Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
5.0ms	27×	body	1280	valid
4.0ms	256×	pre	80	true
4.0ms	27×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify318.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	33	13
3	51	13
4	70	13
5	119	13
6	144	13
7	180	13
8	213	13
9	264	13
10	304	13
11	316	13
12	328	13
13	340	13
done	340	13

prune3.0ms

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: 17.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
19.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series25.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
16.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	124	1134
1	319	1074
2	811	1014
3	2431	1006
done	5001	1005

prune129.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 16.2b

Counts

72 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

29.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series44.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

123 → 123

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	193	1936
1	449	1814
2	1225	1730
3	4055	1698
done	5000	1696

prune192.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Merged error: 3.2b

Counts

135 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

16.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series68.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify891.0ms

Counts

73 → 73

Iterations

Useful iterations: done (889.0ms)

Iter	Nodes	Cost
0	123	1336
1	268	1308
2	628	1180
3	1673	1139
done	5000	1114

prune208.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 3.2b

Counts

79 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
8×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `times-frac` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series53.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	59	1172
1	131	1160
2	290	1040
3	731	1008
4	2720	1008
done	5001	1008

prune256.0ms

Filtered

56 candidates to 72 candidates (-28.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 3.2b

Counts

78 → 6

regimes117.0ms

Accuracy

78.1% (2.8b remaining)

Error of 5.9b against oracle of 3.1b and baseline of 15.8b

bsearch13.0ms

Steps

Iters	Range		Point
6	7170427078.972401	99835565477.3547	18187930964.32793

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	44
1	33	44
done	33	44

end0.0ms

sample890.0ms

Algorithm

intervals

Results

208.0ms	5836×	body	80	valid
147.0ms	854×	body	1280	valid
129.0ms	8000×	pre	80	true
96.0ms	702×	body	640	valid
40.0ms	376×	body	320	valid
16.0ms	232×	body	160	valid

Details

sample33.0ms

simplify318.0ms

prune3.0ms

localize8.0ms

rewrite33.0ms

series25.0ms

simplify1.2s

prune129.0ms

localize9.0ms

rewrite66.0ms

series44.0ms

simplify1.5s

prune192.0ms

localize14.0ms

rewrite62.0ms

series68.0ms

simplify891.0ms

prune208.0ms

localize21.0ms

rewrite61.0ms

series53.0ms

simplify1.4s

prune256.0ms

regimes117.0ms

bsearch13.0ms

simplify2.0ms

end0.0ms

sample890.0ms

Profiling