unpow-prod-down` `cube-prod` `sin-mult` `add-log-exp`
3×	`frac-times` `pow-pow` `flip3-+` `associate-r/` `associate-r` `associate-l*` `pow-prod-down` `frac-add` `pow-exp` `cos-mult` `flip-+` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `unpow3` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`cbrt-prod` `pow1/3` `associate-l/` `-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin lambda2))
6.0ms	(pow (* (sin phi1) (cos phi2)) 3)
8.0ms	(pow (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) 3)
13.0ms	(cbrt (* (pow (* (sin phi1) (cos phi2)) 3) (pow (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) 3)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(pow (* (sin phi1) (cos phi2)) 3)
36.0ms	(pow (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) 3)
52.0ms	(cbrt (* (pow (* (sin phi1) (cos phi2)) 3) (pow (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) 3)))

simplify3.4min

Counts

97 → 97

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	20	23
1	41	23
2	127	23
3	618	23
4	4015	23
done	5000	23
0	20	23
1	41	23
2	127	23
3	618	23
4	4015	23
done	5000	23
0	8	8
1	20	5
2	55	5
3	132	5
4	241	5
5	625	5
6	2425	5
done	5000	5
0	12	14
1	23	11
2	45	11
3	119	11
4	386	11
5	1168	11
6	3165	11
done	5001	11
0	24	38
1	50	38
2	138	36
3	573	36
4	3855	36
done	5001	36
0	7	10
1	22	6
2	48	2
3	61	2
4	88	2
5	155	2
6	350	2
7	1086	2
8	4255	2
done	5000	2
0	23	30
1	60	30
2	194	30
3	802	30
done	5000	30
0	19	42
1	62	34
2	168	34
3	565	34
4	3752	34
done	5000	34
0	23	38
1	62	38
2	183	38
3	861	38
done	5000	38
0	15	18
1	34	16
2	73	16
3	217	16
4	925	16
5	3791	16
done	5000	16
0	22	34
1	48	34
2	152	32
3	749	32
done	5000	32
0	5	6
1	18	1
2	22	1
3	28	1
4	38	1
5	59	1
6	118	1
7	326	1
8	1249	1
done	5000	1
0	21	26
1	58	26
2	208	26
3	973	26
done	5000	26
0	16	38
1	52	29
2	144	29
3	462	29
4	2765	29
done	5000	29
0	21	34
1	60	34
2	197	34
3	1050	34
done	5001	34
0	12	14
1	24	11
2	49	11
3	145	11
4	547	11
5	2031	11
done	5000	11
0	21	26
1	42	26
2	112	26
3	454	26
4	2266	26
done	5001	26
0	4	4
1	13	1
2	17	1
3	23	1
4	33	1
5	56	1
6	115	1
7	333	1
8	1267	1
done	5001	1
0	21	47
1	42	47
2	128	47
3	622	47
4	3960	47
done	5001	47
0	20	23
1	41	23
2	127	23
3	618	23
4	4015	23
done	5000	23
0	21	68
1	43	68
2	130	24
3	635	21
4	4051	21
done	5001	21
0	20	23
1	41	23
2	127	23
3	618	23
4	4015	23
done	5000	23
0	20	23
1	41	23
2	127	23
3	618	23
4	4015	23
done	5000	23
0	12	14
1	16	14
done	16	14
0	12	14
1	16	14
done	16	14
0	3	3
1	6	1
done	6	1
0	13	17
1	20	17
2	27	17
3	51	17
4	109	17
5	264	17
6	886	17
7	3321	17
done	5000	17
0	12	14
1	19	14
2	24	14
3	42	14
4	81	14
5	187	14
6	559	14
7	2172	14
done	5000	14
0	11	13
1	21	11
2	28	11
3	39	11
4	61	11
5	120	11
6	336	11
7	1247	11
done	5000	11
0	13	27
1	26	27
2	47	14
3	92	14
4	245	14
5	692	14
6	2103	14
done	5000	14
0	12	14
1	23	11
2	29	11
3	39	11
4	60	11
5	118	11
6	333	11
7	1254	11
done	5000	11
0	12	14
1	23	14
2	29	14
3	48	14
4	85	14
5	143	14
6	355	14
7	1260	14
done	5000	14
0	12	14
1	23	14
2	29	14
3	48	14
4	85	14
5	143	14
6	355	14
7	1260	14
done	5000	14
0	3	3
1	13	1
done	13	1
0	11	13
1	22	13
2	44	13
3	118	13
4	381	13
5	1193	13
6	3149	13
done	5000	13
0	10	23
1	19	23
2	48	23
3	122	23
4	203	23
5	271	23
6	398	23
7	494	23
done	494	23
0	12	14
1	25	14
2	53	14
3	132	14
4	408	14
5	1248	14
6	3352	14
done	5000	14
0	12	14
1	23	14
2	51	14
3	149	14
4	495	14
5	1634	14
done	5001	14
0	13	29
1	23	23
2	45	23
3	119	23
4	382	23
5	1165	23
6	3144	23
done	5000	23
0	12	14
1	23	11
2	45	11
3	119	11
4	386	11
5	1168	11
6	3165	11
done	5001	11
0	13	41
1	28	27
2	83	15
3	361	15
4	1994	15
done	5000	15
0	13	27
1	26	27
2	47	14
3	92	14
4	245	14
5	692	14
6	2103	14
done	5000	14
0	12	14
1	23	11
2	29	11
3	39	11
4	60	11
5	118	11
6	333	11
7	1254	11
done	5000	11
0	12	14
1	23	14
2	29	14
3	48	14
4	85	14
5	143	14
6	355	14
7	1260	14
done	5000	14
0	12	14
1	23	14
2	29	14
3	48	14
4	85	14
5	143	14
6	355	14
7	1260	14
done	5000	14
0	3	3
1	13	1
done	13	1
0	11	13
1	22	13
2	44	13
3	118	13
4	381	13
5	1193	13
6	3149	13
done	5000	13
0	14	25
1	30	25
2	70	23
3	221	23
4	1224	23
done	5000	17
0	4	5
1	15	3
2	23	1
3	29	1
4	39	1
5	62	1
6	117	1
7	327	1
8	1236	1
done	5000	1
0	13	17
1	40	17
2	126	17
3	458	17
4	3014	17
done	5000	17
0	15	37
1	51	31
2	143	31
3	461	31
4	2792	31
done	5000	31
0	13	25
1	42	25
2	115	25
3	456	25
4	3429	25
done	5000	25
0	11	13
1	23	13
2	48	13
3	144	13
4	544	13
5	2010	13
done	5000	13
0	10	23
1	19	23
2	48	23
3	122	23
4	203	23
5	271	23
6	398	23
7	494	23
done	494	23
0	12	14
1	23	14
2	46	14
3	120	14
4	381	14
5	1160	14
6	3155	14
done	5001	14
0	12	14
1	23	14
2	46	14
3	120	14
4	381	14
5	1160	14
6	3155	14
done	5001	14
0	13	15
1	20	13
2	26	13
3	37	13
4	58	13
5	116	13
6	327	13
7	1226	13
done	5000	13
0	13	15
1	20	13
2	26	13
3	37	13
4	58	13
5	116	13
6	327	13
7	1226	13
done	5000	13
0	9	9
1	11	9
2	19	9
done	19	9
0	8	8
1	13	8
2	20	8
3	21	8
done	21	8
0	8	8
1	13	8
2	20	8
3	21	8
done	21	8
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	9	11
1	14	11
2	21	11
3	45	11
4	101	11
5	262	11
6	870	11
7	3266	11
done	5000	11
0	8	8
1	13	8
2	18	8
3	36	8
4	75	8
5	184	8
6	563	8
7	2176	8
done	5000	8
0	7	7
1	15	5
2	22	5
3	33	5
4	55	5
5	116	5
6	328	5
7	1249	5
done	5001	5
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	6	11
1	14	11
2	25	11
done	25	11
0	8	8
1	22	8
2	70	8
3	193	8
4	438	8
5	1053	8
6	3796	8
done	5000	8
0	8	8
1	20	8
2	63	8
3	180	8
4	439	8
5	1304	8
6	4887	8
done	5000	8
0	9	17
1	20	11
2	55	11
3	129	11
4	237	11
5	609	11
6	2399	11
done	5000	11
0	8	8
1	20	5
2	55	5
3	132	5
4	241	5
5	625	5
6	2425	5
done	5000	5
0	9	23
1	25	15
2	104	9
3	702	9
done	5000	9
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	9	11
1	21	11
2	44	11
3	86	11
4	175	11
5	426	11
6	1308	11
7	3394	11
done	5000	11
0	3	3
1	12	1
2	16	1
3	22	1
4	32	1
5	53	1
6	113	1
7	324	1
8	1257	1
done	5000	1
0	6	11
1	14	11
2	25	11
done	25	11
0	8	8
1	20	8
2	56	8
3	132	8
4	238	8
5	612	8
6	2352	8
done	5000	8
0	8	8
1	20	8
2	56	8
3	132	8
4	238	8
5	612	8
6	2352	8
done	5000	8
0	9	9
1	14	7
2	21	7
3	31	7
4	54	7
5	112	7
6	323	7
7	1256	7
done	5000	7
0	9	9
1	14	7
2	21	7
3	31	7
4	54	7
5	112	7
6	323	7
7	1256	7
done	5000	7
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	1	1
done	1	1
0	15	17
1	28	17
2	65	17
3	132	17
4	183	17
done	183	17
0	15	17
1	28	17
2	65	17
3	132	17
4	183	17
done	183	17
0	12	13
1	28	13
2	62	13
3	113	11
4	239	11
5	597	11
6	1991	11
done	5000	11
0	11	13
1	22	13
2	44	13
3	118	13
4	381	13
5	1193	13
6	3149	13
done	5000	13
0	11	13
1	22	13
2	44	13
3	118	13
4	381	13
5	1193	13
6	3149	13
done	5000	13
0	15	19
1	40	19
2	116	19
3	318	19
4	1012	17
5	3623	17
done	5000	17
0	8	9
1	22	9
2	59	9
3	175	9
4	541	9
5	2123	7
done	5000	7
0	8	9
1	22	9
2	59	9
3	175	9
4	541	9
5	2123	7
done	5000	7
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

prune202.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	96	15	111

Merged error: 0.0b

Counts

111 → 15

regimes869.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	43
1	37	43
done	37	43

end0.0ms

sample9.3s

Algorithm

intervals

Results

6.6s	4598×	body	1280	valid
1.6s	1926×	body	640	valid
348.0ms	569×	body	320	valid
120.0ms	692×	body	80	valid
81.0ms	215×	body	160	valid

Details

sample312.0ms

simplify41.0ms

prune6.0ms

localize26.0ms

rewrite27.0ms

series59.0ms

simplify45.2s

prune211.0ms

localize34.0ms

rewrite30.0ms

series85.0ms

simplify54.8s

prune199.0ms

localize35.0ms

rewrite38.0ms

series110.0ms

simplify1.2min

prune261.0ms

localize44.0ms

rewrite36.0ms

series117.0ms

simplify3.4min

prune202.0ms

regimes869.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample9.3s

Profiling