Details

sample32.0ms

Algorithm

intervals

Results

14.0ms

275×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	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: 24.0b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* a c) (* b d))
23.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+ (* a c) (* b d))
9.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(+ (* a c) (* b d))
35.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify35.4s

Counts

48 → 48

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	19	17
2	20	17
done	20	17
0	12	16
1	19	16
2	21	16
3	22	16
done	22	16
0	12	16
1	16	16
done	16	16
0	15	47
1	52	47
2	196	19
3	661	17
4	2051	17
done	5000	17
0	13	33
1	17	33
done	17	33
0	12	16
1	16	16
done	16	16
0	13	47
1	24	47
2	56	17
3	160	17
4	477	17
5	1462	17
6	4309	17
done	5001	17
0	12	16
1	16	16
done	16	16
0	12	16
1	16	16
done	16	16
0	8	8
1	14	8
2	28	8
3	29	8
done	29	8
0	6	8
1	10	8
2	18	8
3	19	8
done	19	8
0	15	35
1	25	35
2	34	35
3	40	35
done	40	35
0	13	17
1	17	17
done	17	17
0	14	26
1	20	26
2	22	26
3	23	26
done	23	26
0	13	17
1	17	17
done	17	17
0	11	19
1	18	17
2	24	17
3	29	17
done	29	17
0	12	16
1	16	16
done	16	16
0	14	26
1	20	26
done	20	26
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	10	10
1	15	8
2	17	8
done	17	8
0	12	16
1	16	16
done	16	16
0	9	19
1	14	19
done	14	19
0	12	16
1	16	16
done	16	16
0	8	10
1	11	10
done	11	10
0	12	16
1	16	16
done	16	16
0	2	3
1	4	1
done	4	1
0	11	15
1	15	15
done	15	15
0	7	9
1	10	9
done	10	9
0	11	15
1	15	15
done	15	15
0	13	25
1	19	25
done	19	25
0	12	16
1	16	16
done	16	16
0	9	9
1	14	7
2	16	7
done	16	7
0	12	16
1	16	16
done	16	16
0	12	16
1	16	16
done	16	16
0	11	15
1	15	15
done	15	15
0	14	19
1	35	19
2	72	15
3	123	15
4	263	15
5	681	15
6	2339	15
done	5000	15
0	13	23
1	29	23
2	50	19
3	100	15
4	233	15
5	604	15
6	1523	15
done	5000	15
0	15	31
1	49	27
2	170	27
3	612	27
4	1919	27
5	4961	27
done	5000	27
0	11	15
1	17	15
2	38	15
3	99	15
4	255	15
5	398	15
6	543	15
7	722	15
8	1170	15
9	2492	15
10	4208	15
done	5000	15
0	9	9
1	18	8
2	30	8
3	58	8
4	175	8
5	619	8
6	2814	8
done	5000	8
0	8	8
1	11	8
done	11	8
0	8	8
1	14	8
2	23	8
3	36	8
4	88	8
5	282	8
6	1033	8
done	5001	8
0	9	17
1	12	17
done	12	17
0	8	8
1	11	8
done	11	8
0	9	23
1	25	23
2	89	9
3	330	9
4	988	9
5	2567	9
done	5000	9
0	8	8
1	11	8
done	11	8
0	8	8
1	11	8
done	11	8
0	10	11
1	32	11
2	99	11
3	244	11
4	477	11
5	1224	11
6	4678	11
done	5000	11
0	11	23
1	39	19
2	109	19
3	233	19
4	424	19
5	554	19
6	721	19
7	842	19
8	1136	19
9	1729	19
done	1729	19
0	9	15
1	30	15
2	71	15
3	129	15
4	194	15
5	325	15
6	521	15
7	887	15
8	2712	15
done	5000	15
0	7	7
1	11	7
2	18	7
done	18	7
0	1	1
done	1	1
0	1	1
done	1	1
0	1	1
done	1	1
0	1	1
done	1	1
0	7	7
1	10	7
done	10	7
0	7	7
1	10	7
done	10	7

prune100.0ms

Filtered

40 candidates to 48 candidates (-20.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Merged error: 23.3b

Counts

49 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* a c) (* b d))
15.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

5.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* a c) (* b d))
43.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1min

Counts

96 → 96

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	14	18
1	20	18
2	21	18
done	21	18
0	13	17
1	20	17
2	22	17
3	23	17
done	23	17
0	13	17
1	17	17
done	17	17
0	16	50
1	41	40
2	144	20
3	465	18
4	1392	18
5	4257	18
done	5001	18
0	14	35
1	18	35
done	18	35
0	13	17
1	17	17
done	17	17
0	14	50
1	25	50
2	57	18
3	161	18
4	466	18
5	1383	18
6	3903	18
done	5001	18
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	8	8
1	14	8
2	28	8
3	29	8
done	29	8
0	7	9
1	8	9
done	8	9
0	16	37
1	26	37
2	35	37
3	41	37
done	41	37
0	14	18
1	18	18
done	18	18
0	16	36
1	23	27
2	25	27
3	26	27
done	26	27
0	14	18
1	18	18
done	18	18
0	15	27
1	21	27
2	23	27
3	24	27
done	24	27
0	14	18
1	18	18
done	18	18
0	12	20
1	19	19
2	21	19
3	22	17
4	29	17
done	29	17
0	13	17
1	17	17
done	17	17
0	15	27
1	21	27
2	23	27
3	24	27
done	24	27
0	14	18
1	18	18
done	18	18
0	11	19
1	18	17
2	24	17
3	29	17
done	29	17
0	13	17
1	17	17
done	17	17
0	15	28
1	21	28
done	21	28
0	14	18
1	18	18
done	18	18
0	15	27
1	20	18
done	20	18
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	11	11
1	16	10
done	16	10
0	13	17
1	17	17
done	17	17
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	10	10
1	15	8
2	17	8
done	17	8
0	13	17
1	17	17
done	17	17
0	10	21
1	15	21
done	15	21
0	13	17
1	17	17
done	17	17
0	10	20
1	14	11
done	14	11
0	13	17
1	17	17
done	17	17
0	9	11
1	12	11
done	12	11
0	13	17
1	17	17
done	17	17
0	3	4
1	5	3
done	5	3
0	12	16
1	16	16
done	16	16
0	9	11
1	12	11
done	12	11
0	13	17
1	17	17
done	17	17
0	2	3
1	4	1
done	4	1
0	12	16
1	16	16
done	16	16
0	8	10
1	11	10
done	11	10
0	12	16
1	16	16
done	16	16
0	14	27
1	20	27
done	20	27
0	14	26
1	19	17
done	19	17
0	13	17
1	17	17
done	17	17
0	10	10
1	15	9
done	15	9
0	13	17
1	17	17
done	17	17
0	9	9
1	14	7
2	16	7
done	16	7
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	12	16
1	16	16
done	16	16
0	15	20
1	36	20
2	73	16
3	132	16
4	272	16
5	707	16
6	2301	16
done	5000	16
0	14	24
1	30	24
2	51	20
3	97	16
4	222	16
5	583	16
6	1494	16
done	5000	16
0	16	32
1	50	28
2	147	28
3	402	28
4	915	28
5	1553	28
6	1927	28
7	2376	28
8	3375	28
done	5000	28
0	12	16
1	18	16
2	31	16
3	60	16
4	72	16
5	80	16
done	80	16
0	9	9
1	18	8
2	30	8
3	58	8
4	175	8
5	619	8
6	2814	8
done	5000	8
0	8	8
1	11	8
done	11	8
0	8	8
1	14	8
2	23	8
3	36	8
4	88	8
5	282	8
6	1033	8
done	5001	8
0	9	17
1	12	17
done	12	17
0	8	8
1	11	8
done	11	8
0	9	23
1	25	23
2	89	9
3	330	9
4	988	9
5	2567	9
done	5000	9
0	8	8
1	11	8
done	11	8
0	8	8
1	11	8
done	11	8
0	10	11
1	32	11
2	99	11
3	244	11
4	477	11
5	1224	11
6	4678	11
done	5000	11
0	11	23
1	39	19
2	109	19
3	233	19
4	424	19
5	554	19
6	721	19
7	842	19
8	1136	19
9	1729	19
done	1729	19
0	9	15
1	30	15
2	71	15
3	129	15
4	194	15
5	325	15
6	521	15
7	887	15
8	2712	15
done	5000	15
0	7	7
1	11	7
2	18	7
done	18	7
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	1	1
done	1	1
0	7	7
1	10	7
done	10	7
0	7	7
1	10	7
done	10	7

prune148.0ms

Filtered

79 candidates to 96 candidates (-21.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	91	12	103

Merged error: 21.8b

Counts

103 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
15.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

27.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
15.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
37.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.8min

Counts

172 → 172

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	14	18
1	20	18
2	21	18
done	21	18
0	13	17
1	20	17
2	22	17
3	23	17
done	23	17
0	13	17
1	17	17
done	17	17
0	16	50
1	41	40
2	144	20
3	465	18
4	1392	18
5	4257	18
done	5001	18
0	14	35
1	18	35
done	18	35
0	13	17
1	17	17
done	17	17
0	14	50
1	25	50
2	57	18
3	161	18
4	466	18
5	1383	18
6	3903	18
done	5001	18
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	8	8
1	14	8
2	28	8
3	29	8
done	29	8
0	7	9
1	8	9
done	8	9
0	16	37
1	26	37
2	35	37
3	41	37
done	41	37
0	14	18
1	18	18
done	18	18
0	16	36
1	23	27
2	25	27
3	26	27
done	26	27
0	14	18
1	18	18
done	18	18
0	15	27
1	21	27
2	23	27
3	24	27
done	24	27
0	14	18
1	18	18
done	18	18
0	12	20
1	19	19
2	21	19
3	22	17
4	29	17
done	29	17
0	13	17
1	17	17
done	17	17
0	15	27
1	21	27
2	23	27
3	24	27
done	24	27
0	14	18
1	18	18
done	18	18
0	11	19
1	18	17
2	24	17
3	29	17
done	29	17
0	13	17
1	17	17
done	17	17
0	15	28
1	21	28
done	21	28
0	14	18
1	18	18
done	18	18
0	15	27
1	20	18
done	20	18
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	11	11
1	16	10
done	16	10
0	13	17
1	17	17
done	17	17
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	10	10
1	15	8
2	17	8
done	17	8
0	13	17
1	17	17
done	17	17
0	10	21
1	15	21
done	15	21
0	13	17
1	17	17
done	17	17
0	10	20
1	14	11
done	14	11
0	13	17
1	17	17
done	17	17
0	9	11
1	12	11
done	12	11
0	13	17
1	17	17
done	17	17
0	3	4
1	5	3
done	5	3
0	12	16
1	16	16
done	16	16
0	9	11
1	12	11
done	12	11
0	13	17
1	17	17
done	17	17
0	2	3
1	4	1
done	4	1
0	12	16
1	16	16
done	16	16
0	8	10
1	11	10
done	11	10
0	12	16
1	16	16
done	16	16
0	14	27
1	20	27
done	20	27
0	14	26
1	19	17
done	19	17
0	13	17
1	17	17
done	17	17
0	10	10
1	15	9
done	15	9
0	13	17
1	17	17
done	17	17
0	9	9
1	14	7
2	16	7
done	16	7
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	12	16
1	16	16
done	16	16
0	15	20
1	36	20
2	73	16
3	132	16
4	272	16
5	707	16
6	2301	16
done	5000	16
0	14	24
1	30	24
2	51	20
3	97	16
4	222	16
5	583	16
6	1494	16
done	5000	16
0	16	32
1	50	28
2	147	28
3	402	28
4	915	28
5	1553	28
6	1927	28
7	2376	28
8	3375	28
done	5000	28
0	12	16
1	18	16
2	31	16
3	60	16
4	72	16
5	80	16
done	80	16
0	15	27
1	26	27
2	42	25
3	127	25
4	293	15
5	507	15
6	599	15
7	607	15
done	607	15
0	16	29
1	24	29
2	28	28
3	39	21
4	48	20
5	57	20
6	71	20
7	81	20
8	84	20
done	84	20
0	16	28
1	23	28
2	29	27
3	39	27
4	51	20
5	59	20
6	69	20
7	77	20
8	87	20
9	90	20
done	90	20
0	17	30
1	29	29
2	53	28
3	116	21
4	225	20
5	290	20
6	307	20
done	307	20
0	17	29
1	28	28
2	48	27
3	90	27
4	210	20
5	294	20
6	314	20
done	314	20
0	18	31
1	32	30
2	54	28
3	116	28
4	252	20
5	343	20
6	359	20
done	359	20
0	18	30
1	31	29
2	48	28
3	92	27
4	210	21
5	285	20
6	299	20
7	314	20
done	314	20
0	18	30
1	31	29
2	44	28
3	92	21
4	164	20
5	216	20
6	236	20
done	236	20
0	17	29
1	30	28
2	41	27
3	73	27
4	149	20
5	213	20
6	268	20
done	268	20
0	16	28
1	30	28
2	54	26
3	157	26
4	380	16
5	689	16
6	853	16
7	928	16
done	928	16
0	16	28
1	29	28
2	51	26
3	165	26
4	437	16
5	954	16
6	2252	16
done	5000	16
0	21	83
1	60	59
2	235	31
3	1334	29
done	5000	29
0	21	83
1	47	69
2	143	29
3	591	29
4	2682	28
done	5000	28
0	21	83
1	60	73
2	239	33
3	1072	29
4	4834	28
done	5000	28
0	19	83
1	44	83
2	133	31
3	480	31
4	1959	17
done	5001	17
0	17	57
1	28	57
2	44	53
3	129	53
4	296	33
5	528	33
6	620	33
7	632	33
done	632	33
0	16	28
1	27	28
2	43	26
3	128	26
4	292	16
5	502	16
6	594	16
7	606	16
done	606	16
0	17	83
1	38	83
2	127	27
3	536	27
4	2328	17
done	5000	17
0	16	28
1	27	28
2	43	26
3	128	26
4	292	16
5	502	16
6	594	16
7	606	16
done	606	16
0	16	28
1	27	28
2	43	26
3	128	26
4	292	16
5	502	16
6	594	16
7	606	16
done	606	16
0	9	9
1	21	7
2	47	7
3	71	7
done	71	7
0	7	17
1	8	7
2	9	7
done	9	7
0	17	29
1	24	29
done	24	29
0	17	29
1	24	29
done	24	29
0	18	30
1	27	30
2	30	30
3	34	30
4	35	30
done	35	30
0	18	30
1	27	30
2	30	30
3	34	30
4	35	30
done	35	30
0	18	30
1	27	30
2	30	30
3	34	30
4	35	30
done	35	30
0	18	30
1	27	30
2	30	30
3	34	30
4	35	30
done	35	30
0	18	30
1	27	29
2	30	29
3	32	27
4	46	27
done	46	27
0	18	30
1	27	29
2	30	29
3	32	27
4	46	27
done	46	27
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	18	30
1	27	29
2	30	29
3	32	27
4	46	27
done	46	27
0	18	30
1	27	29
2	30	29
3	32	27
4	46	27
done	46	27
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	18	31
1	29	30
2	37	30
3	49	28
4	99	17
5	104	17
done	104	17
0	17	29
1	26	29
2	29	27
3	42	27
4	47	27
done	47	27
0	17	29
1	26	29
2	29	27
3	42	27
4	47	27
done	47	27
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	29
1	26	29
2	29	27
3	42	27
4	47	27
done	47	27
0	17	29
1	26	29
2	29	27
3	42	27
4	47	27
done	47	27
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	30
1	28	30
2	36	28
3	77	28
4	129	17
5	131	17
done	131	17
0	17	46
1	28	46
2	36	44
3	64	44
4	79	44
5	80	44
6	83	44
7	88	44
8	98	44
9	124	44
10	155	44
11	177	44
12	213	44
13	219	44
14	227	44
15	231	44
done	231	44
0	16	28
1	25	28
2	28	26
3	41	26
4	46	26
5	47	26
6	50	26
7	55	26
8	65	26
9	91	26
10	124	26
11	146	26
12	176	26
13	182	26
14	190	26
15	194	26
done	194	26
0	19	48
1	36	48
2	77	46
3	225	46
4	532	46
5	836	46
6	854	46
done	854	46
0	20	47
1	34	38
2	52	36
3	129	36
4	245	36
5	311	36
6	323	36
done	323	36
0	18	38
1	31	38
2	49	36
3	126	36
4	250	36
5	316	36
6	327	36
done	327	36
0	18	31
1	31	30
2	49	28
3	126	26
4	265	26
5	267	26
done	267	26
0	18	38
1	31	38
2	49	36
3	126	36
4	250	36
5	316	36
6	327	36
done	327	36
0	17	30
1	30	28
2	56	26
3	183	26
4	238	26
5	239	26
done	239	26
0	18	39
1	31	39
2	50	37
3	124	37
4	251	37
5	402	37
6	415	37
done	415	37
0	19	38
1	31	29
2	40	27
3	79	27
4	123	27
5	161	27
6	170	27
done	170	27
0	17	29
1	28	29
2	37	27
3	76	27
4	127	27
5	170	27
6	180	27
done	180	27
0	17	22
1	28	21
2	37	19
3	76	17
4	145	17
5	146	17
done	146	17
0	17	29
1	28	29
2	37	27
3	76	27
4	127	27
5	170	27
6	180	27
done	180	27
0	16	21
1	27	19
2	40	17
3	84	17
4	101	17
done	101	17
0	12	32
1	22	32
2	40	30
3	89	30
4	137	30
done	137	30
0	13	31
1	22	22
2	31	20
3	50	20
4	59	20
done	59	20
0	11	22
1	19	22
2	28	20
3	47	20
4	56	20
done	56	20
0	11	15
1	19	14
2	27	10
3	33	10
4	43	10
done	43	10
0	11	22
1	19	22
2	28	20
3	47	20
4	56	20
done	56	20
0	10	14
1	18	10
2	22	10
3	29	10
done	29	10
0	9	12
1	15	10
done	15	10
0	14	18
1	29	18
2	61	16
3	126	16
4	253	16
5	261	16
done	261	16
0	20	31
1	49	31
2	103	25
3	224	25
4	470	25
5	1099	25
6	2856	25
done	5000	25
0	19	35
1	42	35
2	79	29
3	191	25
4	424	25
5	996	25
6	2057	25
done	5001	25
0	16	28
1	25	28
2	36	28
3	56	28
4	69	28
5	87	28
6	115	28
7	159	28
8	189	28
9	203	28
done	203	28
0	16	28
1	25	28
2	36	28
3	56	28
4	69	28
5	87	28
6	115	28
7	159	28
8	189	28
9	203	28
done	203	28
0	17	29
1	28	28
2	45	28
3	90	26
4	209	26
5	413	26
6	577	26
7	787	26
8	859	26
9	888	26
done	888	26
0	18	29
1	29	28
2	46	28
3	91	26
4	212	26
5	414	26
6	581	26
7	782	26
8	850	26
9	878	26
done	878	26
0	17	29
1	28	28
2	45	28
3	90	26
4	209	26
5	413	26
6	577	26
7	787	26
8	859	26
9	888	26
done	888	26
0	16	28
1	27	27
2	43	27
3	83	25
4	213	15
5	392	15
6	474	15
7	528	15
8	542	15
done	542	15
0	17	29
1	28	28
2	45	28
3	90	26
4	209	26
5	413	26
6	577	26
7	787	26
8	859	26
9	888	26
done	888	26
0	16	28
1	27	27
2	43	27
3	83	25
4	213	15
5	392	15
6	474	15
7	528	15
8	542	15
done	542	15
0	17	29
1	28	28
2	45	28
3	90	26
4	209	26
5	413	26
6	577	26
7	787	26
8	859	26
9	888	26
done	888	26
0	18	29
1	29	28
2	46	28
3	91	26
4	212	26
5	414	26
6	581	26
7	782	26
8	850	26
9	878	26
done	878	26
0	17	29
1	28	28
2	45	28
3	90	26
4	209	26
5	413	26
6	577	26
7	787	26
8	859	26
9	888	26
done	888	26
0	16	28
1	27	27
2	43	27
3	83	25
4	213	15
5	392	15
6	474	15
7	528	15
8	542	15
done	542	15
0	17	29
1	28	28
2	45	28
3	90	26
4	209	26
5	413	26
6	577	26
7	787	26
8	859	26
9	888	26
done	888	26
0	16	28
1	27	27
2	43	27
3	83	25
4	213	15
5	392	15
6	474	15
7	528	15
8	542	15
done	542	15
0	16	28
1	27	28
2	44	26
3	111	26
4	224	26
5	427	26
6	587	26
7	782	26
8	846	26
9	874	26
done	874	26
0	17	28
1	28	28
2	45	26
3	112	26
4	229	26
5	429	26
6	594	26
7	776	26
8	840	26
9	865	26
done	865	26
0	16	28
1	27	28
2	44	26
3	111	26
4	224	26
5	427	26
6	587	26
7	782	26
8	846	26
9	874	26
done	874	26
0	15	27
1	26	27
2	42	25
3	127	25
4	293	15
5	507	15
6	599	15
7	607	15
done	607	15
0	16	28
1	27	28
2	44	26
3	111	26
4	224	26
5	427	26
6	587	26
7	782	26
8	846	26
9	874	26
done	874	26
0	15	27
1	26	27
2	42	25
3	127	25
4	293	15
5	507	15
6	599	15
7	607	15
done	607	15
0	15	27
1	26	27
2	42	25
3	127	25
4	293	15
5	507	15
6	599	15
7	607	15
done	607	15
0	15	27
1	26	27
2	42	25
3	127	25
4	293	15
5	507	15
6	599	15
7	607	15
done	607	15
0	19	41
1	48	37
2	111	35
3	225	33
4	367	33
5	798	33
6	2082	33
done	5001	33
0	15	25
1	27	25
2	45	25
3	80	25
4	114	25
5	173	25
6	265	25
7	477	25
8	1826	25
done	5001	25
0	14	18
1	29	18
2	61	16
3	126	16
4	253	16
5	261	16
done	261	16
0	14	18
1	23	16
2	41	16
3	71	16
4	109	16
5	132	16
6	164	16
7	170	16
8	178	16
9	182	16
done	182	16
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	1	1
done	1	1
0	1	1
done	1	1
0	1	1
done	1	1

prune201.0ms

Filtered

118 candidates to 172 candidates (-45.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	3	6	9
Picked	0	1	1
Done	0	2	2
Total	171	13	184

Merged error: 21.8b

Counts

184 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

15.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
5.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1min

Counts

100 → 100

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	14	18
1	20	18
2	21	18
done	21	18
0	13	17
1	20	17
2	22	17
3	23	17
done	23	17
0	13	17
1	17	17
done	17	17
0	16	50
1	41	40
2	144	20
3	465	18
4	1392	18
5	4257	18
done	5001	18
0	14	35
1	18	35
done	18	35
0	13	17
1	17	17
done	17	17
0	14	50
1	25	50
2	57	18
3	161	18
4	466	18
5	1383	18
6	3903	18
done	5001	18
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	8	8
1	14	8
2	28	8
3	29	8
done	29	8
0	7	9
1	8	9
done	8	9
0	16	37
1	26	37
2	35	37
3	41	37
done	41	37
0	14	18
1	18	18
done	18	18
0	16	36
1	23	27
2	25	27
3	26	27
done	26	27
0	14	18
1	18	18
done	18	18
0	15	27
1	21	27
2	23	27
3	24	27
done	24	27
0	14	18
1	18	18
done	18	18
0	12	20
1	19	19
2	21	19
3	22	17
4	29	17
done	29	17
0	13	17
1	17	17
done	17	17
0	15	27
1	21	27
2	23	27
3	24	27
done	24	27
0	14	18
1	18	18
done	18	18
0	11	19
1	18	17
2	24	17
3	29	17
done	29	17
0	13	17
1	17	17
done	17	17
0	15	28
1	21	28
done	21	28
0	14	18
1	18	18
done	18	18
0	15	27
1	20	18
done	20	18
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	11	11
1	16	10
done	16	10
0	13	17
1	17	17
done	17	17
0	14	18
1	18	18
done	18	18
0	14	18
1	18	18
done	18	18
0	10	10
1	15	8
2	17	8
done	17	8
0	13	17
1	17	17
done	17	17
0	10	21
1	15	21
done	15	21
0	13	17
1	17	17
done	17	17
0	10	20
1	14	11
done	14	11
0	13	17
1	17	17
done	17	17
0	9	11
1	12	11
done	12	11
0	13	17
1	17	17
done	17	17
0	3	4
1	5	3
done	5	3
0	12	16
1	16	16
done	16	16
0	9	11
1	12	11
done	12	11
0	13	17
1	17	17
done	17	17
0	2	3
1	4	1
done	4	1
0	12	16
1	16	16
done	16	16
0	8	10
1	11	10
done	11	10
0	12	16
1	16	16
done	16	16
0	14	27
1	20	27
done	20	27
0	14	26
1	19	17
done	19	17
0	13	17
1	17	17
done	17	17
0	10	10
1	15	9
done	15	9
0	13	17
1	17	17
done	17	17
0	9	9
1	14	7
2	16	7
done	16	7
0	13	17
1	17	17
done	17	17
0	13	17
1	17	17
done	17	17
0	12	16
1	16	16
done	16	16
0	15	20
1	36	20
2	73	16
3	132	16
4	272	16
5	707	16
6	2301	16
done	5000	16
0	14	24
1	30	24
2	51	20
3	97	16
4	222	16
5	583	16
6	1494	16
done	5000	16
0	16	32
1	50	28
2	147	28
3	402	28
4	915	28
5	1553	28
6	1927	28
7	2376	28
8	3375	28
done	5000	28
0	12	16
1	18	16
2	31	16
3	60	16
4	72	16
5	80	16
done	80	16
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	1	1
done	1	1
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2

prune111.0ms

Filtered

82 candidates to 100 candidates (-22.0%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	8	9
Picked	0	1	1
Done	0	3	3
Total	99	14	113

Merged error: 21.8b

Counts

113 → 14

regimes550.0ms

Accuracy

0% (3.0b remaining)

Error of 25.9b against oracle of 23.0b and baseline of 25.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	17	25
done	17	25

end0.0ms

sample840.0ms

Algorithm

intervals

Results

411.0ms

8441×

body

valid

Details

sample32.0ms

simplify4.0ms

prune4.0ms

localize10.0ms

rewrite15.0ms

series47.0ms

simplify35.4s

prune100.0ms

localize14.0ms

rewrite27.0ms

series67.0ms

simplify1.1min

prune148.0ms

localize14.0ms

rewrite58.0ms

series83.0ms

simplify1.8min

prune201.0ms

localize16.0ms

rewrite26.0ms

series62.0ms

simplify1.1min

prune111.0ms

regimes550.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample840.0ms

Profiling