Details

sample81.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
24.0ms	237×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune5.0ms

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: 32.0b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

7.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
11.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
5.0ms	(sqrt (+ (* re re) (* im im)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
28.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2min

Counts

122 → 122

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	2	3
1	6	1
done	6	1
0	3	5
done	3	5
0	2	3
1	6	1
done	6	1
0	4	7
1	6	5
2	7	5
done	7	5
0	4	6
1	6	6
2	8	5
3	9	5
done	9	5
0	4	6
1	7	4
2	13	4
3	18	4
4	36	4
5	76	4
6	184	4
7	565	4
8	2216	4
done	5001	4
0	5	17
1	12	17
2	21	9
3	34	4
4	67	4
5	147	4
6	370	4
7	1337	4
done	5000	4
0	5	13
done	5	13
0	4	6
done	4	6
0	5	17
1	13	17
2	20	7
3	34	4
4	68	4
5	153	4
6	379	4
7	1358	4
done	5000	4
0	4	6
1	5	3
done	5	3
0	4	6
1	5	3
done	5	3
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	5	15
1	9	15
2	11	9
3	20	5
4	35	5
5	61	5
6	131	5
7	348	5
8	1255	5
done	5001	5
0	4	7
done	4	7
0	4	7
done	4	2
0	4	7
done	4	2
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	4	7
done	4	2
0	4	7
done	4	2
0	3	3
1	6	1
done	6	1
0	6	9
1	9	9
2	15	8
3	21	8
4	25	8
done	25	8
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	5
1	8	4
done	8	1
0	3	5
done	3	5
0	6	9
1	9	9
2	15	8
3	21	8
4	25	8
done	25	8
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	5
1	8	4
done	8	1
0	3	5
done	3	5
0	4	4
1	7	2
2	10	2
done	10	2
0	5	10
1	8	10
2	10	10
done	10	10
0	4	6
1	5	6
done	5	6
0	4	4
1	7	2
2	10	2
done	10	2
0	3	5
done	3	5
0	4	6
1	5	6
done	5	6
0	4	6
1	5	6
done	5	6
0	3	5
done	3	5
0	20	30
1	27	30
2	28	30
done	28	30
0	19	29
1	27	29
2	29	29
3	30	29
done	30	29
0	19	29
1	24	29
done	24	29
0	22	86
1	60	86
2	204	32
3	666	30
4	2026	30
done	5000	30
0	20	59
1	25	59
done	25	59
0	19	29
1	24	29
done	24	29
0	20	86
1	32	86
2	64	30
3	168	30
4	489	30
5	1481	30
6	4343	30
done	5000	30
0	19	29
1	24	29
done	24	29
0	19	29
1	24	29
done	24	29
0	15	19
1	22	19
2	36	19
3	37	19
done	37	19
0	7	10
1	11	10
2	19	10
3	20	10
done	20	10
0	22	61
1	33	61
2	42	61
3	48	61
done	48	61
0	20	30
1	25	30
done	25	30
0	21	50
1	28	50
2	30	50
3	31	50
done	31	50
0	20	30
1	25	30
done	25	30
0	18	41
1	26	39
2	32	39
3	37	39
done	37	39
0	19	29
1	24	29
done	24	29
0	21	41
1	28	41
done	28	41
0	20	30
1	25	30
done	25	30
0	20	30
1	25	30
done	25	30
0	20	30
1	25	30
done	25	30
0	17	21
1	23	19
2	25	19
done	25	19
0	19	29
1	24	29
done	24	29
0	10	23
1	15	23
done	15	23
0	19	29
1	24	29
done	24	29
0	9	12
1	12	12
done	12	12
0	19	29
1	24	29
done	24	29
0	2	3
1	4	1
done	4	1
0	18	28
1	23	28
done	23	28
0	8	11
1	11	11
done	11	11
0	18	28
1	23	28
done	23	28
0	20	40
1	27	40
done	27	40
0	19	29
1	24	29
done	24	29
0	16	20
1	22	18
2	24	18
done	24	18
0	19	29
1	24	29
done	24	29
0	19	29
1	24	29
done	24	29
0	18	28
1	23	28
done	23	28
0	21	32
1	43	32
2	80	27
3	137	27
4	275	27
5	704	27
6	2340	27
done	5000	27
0	20	38
1	37	38
2	60	32
3	110	27
4	243	27
5	607	27
6	1531	27
done	5001	27
0	22	66
1	57	60
2	178	60
3	617	53
4	1924	53
5	4853	53
done	5000	53
0	18	28
1	25	28
2	46	28
3	107	28
4	261	28
5	412	28
6	559	28
7	738	28
8	1190	28
9	2515	28
10	4189	28
done	5000	28
0	10	12
1	12	12
done	12	12
0	12	14
1	14	14
done	14	14
0	11	13
1	16	13
2	17	13
done	17	13
0	11	13
1	16	11
2	25	11
3	35	11
4	58	11
5	114	11
6	255	11
7	713	11
8	2694	11
done	5001	11
0	14	38
1	22	38
2	47	16
3	89	16
4	141	14
5	262	14
6	661	14
7	2493	14
done	5001	14
0	12	27
1	14	27
done	14	27
0	11	13
1	13	13
done	13	13
0	12	38
1	24	38
2	53	14
3	97	14
4	113	14
5	159	14
6	295	14
7	740	14
8	2752	14
done	5000	14
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	12	14
1	14	14
done	14	14
0	12	14
1	14	14
done	14	14
0	12	16
1	16	16
2	22	15
3	28	15
4	32	15
done	32	15
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	10	12
1	14	11
done	14	1
0	10	12
1	12	12
done	12	12
0	12	16
1	16	16
2	22	15
3	28	15
4	32	15
done	32	15
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	10	12
1	14	11
done	14	1
0	10	12
1	12	12
done	12	12
0	9	11
1	13	9
2	16	9
done	16	9
0	12	17
1	16	17
2	18	17
done	18	17
0	11	13
1	13	13
done	13	13
0	9	11
1	13	9
2	16	9
done	16	9
0	9	11
1	11	11
done	11	11
0	10	12
1	12	12
done	12	12
0	9	11
1	11	11
done	11	11
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	10	12
1	12	12
done	12	12
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	7	7
1	14	6
2	28	4
3	48	4
4	70	4
5	150	4
6	433	4
7	1524	4
done	5000	4
0	8	9
1	19	7
2	35	4
3	73	4
4	106	4
5	223	4
6	782	4
7	3802	4
done	5000	4
0	8	9
1	17	9
2	36	9
3	97	6
4	281	4
5	869	4
done	5000	4
0	9	11
1	13	9
done	13	5
0	11	15
1	26	11
2	38	5
3	65	5
4	69	5
5	70	5
done	70	5
0	13	15
1	26	14
2	41	13
3	69	10
4	121	8
5	244	8
6	525	8
7	1206	8
8	3329	8
done	5001	8
0	9	11
1	20	9
2	44	5
3	53	5
done	53	5
0	11	15
1	24	11
2	43	5
3	96	5
4	117	5
5	121	5
done	121	5
0	13	15
1	24	14
2	46	13
3	137	10
4	438	8
5	1194	8
6	4503	8
done	5000	8

prune272.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	106	16	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	16	123

Merged error: 6.8b

Counts

123 → 16

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (+ (* re re) (* im im))))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2min

Counts

73 → 73

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	8	10
1	9	10
done	9	10
0	8	10
1	9	10
done	9	10
0	9	20
1	10	20
done	10	20
0	8	10
1	9	10
done	9	10
0	9	19
1	11	10
done	11	10
0	8	10
1	9	10
done	9	10
0	8	10
1	9	10
done	9	10
0	8	10
1	9	10
done	9	10
0	3	3
1	5	2
done	5	2
0	7	9
1	8	9
done	8	9
0	8	10
1	9	10
done	9	10
0	8	10
1	9	10
done	9	10
0	2	2
1	4	1
done	4	1
0	7	9
1	8	9
done	8	9
0	10	13
1	28	13
2	65	9
3	118	9
4	258	9
5	683	9
6	2321	9
done	5000	9
0	11	25
1	33	21
2	87	19
3	180	17
4	312	17
5	726	17
6	1983	17
done	5001	17
0	9	17
1	22	17
2	43	13
3	89	9
4	214	9
5	585	9
6	1494	9
done	5000	9
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	9	21
1	10	21
done	10	21
0	8	10
1	9	10
done	9	10
0	9	29
1	11	29
2	13	11
3	18	8
4	24	8
5	34	8
6	55	8
7	120	8
8	340	8
9	1270	8
done	5000	8
0	8	10
1	9	10
done	9	10
0	8	10
1	9	10
done	9	10
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	21	27
1	49	25
2	107	19
3	283	14
4	791	12
5	3012	12
done	5000	12
0	11	12
1	22	10
2	46	8
3	130	5
4	285	3
5	617	2
6	1981	2
done	5000	2
0	12	12
1	23	11
2	44	9
3	126	7
4	324	5
5	874	4
6	2893	3
done	5000	3

prune198.0ms

Filtered

59 candidates to 73 candidates (-23.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	73	16	89

Merged error: 6.8b

Counts

89 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

7.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
11.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
51.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
17.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2min

Counts

122 → 122

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	2	3
1	6	1
done	6	1
0	3	5
done	3	5
0	2	3
1	6	1
done	6	1
0	4	7
1	6	5
2	7	5
done	7	5
0	4	6
1	6	6
2	8	5
3	9	5
done	9	5
0	4	6
1	7	4
2	13	4
3	18	4
4	36	4
5	76	4
6	184	4
7	565	4
8	2216	4
done	5001	4
0	5	17
1	12	17
2	21	9
3	34	4
4	67	4
5	147	4
6	370	4
7	1337	4
done	5000	4
0	5	13
done	5	13
0	4	6
done	4	6
0	5	17
1	13	17
2	20	7
3	34	4
4	68	4
5	153	4
6	379	4
7	1358	4
done	5000	4
0	4	6
1	5	3
done	5	3
0	4	6
1	5	3
done	5	3
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	5	15
1	9	15
2	11	9
3	20	5
4	35	5
5	61	5
6	131	5
7	348	5
8	1255	5
done	5001	5
0	4	7
done	4	7
0	4	7
done	4	2
0	4	7
done	4	2
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	2	3
1	4	1
done	4	1
0	3	5
done	3	5
0	4	7
done	4	2
0	4	7
done	4	2
0	3	3
1	6	1
done	6	1
0	6	9
1	9	9
2	15	8
3	21	8
4	25	8
done	25	8
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	5
1	8	4
done	8	1
0	3	5
done	3	5
0	6	9
1	9	9
2	15	8
3	21	8
4	25	8
done	25	8
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	6
1	6	6
done	6	6
0	5	5
1	8	4
done	8	1
0	3	5
done	3	5
0	4	4
1	7	2
2	10	2
done	10	2
0	5	10
1	8	10
2	10	10
done	10	10
0	4	6
1	5	6
done	5	6
0	4	4
1	7	2
2	10	2
done	10	2
0	3	5
done	3	5
0	4	6
1	5	6
done	5	6
0	4	6
1	5	6
done	5	6
0	3	5
done	3	5
0	20	30
1	27	30
2	28	30
done	28	30
0	19	29
1	27	29
2	29	29
3	30	29
done	30	29
0	19	29
1	24	29
done	24	29
0	22	86
1	60	86
2	204	32
3	665	30
4	2035	30
done	5000	30
0	20	59
1	25	59
done	25	59
0	19	29
1	24	29
done	24	29
0	20	86
1	32	86
2	64	30
3	156	30
4	411	30
5	1119	30
6	3019	30
done	5001	30
0	19	29
1	24	29
done	24	29
0	19	29
1	24	29
done	24	29
0	7	10
1	11	10
2	19	10
3	20	10
done	20	10
0	15	19
1	22	19
2	36	19
3	37	19
done	37	19
0	22	61
1	33	61
2	42	61
3	48	61
done	48	61
0	20	30
1	25	30
done	25	30
0	21	41
1	28	41
2	30	41
3	31	41
done	31	41
0	20	30
1	25	30
done	25	30
0	10	23
1	15	21
2	21	21
3	26	21
done	26	21
0	19	29
1	24	29
done	24	29
0	21	50
1	28	50
done	28	50
0	20	30
1	25	30
done	25	30
0	20	30
1	25	30
done	25	30
0	20	30
1	25	30
done	25	30
0	9	12
1	12	10
2	14	10
done	14	10
0	19	29
1	24	29
done	24	29
0	18	41
1	26	41
done	26	41
0	19	29
1	24	29
done	24	29
0	17	21
1	23	21
done	23	21
0	19	29
1	24	29
done	24	29
0	2	3
1	4	1
done	4	1
0	18	28
1	23	28
done	23	28
0	16	20
1	22	20
done	22	20
0	18	28
1	23	28
done	23	28
0	20	49
1	27	49
done	27	49
0	19	29
1	24	29
done	24	29
0	8	11
1	11	9
2	13	9
done	13	9
0	19	29
1	24	29
done	24	29
0	19	29
1	24	29
done	24	29
0	18	28
1	23	28
done	23	28
0	21	32
1	45	32
2	110	32
3	255	32
4	461	32
5	1226	32
6	4727	32
done	5000	32
0	20	47
1	41	47
2	84	47
3	145	47
4	214	47
5	355	47
6	551	47
7	921	47
8	2725	47
done	5001	47
0	22	48
1	55	44
2	156	40
3	530	37
4	1785	37
done	5001	37
0	18	28
1	28	28
2	53	28
3	159	28
4	546	28
5	1307	28
6	3323	28
done	5000	28
0	10	12
1	12	12
done	12	12
0	12	14
1	14	14
done	14	14
0	11	13
1	16	13
2	17	13
done	17	13
0	11	13
1	16	11
2	25	11
3	35	11
4	58	11
5	114	11
6	255	11
7	713	11
8	2694	11
done	5001	11
0	14	38
1	22	38
2	47	16
3	89	16
4	141	14
5	262	14
6	661	14
7	2493	14
done	5001	14
0	12	27
1	14	27
done	14	27
0	11	13
1	13	13
done	13	13
0	12	38
1	24	38
2	53	14
3	97	14
4	113	14
5	159	14
6	295	14
7	740	14
8	2752	14
done	5000	14
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	12	14
1	14	14
done	14	14
0	12	14
1	14	14
done	14	14
0	12	16
1	16	16
2	22	15
3	28	15
4	32	15
done	32	15
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	10	12
1	14	11
done	14	1
0	10	12
1	12	12
done	12	12
0	12	16
1	16	16
2	22	15
3	28	15
4	32	15
done	32	15
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	10	12
1	14	11
done	14	1
0	10	12
1	12	12
done	12	12
0	9	11
1	13	9
2	16	9
done	16	9
0	12	17
1	16	17
2	18	17
done	18	17
0	11	13
1	13	13
done	13	13
0	9	11
1	13	9
2	16	9
done	16	9
0	9	11
1	11	11
done	11	11
0	10	12
1	12	12
done	12	12
0	9	11
1	11	11
done	11	11
0	11	13
1	13	13
done	13	13
0	11	13
1	13	13
done	13	13
0	10	12
1	12	12
done	12	12
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	7	7
1	14	6
2	28	4
3	48	4
4	70	4
5	150	4
6	433	4
7	1524	4
done	5000	4
0	8	9
1	19	7
2	35	4
3	73	4
4	106	4
5	223	4
6	782	4
7	3802	4
done	5000	4
0	8	9
1	17	9
2	36	9
3	97	6
4	281	4
5	869	4
done	5000	4
0	9	11
1	13	9
done	13	5
0	11	15
1	26	11
2	38	5
3	65	5
4	69	5
5	70	5
done	70	5
0	13	15
1	26	14
2	40	13
3	69	10
4	115	8
5	250	8
6	699	8
7	1913	8
done	5001	8
0	9	11
1	20	9
2	44	5
3	53	5
done	53	5
0	11	15
1	24	11
2	43	5
3	96	5
4	117	5
5	121	5
done	121	5
0	13	15
1	24	14
2	46	13
3	137	10
4	438	8
5	1194	8
6	4503	8
done	5000	8

prune247.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	118	20	138

Merged error: 6.8b

Counts

138 → 20

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.5b	(cbrt base)
0.5b	(cbrt base)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
2.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
32.0ms	(cbrt base)
27.0ms	(cbrt base)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0min

Counts

80 → 80

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	3	3
done	3	3
0	3	3
done	3	3
0	4	6
done	4	6
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	2	2
1	4	1
done	4	1
0	2	2
done	2	2
0	4	7
done	4	7
0	3	3
done	3	3
0	4	8
1	5	8
2	7	4
3	12	1
4	16	1
5	22	1
6	32	1
7	55	1
8	122	1
9	333	1
10	1272	1
done	5000	1
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	4	6
done	4	6
0	3	3
done	3	3
0	3	3
done	3	3
0	3	3
done	3	3
0	2	2
1	4	1
done	4	1
0	2	2
done	2	2
0	4	7
done	4	7
0	3	3
done	3	3
0	4	8
1	5	8
2	7	4
3	12	1
4	16	1
5	22	1
6	32	1
7	55	1
8	122	1
9	333	1
10	1272	1
done	5000	1
0	3	3
done	3	3
0	3	3
done	3	3
0	26	40
1	43	37
2	64	33
3	73	33
4	74	33
done	74	33
0	25	39
1	43	36
2	65	32
3	77	32
4	78	32
done	78	32
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	28	116
1	76	107
2	273	35
3	1223	33
done	5000	33
0	26	79
1	41	73
2	61	65
3	70	65
4	71	65
done	71	65
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	26	116
1	48	107
2	99	33
3	213	33
4	567	33
5	1898	33
done	5000	33
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	15	19
1	22	19
2	36	19
3	37	19
done	37	19
0	13	20
1	27	17
2	62	13
3	129	12
4	187	12
5	206	12
6	244	12
7	327	12
8	480	12
9	494	12
done	494	12
0	28	81
1	49	75
2	78	67
3	95	67
4	96	67
done	96	67
0	26	40
1	41	37
2	61	33
3	70	33
4	71	33
done	71	33
0	27	60
1	44	57
2	66	53
3	78	53
4	80	53
done	80	53
0	26	40
1	41	37
2	61	33
3	70	33
4	71	33
done	71	33
0	18	41
1	26	39
2	32	39
3	37	39
done	37	39
0	25	39
1	40	36
2	60	32
3	69	32
4	70	32
done	70	32
0	27	61
1	44	55
2	64	47
3	73	47
4	74	47
done	74	47
0	26	40
1	41	37
2	61	33
3	70	33
4	71	33
done	71	33
0	26	40
1	41	37
2	61	33
3	70	33
4	71	33
done	71	33
0	26	40
1	41	37
2	61	33
3	70	33
4	71	33
done	71	33
0	17	21
1	23	19
2	25	19
done	25	19
0	25	39
1	40	36
2	60	32
3	69	32
4	70	32
done	70	32
0	16	43
1	31	37
2	50	29
3	57	29
4	59	29
done	59	29
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	15	22
1	28	19
2	47	15
3	56	15
4	58	15
done	58	15
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	2	3
1	4	1
done	4	1
0	24	38
1	39	35
2	59	31
3	68	31
4	69	31
done	69	31
0	14	21
1	27	18
2	46	14
3	53	14
4	54	14
done	54	14
0	24	38
1	39	35
2	59	31
3	68	31
4	70	31
done	70	31
0	26	60
1	43	54
2	63	46
3	72	46
4	73	46
done	73	46
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	16	20
1	22	18
2	24	18
done	24	18
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	25	39
1	40	36
2	60	32
3	69	32
4	71	32
done	71	32
0	24	38
1	39	35
2	59	31
3	68	31
4	70	31
done	70	31
0	27	42
1	54	39
2	121	33
3	385	33
4	1648	33
done	5000	33
0	26	58
1	53	52
2	141	42
3	428	38
4	1251	38
5	3353	38
done	5000	38
0	28	76
1	74	67
2	233	63
3	1048	56
4	4768	56
done	5000	56
0	24	38
1	41	35
2	88	31
3	242	31
4	793	31
5	2054	31
6	4299	31
done	5000	31
0	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	8	8
1	20	7
2	28	5
3	50	2
4	87	2
5	171	2
6	353	2
7	904	2
8	3078	2
done	5000	2
0	9	10
1	19	8
2	35	5
3	72	2
4	126	2
5	264	2
6	568	2
7	1635	2
done	5000	2
0	12	13
1	23	12
2	40	11
3	95	10
4	227	9
5	544	7
6	1185	6
7	3475	6
done	5001	6
0	8	8
1	20	7
2	28	5
3	50	2
4	87	2
5	171	2
6	353	2
7	904	2
8	3078	2
done	5000	2
0	9	10
1	19	8
2	35	5
3	72	2
4	126	2
5	264	2
6	568	2
7	1635	2
done	5000	2
0	12	13
1	23	12
2	40	11
3	95	10
4	227	9
5	544	7
6	1185	6
7	3475	6
done	5001	6
0	9	11
1	13	9
done	13	5
0	11	15
1	26	11
2	38	5
3	65	5
4	69	5
5	70	5
done	70	5
0	19	24
1	43	22
2	79	19
3	180	19
4	457	17
5	1112	15
6	2496	14
done	5001	14

prune140.0ms

Filtered

66 candidates to 80 candidates (-21.2%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	2	16	18
Picked	0	1	1
Done	0	1	1
Total	79	21	100

Merged error: 6.8b

Counts

100 → 21

regimes1.2s

Accuracy

58.2% (10.2b remaining)

Error of 17.3b against oracle of 7.1b and baseline of 31.5b

bsearch94.0ms

Steps

Iters	Range		Point
9	1.1780322745283183e+122	1.0200671223655964e+127	3.340694489817801e+123
6	-1.7705855973447552e+17	-2.591132052930294e+16	-1.487849500661273e+17

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	96
1	59	96
done	59	96

end0.0ms

sample2.3s

Algorithm

intervals

Results

836.0ms	8000×	body	80	valid
790.0ms	7915×	body	80	nan

Details

sample81.0ms

simplify6.0ms

prune5.0ms

localize20.0ms

rewrite32.0ms

series79.0ms

simplify1.2min

prune272.0ms

localize30.0ms

rewrite21.0ms

series45.0ms

simplify1.2min

prune198.0ms

localize23.0ms

rewrite35.0ms

series105.0ms

simplify1.2min

prune247.0ms

localize32.0ms

rewrite24.0ms

series122.0ms

simplify1.0min

prune140.0ms

regimes1.2s

bsearch94.0ms

simplify5.0ms

end0.0ms

sample2.3s

Profiling