Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	193×	body	80	valid
7.0ms	22×	body	2560	valid
5.0ms	13×	body	5120	valid
4.0ms	14×	body	1280	valid
2.0ms	9×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	23	15
done	23	15

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: 40.8b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
32.9b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div` `sqrt-prod`
3×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

3 → 40

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series49.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.3s

Counts

49 → 49

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	9	12
1	13	11
2	14	11
done	14	11
0	8	11
1	10	11
done	10	11
0	8	11
1	13	11
2	14	11
done	14	11
0	9	23
1	11	23
done	11	23
0	8	11
1	10	11
done	10	11
0	9	32
1	24	32
2	55	12
3	120	12
4	320	12
5	1206	12
6	4302	12
done	5001	12
0	8	11
1	10	11
done	10	11
0	8	11
1	10	11
done	10	11
0	10	14
1	24	14
2	33	14
3	59	14
4	116	14
5	252	14
6	669	14
7	2468	14
done	5000	14
0	10	32
1	19	20
2	45	20
3	87	18
4	135	18
5	199	18
6	332	18
7	478	18
8	584	18
9	604	18
done	604	18
0	8	21
1	14	11
2	30	11
3	61	5
4	93	3
5	289	3
6	2219	3
done	5000	3
0	7	10
1	10	10
2	11	10
done	11	10
0	7	10
1	9	10
done	9	10
0	11	14
1	20	14
2	21	14
done	21	14
0	11	14
1	20	14
2	21	14
done	21	14
0	12	29
1	21	29
2	22	29
done	22	29
0	11	14
1	20	14
2	21	14
done	21	14
0	12	41
1	22	26
2	40	15
3	62	15
4	70	15
5	80	15
6	101	15
7	162	15
8	363	15
9	1294	15
done	5000	15
0	2	2
done	2	2
0	8	11
1	10	11
done	10	11
0	13	17
1	34	17
2	68	17
3	133	17
4	267	17
5	606	17
6	1673	17
done	5000	17
0	11	33
1	20	21
2	46	21
3	86	19
4	134	19
5	197	19
6	330	19
7	475	19
8	583	19
9	603	19
done	603	19
0	11	24
1	18	14
2	44	14
3	120	8
4	230	6
5	637	6
6	3987	6
done	5000	6
0	8	11
1	11	11
2	12	11
done	12	11
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	11	14
1	20	14
2	21	14
done	21	14
0	11	14
1	20	14
2	21	14
done	21	14
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	3	3
1	4	3
done	4	3
0	3	3
1	4	3
done	4	3
0	1	1
done	1	1
0	20	28
1	53	28
2	156	23
3	443	23
4	1235	20
5	3183	18
done	5000	18
0	18	26
1	49	26
2	147	26
3	405	23
4	1409	21
done	5000	21
0	1	1
done	1	1

prune122.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 18.5b

Counts

50 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.3b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.9b	(sqrt (+ (* re re) (* im im)))
32.9b	(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
17.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7min

Counts

136 → 136

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	11	23
1	17	11
2	23	11
3	32	11
4	58	11
5	123	11
6	314	11
7	1003	11
8	4055	11
done	5000	11
0	10	22
1	12	11
2	13	11
done	13	11
0	10	22
1	15	11
2	19	11
3	23	11
4	32	11
5	60	11
6	126	11
7	315	11
8	999	11
9	4036	11
done	5000	11
0	11	45
1	13	23
2	14	23
done	14	23
0	10	22
1	12	11
2	13	11
done	13	11
0	11	65
1	26	32
2	68	12
3	174	12
4	464	12
5	1512	12
done	5000	12
0	10	22
1	12	11
2	13	11
done	13	11
0	10	22
1	12	11
2	13	11
done	13	11
0	12	25
1	28	14
2	53	14
3	106	14
4	233	14
5	530	14
6	1603	14
done	5000	14
0	12	65
1	27	30
2	53	20
3	108	20
4	193	18
5	333	18
6	700	18
7	1542	18
8	4902	18
done	5000	18
0	10	43
1	20	21
2	30	11
3	67	11
4	132	5
5	240	3
6	895	3
done	5000	3
0	9	21
1	12	10
2	14	10
done	14	10
0	2	3
1	5	1
2	7	1
done	7	1
0	5	5
1	8	1
done	8	1
0	2	3
1	6	1
done	6	1
0	4	7
1	6	3
2	7	1
done	7	1
0	7	9
1	14	3
done	14	1
0	5	5
1	8	3
done	8	1
0	4	7
1	8	3
2	9	1
done	9	1
0	7	9
1	14	3
done	14	1
0	5	11
1	12	5
2	18	1
done	18	1
0	7	17
1	8	7
2	9	7
done	9	7
0	8	19
1	9	8
2	10	8
done	10	8
0	6	15
1	13	15
2	34	15
3	78	15
4	122	15
5	171	15
6	249	15
7	313	15
8	513	15
9	1199	15
10	4162	15
done	5000	15
0	7	17
1	8	7
2	9	7
done	9	7
0	6	15
1	13	15
2	34	15
3	78	15
4	122	15
5	171	15
6	249	15
7	313	15
8	513	15
9	1199	15
10	4162	15
done	5000	15
0	2	3
1	6	1
done	6	1
0	9	21
1	12	12
2	13	12
done	13	12
0	9	20
1	12	9
2	15	9
3	16	9
done	16	9
0	9	20
1	12	9
2	17	9
3	22	9
4	40	9
5	80	9
6	188	9
7	571	9
8	2260	9
done	5001	9
0	10	59
1	18	26
2	30	16
3	60	10
4	117	10
5	213	10
6	450	10
7	1488	10
done	5000	10
0	10	41
1	11	19
2	12	19
done	12	19
0	9	20
1	10	9
2	11	9
done	11	9
0	10	59
1	19	26
2	28	10
3	59	10
4	117	10
5	213	10
6	471	10
7	1519	10
done	5001	10
0	7	17
1	8	7
2	9	7
done	9	7
0	9	20
1	11	9
done	11	9
0	9	20
1	11	9
done	11	9
0	11	27
1	29	12
2	67	8
3	118	8
4	262	8
5	700	8
6	2327	8
done	5000	8
0	12	51
1	34	20
2	89	18
3	182	16
4	313	16
5	726	16
6	1985	16
done	5001	16
0	16	31
1	46	31
2	97	23
3	197	19
4	466	19
5	1284	19
6	3956	19
done	5000	19
0	15	35
1	43	31
2	99	29
3	205	27
4	358	27
5	887	27
6	2364	27
done	5001	27
0	16	31
1	46	31
2	101	23
3	201	19
4	472	19
5	1289	19
6	3970	19
done	5000	19
0	15	35
1	43	31
2	97	29
3	204	27
4	355	27
5	887	27
6	2374	27
done	5000	27
0	10	35
1	23	16
2	47	12
3	93	8
4	218	8
5	585	8
6	1494	8
done	5000	8
0	8	19
1	13	8
2	21	8
3	36	8
4	61	8
5	102	8
6	158	8
7	326	8
8	1613	8
done	5000	8
0	10	43
1	15	43
2	17	23
3	26	12
4	41	12
5	67	12
6	137	12
7	352	12
8	1259	12
done	5000	12
0	9	21
1	10	21
done	10	21
0	10	41
1	12	19
2	13	19
done	13	19
0	9	21
1	10	9
2	11	9
done	11	9
0	10	39
1	12	9
2	13	9
done	13	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	4	7
1	6	1
done	6	1
0	8	19
1	9	8
2	10	8
done	10	8
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	3	5
1	5	1
done	5	1
0	8	19
1	9	8
2	10	8
done	10	8
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	2	3
1	4	1
done	4	1
0	8	19
1	9	8
2	10	8
done	10	8
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	9	21
1	10	9
2	11	9
done	11	9
0	3	3
1	5	1
2	7	1
done	7	1
0	3	3
1	6	1
done	6	1
0	4	5
1	9	3
2	11	1
done	11	1
0	4	5
1	10	1
done	10	1
0	5	7
1	14	5
2	22	1
done	22	1
0	10	31
1	14	31
2	16	31
done	16	31
0	11	30
1	14	20
done	14	20
0	12	29
1	15	20
done	15	20
0	9	20
1	11	20
done	11	20
0	11	13
1	15	11
done	15	11
0	9	20
1	11	20
done	11	20
0	10	12
1	14	11
done	14	11
0	9	20
1	11	20
done	11	20
0	9	11
1	13	9
2	16	9
done	16	9
0	9	20
1	11	20
done	11	20
0	10	20
1	12	20
done	12	20
0	11	20
1	13	20
done	13	20
0	9	20
1	11	20
done	11	20
0	8	19
1	9	8
2	10	8
done	10	8
0	9	20
1	11	20
done	11	20
0	8	19
1	9	8
2	10	8
done	10	8
0	9	20
1	11	20
done	11	20
0	8	19
1	9	8
2	10	8
done	10	8
0	14	23
1	34	23
2	71	19
3	130	19
4	272	19
5	730	19
6	2335	19
done	5000	19
0	13	27
1	27	27
2	47	23
3	93	19
4	218	19
5	589	19
6	1501	19
done	5000	19
0	14	23
1	34	23
2	71	19
3	126	19
4	266	19
5	682	19
6	2333	19
done	5000	19
0	13	27
1	27	27
2	49	23
3	95	19
4	220	19
5	587	19
6	1505	19
done	5001	19
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	3	3
1	4	3
done	4	3
0	3	3
1	4	3
done	4	3
0	1	1
done	1	1
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2

prune169.0ms

Filtered

79 candidates to 136 candidates (-72.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 18.5b

Counts

143 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

8.1b	(+ (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
32.9b	(sqrt (+ (* re re) (* im im)))
32.9b	(sqrt (+ (* re re) (* im im)))
32.9b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

18.0ms	(+ (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4min

Counts

68 → 68

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	15	35
1	25	34
2	43	34
3	69	34
4	141	34
5	333	34
6	838	34
7	2346	34
done	5000	34
0	14	34
1	20	34
2	26	34
done	26	34
0	14	34
1	23	34
2	36	34
3	54	34
4	105	34
5	241	34
6	591	34
7	1575	34
done	5000	34
0	15	69
1	21	69
2	27	69
done	27	69
0	14	34
1	20	34
2	26	34
done	26	34
0	15	101
1	34	101
2	95	35
3	397	35
4	1559	35
5	4364	35
done	5000	35
0	14	34
1	20	34
2	26	34
done	26	34
0	14	34
1	20	34
2	26	34
done	26	34
0	16	37
1	37	37
2	98	37
3	372	37
4	1332	37
5	3154	37
done	5001	37
0	16	101
1	38	99
2	116	87
3	356	67
4	705	67
5	1523	67
6	2803	67
7	3101	67
8	3335	67
9	3404	67
done	3404	67
0	14	67
1	31	67
2	83	55
3	214	44
4	333	44
5	526	44
6	718	44
7	1138	44
8	2988	44
done	5000	44
0	13	33
1	20	33
2	27	33
done	27	33
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	28	51
1	70	49
2	156	43
3	437	27
4	1362	26
done	5001	26
0	20	25
1	45	23
2	84	21
3	200	18
4	435	16
5	1202	16
6	3990	16
done	5000	16
0	21	25
1	46	24
2	82	22
3	196	19
4	476	18
5	1418	18
6	4761	16
done	5000	16

prune154.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	67	8	75

Merged error: 18.5b

Counts

75 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

8.1b	(+ (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
32.9b	(sqrt (+ (* re re) (* im im)))
32.9b	(sqrt (+ (* re re) (* im im)))
32.9b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

18.0ms	(+ (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4min

Counts

68 → 68

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	8	19
1	9	19
done	9	19
0	7	9
1	8	9
done	8	9
0	8	26
1	10	16
2	21	10
3	34	10
4	42	10
5	52	10
6	73	10
7	134	10
8	350	10
9	1295	10
done	5000	10
0	8	18
1	10	9
done	10	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	2	2
1	4	1
done	4	1
0	6	8
1	7	8
done	7	8
0	9	12
1	27	12
2	64	8
3	119	8
4	261	8
5	697	8
6	2312	8
done	5000	8
0	10	24
1	32	20
2	84	18
3	177	16
4	309	16
5	723	16
6	1972	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	3	3
1	6	1
done	6	1
0	7	9
1	8	9
done	8	9
0	7	9
1	8	9
done	8	9
0	15	35
1	25	34
2	43	34
3	69	34
4	141	34
5	333	34
6	838	34
7	2346	34
done	5000	34
0	14	34
1	20	34
2	26	34
done	26	34
0	14	34
1	23	34
2	36	34
3	54	34
4	105	34
5	241	34
6	591	34
7	1575	34
done	5000	34
0	15	69
1	21	69
2	27	69
done	27	69
0	14	34
1	20	34
2	26	34
done	26	34
0	15	101
1	34	101
2	95	35
3	397	35
4	1559	35
5	4364	35
done	5000	35
0	14	34
1	20	34
2	26	34
done	26	34
0	14	34
1	20	34
2	26	34
done	26	34
0	16	37
1	37	37
2	98	37
3	372	37
4	1332	37
5	3154	37
done	5001	37
0	16	101
1	38	99
2	116	87
3	356	67
4	705	67
5	1523	67
6	2803	67
7	3101	67
8	3335	67
9	3404	67
done	3404	67
0	14	67
1	31	67
2	83	55
3	214	44
4	333	44
5	526	44
6	718	44
7	1138	44
8	2988	44
done	5000	44
0	13	33
1	20	33
2	27	33
done	27	33
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	28	51
1	70	49
2	156	43
3	437	27
4	1362	26
done	5001	26
0	20	25
1	45	23
2	84	21
3	200	18
4	435	16
5	1202	16
6	3990	16
done	5000	16
0	21	25
1	46	24
2	82	22
3	196	19
4	476	18
5	1418	18
6	4761	16
done	5000	16

prune160.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	67	9	76

Merged error: 18.5b

Counts

76 → 9

regimes313.0ms

Accuracy

55.1% (9.7b remaining)

Error of 26.9b against oracle of 17.2b and baseline of 38.8b

bsearch59.0ms

Steps

Iters	Range	Point
9	2.4540169358802756e+30	3.519108532790208e+36	3.466178613033722e+36
8	3.8885538970219946e-190	3.3867492948767555e-187	4.272863498107774e-190
8	-3.1189153377596726e-255	-7.903551994781705e-258	-4.0920801532101425e-256

Iters

Range

Point

2.4540169358802756e+30

3.519108532790208e+36

3.466178613033722e+36

3.8885538970219946e-190

3.3867492948767555e-187

4.272863498107774e-190

-3.1189153377596726e-255

-7.903551994781705e-258

-4.0920801532101425e-256

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	74
1	48	74
done	48	74

end0.0ms

sample1.2s

Algorithm

intervals

Results

337.0ms	6009×	body	80	valid
219.0ms	687×	body	2560	valid
143.0ms	512×	body	1280	valid
121.0ms	287×	body	5120	valid
62.0ms	295×	body	640	valid
22.0ms	137×	body	320	valid
8.0ms	73×	body	160	valid

Details

sample48.0ms

simplify9.0ms

prune4.0ms

localize12.0ms

rewrite21.0ms

series49.0ms

simplify47.3s

prune122.0ms

localize14.0ms

rewrite49.0ms

series35.0ms

simplify1.7min

prune169.0ms

localize19.0ms

rewrite33.0ms

series58.0ms

simplify1.4min

prune154.0ms

localize27.0ms

rewrite35.0ms

series54.0ms

simplify1.4min

prune160.0ms

regimes313.0ms

bsearch59.0ms

simplify4.0ms

end0.0ms

sample1.2s

Profiling