Details

sample183.0ms

Algorithm

intervals

Results

65.0ms	880×	body	80	nan
26.0ms	351×	body	80	valid
18.0ms	31×	body	1280	nan
14.0ms	24×	body	640	nan
11.0ms	83×	body	80	overflowed
4.0ms	12×	body	320	nan
2.0ms	9×	body	160	nan

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	57	16
3	113	16
4	291	16
5	793	16
6	3005	16
done	5000	16

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: 0.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 149

Calls

4 calls:

12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series95.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
18.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.2s

Counts

161 → 161

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	357	2874
1	955	2706
2	3427	2506
done	5000	2500

prune342.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	11	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	11	162

Merged error: 0.0b

Counts

162 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ k 2.0))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.3b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1` `add-exp-log` `pow-unpow`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
8.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
8.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series48.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
3.0ms	(* (* 2.0 PI) n)
4.0ms	(* (* 2.0 PI) n)
26.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify897.0ms

Counts

106 → 106

Iterations

Useful iterations: done (894.0ms)

Iter	Nodes	Cost
0	173	1115
1	451	1048
2	1507	960
done	5000	951

prune230.0ms

Filtered

71 candidates to 106 candidates (-49.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.3b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
22×	`add-exp-log`
20×	`pow1`
16×	`add-cbrt-cube`
13×	`pow-unpow`
12×	`sqrt-prod`
9×	`pow-prod-down` `prod-exp`
6×	`associate-r` `associate-/r*` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-pow` `pow-exp` `associate-/l*`
2×	`associate-l` `*-commutative` `div-inv`
1×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `frac-2neg` `div-exp` `clear-num` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series44.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt k))
28.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify2.4s

Counts

116 → 116

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	190	1106
1	440	1024
2	1307	934
3	4371	932
done	5001	932

prune229.0ms

Filtered

75 candidates to 116 candidates (-54.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	116	11	127

Merged error: 0.0b

Counts

127 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.3b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.4b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
49×	`times-frac`
46×	`add-exp-log`
41×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
16×	`add-cbrt-cube`
15×	`pow1`
13×	`pow-unpow`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-inv` `associate-/l*`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 140

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 2.0 PI) n)
11.0ms	(/ 1.0 (sqrt k))
25.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
92.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify989.0ms

Counts

152 → 152

Iterations

Useful iterations: done (984.0ms)

Iter	Nodes	Cost
0	282	2219
1	732	2074
2	2354	1883
done	5000	1877

prune279.0ms

Filtered

100 candidates to 152 candidates (-52.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	152	11	163

Merged error: 0.0b

Counts

163 → 11

regimes360.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	18	24
done	18	24

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.1s	26913×	body	80	nan
823.0ms	10648×	body	80	valid
635.0ms	1054×	body	1280	nan
389.0ms	879×	body	640	nan
339.0ms	2518×	body	80	overflowed
143.0ms	457×	body	320	nan
38.0ms	210×	body	160	nan

Details

sample183.0ms

simplify2.4s

prune3.0ms

localize12.0ms

rewrite42.0ms

series95.0ms

simplify1.2s

prune342.0ms

localize16.0ms

rewrite31.0ms

series48.0ms

simplify897.0ms

prune230.0ms

localize16.0ms

rewrite26.0ms

series44.0ms

simplify2.4s

prune229.0ms

localize16.0ms

rewrite35.0ms

series132.0ms

simplify989.0ms

prune279.0ms

regimes360.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.7s

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