Details

sample314.0ms

Algorithm

intervals

Results

223.0ms	163×	body	1280	valid
48.0ms	63×	body	640	valid
12.0ms	22×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	4×	body	80	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	19
1	26	19
2	33	19
done	33	19

prune7.0ms

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: 15.5b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.5b	(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

5.0ms	(* (sin phi1) (sin phi2))
4.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms	(cos (- lambda1 lambda2))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin phi1) (sin phi2))
30.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
15.0ms	(cos (- lambda1 lambda2))

simplify27.7s

Counts

67 → 67

Iterations

Useful iterations: 1 (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	3	3
done	3	3
0	15	17
1	23	17
2	30	17
done	30	17
0	16	18
1	24	18
2	31	18
done	31	18
0	16	18
1	24	18
2	31	18
done	31	18
0	17	37
1	25	37
2	32	37
done	32	37
0	16	18
1	24	18
2	31	18
done	31	18
0	17	53
1	26	53
2	35	19
3	40	19
4	46	19
5	56	19
6	79	19
7	138	19
8	347	19
9	1273	19
done	5001	19
0	16	18
1	24	18
2	31	18
done	31	18
0	16	18
1	24	18
2	31	18
done	31	18
0	17	19
1	26	19
2	33	19
done	33	19
0	19	21
1	28	21
2	35	21
3	37	21
done	37	21
0	18	20
1	30	20
2	38	20
3	40	20
done	40	20
0	18	20
1	29	20
2	42	20
3	50	20
4	73	20
5	131	20
6	273	20
7	732	20
8	2495	20
done	5001	20
0	21	59
1	36	59
2	68	23
3	106	23
4	166	21
5	290	21
6	686	21
7	2572	21
done	5000	21
0	19	41
1	28	41
2	35	41
3	37	41
done	37	41
0	18	20
1	27	20
2	34	20
done	34	20
0	19	59
1	38	59
2	74	21
3	120	21
4	134	21
5	180	21
6	316	21
7	767	21
8	2818	21
done	5000	21
0	18	20
1	27	20
2	34	20
done	34	20
0	18	20
1	27	20
2	34	20
done	34	20
0	19	21
1	28	21
2	35	21
3	37	21
done	37	21
0	19	21
1	28	21
2	35	21
3	37	21
done	37	21
0	19	23
1	30	23
2	39	23
done	39	23
0	18	20
1	27	20
2	34	20
done	34	20
0	17	19
1	28	17
2	38	17
3	40	17
done	40	17
0	18	20
1	27	20
2	34	20
done	34	20
0	18	20
1	27	20
2	34	20
done	34	20
0	17	19
1	26	19
2	33	19
done	33	19
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	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	15	17
1	23	17
2	30	17
done	30	17
0	15	17
1	23	17
2	30	17
done	30	17
0	15	17
1	23	17
2	30	17
done	30	17
0	17	19
1	26	19
2	33	19
done	33	19
0	17	19
1	26	19
2	33	19
done	33	19
0	17	19
1	26	19
2	33	19
done	33	19
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

prune183.0ms

Filtered

49 candidates to 67 candidates (-36.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	54	13	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	13	68

Merged error: 3.1b

Counts

68 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin lambda1) (sin lambda2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite25.0ms

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`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 72

Calls

4 calls:

12.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
4.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
6.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
50.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
11.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.1min

Counts

84 → 84

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	3	3
done	3	3
0	20	24
1	35	24
2	82	24
3	152	24
4	176	24
done	176	24
0	21	25
1	36	25
2	83	25
3	147	25
4	171	25
done	171	25
0	21	25
1	36	25
2	83	25
3	147	25
4	171	25
done	171	25
0	22	51
1	37	51
2	84	51
3	154	51
4	178	51
done	178	51
0	21	25
1	36	25
2	83	25
3	147	25
4	171	25
done	171	25
0	22	74
1	38	74
2	87	26
3	156	26
4	186	26
5	196	26
6	217	26
7	279	26
8	490	26
9	1429	26
done	5000	26
0	21	25
1	36	25
2	83	25
3	147	25
4	171	25
done	171	25
0	21	25
1	36	25
2	83	25
3	147	25
4	171	25
done	171	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	22	26
1	38	26
2	85	26
3	149	26
4	175	26
done	175	26
0	24	28
1	40	28
2	87	28
3	153	28
4	175	28
done	175	28
0	23	27
1	42	27
2	90	27
3	154	27
4	172	27
done	172	27
0	23	27
1	41	27
2	94	27
3	164	27
4	213	27
5	269	27
6	415	27
7	882	27
8	2614	27
done	5000	27
0	26	80
1	48	80
2	120	30
3	228	30
4	306	28
5	433	28
6	844	28
7	2708	28
done	5000	28
0	24	55
1	40	55
2	87	55
3	153	55
4	175	55
done	175	55
0	23	27
1	39	27
2	86	27
3	148	27
4	176	27
done	176	27
0	24	80
1	50	80
2	126	28
3	235	28
4	271	28
5	317	28
6	458	28
7	915	28
8	2893	28
done	5000	28
0	23	27
1	39	27
2	86	27
3	148	27
4	176	27
done	176	27
0	23	27
1	39	27
2	86	27
3	148	27
4	176	27
done	176	27
0	24	28
1	40	28
2	87	28
3	153	28
4	175	28
done	175	28
0	24	28
1	40	28
2	87	28
3	153	28
4	175	28
done	175	28
0	24	30
1	42	30
2	91	30
3	151	30
4	169	30
done	169	30
0	23	27
1	39	27
2	86	27
3	148	27
4	176	27
done	176	27
0	22	26
1	40	24
2	90	24
3	156	24
4	178	24
done	178	24
0	23	27
1	39	27
2	86	27
3	148	27
4	176	27
done	176	27
0	23	27
1	39	27
2	86	27
3	148	27
4	176	27
done	176	27
0	22	26
1	38	26
2	85	26
3	149	26
4	175	26
done	175	26
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	962	33
5	2421	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	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
0	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
0	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
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	23	32
1	42	32
2	92	26
3	159	26
4	169	26
done	169	26
0	23	32
1	42	32
2	92	26
3	159	26
4	169	26
done	169	26
0	23	32
1	42	32
2	92	26
3	159	26
4	169	26
done	169	26
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	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

prune245.0ms

Filtered

65 candidates to 84 candidates (-29.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	73	11	84
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	79	18	97

Merged error: 3.1b

Counts

97 → 18

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.2b	(* (sin lambda1) (sin lambda2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.5b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
6.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
15.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
11.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify2.3min

Counts

71 → 71

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	9	16
1	14	16
2	21	10
3	30	10
4	53	10
5	111	10
6	256	10
7	725	10
8	2743	10
done	5000	10
0	8	8
1	11	8
2	17	8
3	25	8
4	48	8
5	104	8
6	248	8
7	706	8
8	2706	8
done	5000	8
0	8	8
1	11	8
2	17	8
3	26	8
4	50	8
5	108	8
6	251	8
7	715	8
8	2725	8
done	5000	8
0	8	8
1	11	8
2	17	8
3	26	8
4	50	8
5	108	8
6	251	8
7	715	8
8	2725	8
done	5000	8
0	2	2
1	4	1
done	4	1
0	7	7
1	10	5
2	18	5
3	31	5
4	64	5
5	160	5
6	483	5
7	1808	5
done	5001	5
0	4	4
done	4	2
0	7	7
1	10	5
2	18	5
3	31	5
4	64	5
5	160	5
6	483	5
7	1808	5
done	5001	5
0	4	4
done	4	2
0	8	8
1	11	6
2	23	6
3	36	6
4	69	6
5	170	6
6	513	6
7	1923	6
done	5000	6
0	8	8
1	11	6
2	19	6
3	32	6
4	65	6
5	163	6
6	488	6
7	1818	6
done	5001	6
0	9	17
1	12	13
2	20	13
3	33	13
4	66	13
5	162	13
6	487	13
7	1806	13
done	5000	13
0	8	8
1	11	6
2	19	6
3	32	6
4	65	6
5	163	6
6	488	6
7	1816	6
done	5000	6
0	9	23
1	13	17
2	43	7
3	121	7
4	238	7
5	595	7
6	2484	7
done	5000	7
0	8	8
1	11	6
2	19	6
3	32	6
4	65	6
5	163	6
6	488	6
7	1816	6
done	5000	6
0	8	8
1	11	6
2	19	6
3	32	6
4	65	6
5	163	6
6	488	6
7	1816	6
done	5000	6
0	3	3
done	3	3
0	22	26
1	39	24
2	94	24
3	184	24
4	252	24
5	461	24
6	1250	24
7	4635	24
done	5000	24
0	23	27
1	40	25
2	95	25
3	179	25
4	255	25
5	464	25
6	1252	25
7	4649	25
done	5001	25
0	23	27
1	40	25
2	95	25
3	179	25
4	255	25
5	464	25
6	1252	25
7	4649	25
done	5001	25
0	24	55
1	41	51
2	96	51
3	178	51
4	258	51
5	465	51
6	1255	51
7	4674	51
done	5000	51
0	23	27
1	40	25
2	95	25
3	179	25
4	255	25
5	464	25
6	1252	25
7	4649	25
done	5001	25
0	24	80
1	42	74
2	99	26
3	189	26
4	271	26
5	489	26
6	1300	26
7	4799	26
done	5000	26
0	23	27
1	40	25
2	95	25
3	179	25
4	255	25
5	464	25
6	1252	25
7	4649	25
done	5001	25
0	23	27
1	40	25
2	95	25
3	179	25
4	255	25
5	464	25
6	1252	25
7	4649	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	24	28
1	42	26
2	97	26
3	183	26
4	261	26
5	468	26
6	1257	26
7	4678	26
done	5000	26
0	26	30
1	44	28
2	99	28
3	181	28
4	249	28
5	456	28
6	1249	28
7	4646	28
done	5000	28
0	25	29
1	46	27
2	102	27
3	186	27
4	264	27
5	473	27
6	1267	27
7	4710	27
done	5000	27
0	25	29
1	45	27
2	105	27
3	199	27
4	304	27
5	564	27
6	1487	27
done	5000	27
0	28	86
1	52	80
2	132	30
3	251	30
4	390	28
5	713	28
6	1913	28
done	5000	28
0	26	59
1	44	55
2	99	55
3	181	55
4	249	55
5	456	55
6	1249	55
7	4646	55
done	5000	55
0	25	29
1	43	27
2	98	27
3	186	27
4	268	27
5	475	27
6	1264	27
7	4704	27
done	5000	27
0	26	86
1	54	80
2	138	28
3	272	28
4	370	28
5	624	28
6	1564	28
done	5000	28
0	25	29
1	43	27
2	98	27
3	186	27
4	268	27
5	475	27
6	1264	27
7	4704	27
done	5000	27
0	25	29
1	43	27
2	98	27
3	186	27
4	268	27
5	475	27
6	1264	27
7	4704	27
done	5000	27
0	26	30
1	44	28
2	99	28
3	181	28
4	249	28
5	456	28
6	1249	28
7	4646	28
done	5000	28
0	26	30
1	44	28
2	99	28
3	181	28
4	249	28
5	456	28
6	1249	28
7	4646	28
done	5000	28
0	26	32
1	46	30
2	103	30
3	183	30
4	257	30
5	464	30
6	1257	30
7	4685	30
done	5000	30
0	25	29
1	43	27
2	98	27
3	186	27
4	268	27
5	475	27
6	1264	27
7	4704	27
done	5000	27
0	24	28
1	44	24
2	102	24
3	190	24
4	270	24
5	476	24
6	1265	24
7	4683	24
done	5000	24
0	25	29
1	43	27
2	98	27
3	186	27
4	268	27
5	475	27
6	1264	27
7	4704	27
done	5000	27
0	25	29
1	43	27
2	98	27
3	186	27
4	268	27
5	475	27
6	1264	27
7	4704	27
done	5000	27
0	24	28
1	42	26
2	97	26
3	183	26
4	261	26
5	468	26
6	1257	26
7	4678	26
done	5000	26
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	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
0	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
0	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
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	23	32
1	42	32
2	92	26
3	159	26
4	169	26
done	169	26
0	23	32
1	42	32
2	92	26
3	159	26
4	169	26
done	169	26
0	23	32
1	42	32
2	92	26
3	159	26
4	169	26
done	169	26

prune204.0ms

Filtered

56 candidates to 71 candidates (-26.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	74	15	89

Merged error: 3.0b

Counts

89 → 15

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
27.5b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin lambda2))
6.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
5.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series59.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
11.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify2.4min

Counts

80 → 80

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	21	6
2	60	6
3	134	6
4	240	6
5	623	6
6	2343	6
done	5000	6
0	9	9
1	21	6
2	60	6
3	140	6
4	256	6
5	665	6
6	2495	6
done	5000	6
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	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	7	12
1	15	12
2	26	12
3	28	12
done	28	12
0	6	6
1	7	6
done	7	6
0	10	18
1	21	12
2	56	12
3	132	12
4	239	12
5	620	12
6	2369	12
done	5000	12
0	9	9
1	21	6
2	56	6
3	130	6
4	242	6
5	621	6
6	2384	6
done	5001	6
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	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	6
1	7	6
done	7	6
0	7	12
1	15	12
2	26	12
3	28	12
done	28	12
0	9	9
1	21	9
2	57	9
3	131	9
4	242	9
5	629	9
6	2384	9
done	5000	9
0	9	9
1	21	9
2	57	9
3	131	9
4	242	9
5	629	9
6	2384	9
done	5000	9
0	2	2
1	4	1
done	4	1
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	10	10
1	16	8
2	22	8
3	32	8
4	53	8
5	114	8
6	326	8
7	1266	8
done	5000	8
0	10	10
1	16	8
2	22	8
3	32	8
4	53	8
5	114	8
6	326	8
7	1266	8
done	5000	8
0	10	12
1	23	9
2	43	9
3	91	9
4	215	9
5	598	9
6	2002	9
done	5000	9
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	10	19
1	22	13
2	57	13
3	132	13
4	240	13
5	624	13
6	2351	13
done	5000	13
0	9	9
1	21	6
2	56	6
3	130	6
4	242	6
5	621	6
6	2384	6
done	5001	6
0	10	26
1	20	7
2	55	7
3	129	7
4	251	7
5	635	7
6	2455	7
done	5000	7
0	9	9
1	21	6
2	56	6
3	130	6
4	242	6
5	621	6
6	2384	6
done	5001	6
0	9	9
1	21	6
2	56	6
3	130	6
4	242	6
5	621	6
6	2384	6
done	5001	6
0	3	3
done	3	3
0	23	27
1	49	24
2	131	24
3	273	24
4	406	24
5	773	24
6	2646	24
done	5001	24
0	24	28
1	50	25
2	132	25
3	280	25
4	403	25
5	794	25
6	2618	25
done	5001	25
0	24	28
1	50	25
2	132	25
3	280	25
4	403	25
5	794	25
6	2618	25
done	5001	25
0	25	57
1	51	51
2	133	51
3	268	51
4	400	51
5	781	51
6	2566	51
done	5001	51
0	24	28
1	50	25
2	132	25
3	280	25
4	403	25
5	794	25
6	2618	25
done	5001	25
0	25	83
1	52	74
2	135	26
3	278	26
4	398	26
5	774	26
6	2597	26
done	5000	26
0	24	28
1	50	25
2	132	25
3	280	25
4	403	25
5	794	25
6	2618	25
done	5001	25
0	24	28
1	50	25
2	132	25
3	280	25
4	403	25
5	794	25
6	2618	25
done	5001	25
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	22	11
2	42	11
3	90	11
4	214	11
5	597	11
6	1997	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	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	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
0	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
0	21	30
1	39	30
2	89	24
3	152	24
4	168	24
done	168	24
0	16	27
1	51	25
2	183	23
3	660	23
4	2776	23
done	5000	23
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

prune130.0ms

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	79	16	95

Merged error: 3.0b

Counts

95 → 16

regimes2.2s

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	31
1	34	31
done	34	31

end0.0ms

sample9.2s

Algorithm

intervals

Results

6.2s	4831×	body	1280	valid
1.8s	2080×	body	640	valid
343.0ms	656×	body	320	valid
100.0ms	294×	body	160	valid
40.0ms	11×	body	2560	valid
22.0ms	131×	body	80	valid

Details

sample314.0ms

simplify18.0ms

prune7.0ms

localize32.0ms

rewrite21.0ms

series66.0ms

simplify27.7s

prune183.0ms

localize32.0ms

rewrite25.0ms

series137.0ms

simplify1.1min

prune245.0ms

localize35.0ms

rewrite16.0ms

series93.0ms

simplify2.3min

prune204.0ms

localize35.0ms

rewrite20.0ms

series59.0ms

simplify2.4min

prune130.0ms

regimes2.2s

bsearch0.0ms

simplify4.0ms

end0.0ms

sample9.2s

Profiling