Details

sample191.0ms

Algorithm

intervals

Results

68.0ms	880×	body	80	nan
27.0ms	351×	body	80	valid
19.0ms	31×	body	1280	nan
15.0ms	24×	body	640	nan
11.0ms	83×	body	80	overflowed
4.0ms	12×	body	320	nan
2.0ms	9×	body	160	nan

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	57	16
3	114	16
4	301	16
5	853	16
6	3169	16
done	5001	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

localize20.0ms

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))

rewrite39.0ms

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (/ 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))
19.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify864.0ms

Counts

161 → 161

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	357	2874
1	967	2714
2	3672	2506
done	5000	2500

prune556.0ms

Filtered

109 candidates to 161 candidates (-47.7%)

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))

rewrite30.0ms

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))
5.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
8.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series52.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
3.0ms	(* (* 2.0 PI) n)
4.0ms	(* (* 2.0 PI) n)
27.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify483.0ms

Counts

106 → 106

Iterations

Useful iterations: done (476.0ms)

Iter	Nodes	Cost
0	173	1115
1	455	1048
2	1559	960
done	5000	951

prune229.0ms

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))

rewrite28.0ms

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:

8.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series42.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt k))
27.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify1.1s

Counts

116 → 116

Iterations

Useful iterations: 3 (497.0ms)

Iter	Nodes	Cost
0	190	1106
1	448	1032
2	1427	934
3	4916	932
done	5000	932

prune225.0ms

Filtered

73 candidates to 116 candidates (-58.9%)

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)))

rewrite37.0ms

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

series134.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
27.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
95.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify623.0ms

Counts

152 → 152

Iterations

Useful iterations: done (618.0ms)

Iter	Nodes	Cost
0	282	2219
1	748	2082
2	2603	1883
done	5000	1877

prune284.0ms

Filtered

103 candidates to 152 candidates (-47.6%)

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

regimes368.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.2s	26913×	body	80	nan
841.0ms	10648×	body	80	valid
657.0ms	1054×	body	1280	nan
410.0ms	879×	body	640	nan
348.0ms	2518×	body	80	overflowed
143.0ms	457×	body	320	nan
41.0ms	210×	body	160	nan

Details

sample191.0ms

simplify1.0s

prune3.0ms

localize20.0ms

rewrite39.0ms

series99.0ms

simplify864.0ms

prune556.0ms

localize16.0ms

rewrite30.0ms

series52.0ms

simplify483.0ms

prune229.0ms

localize16.0ms

rewrite28.0ms

series42.0ms

simplify1.1s

prune225.0ms

localize16.0ms

rewrite37.0ms

series134.0ms

simplify623.0ms

prune284.0ms

regimes368.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.0s

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