Details

sample188.0ms

Algorithm

intervals

Results

67.0ms	880×	body	80	nan
27.0ms	351×	body	80	valid
19.0ms	31×	body	1280	nan
15.0ms	83×	body	80	overflowed
11.0ms	24×	body	640	nan
4.0ms	12×	body	320	nan
2.0ms	9×	body	160	nan

simplify1.1s

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	864	16
6	3276	16
done	5000	16

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: 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))

rewrite38.0ms

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))
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series97.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(* (* 2.0 PI) n)
12.0ms	(/ 1.0 (sqrt k))
19.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify902.0ms

Counts

161 → 161

Iterations

Useful iterations: done (897.0ms)

Iter	Nodes	Cost
0	357	2874
1	967	2748
2	3731	2552
done	5000	2529

prune359.0ms

Filtered

113 candidates to 161 candidates (-42.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	151	10	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	10	162

Merged error: 0.0b

Counts

162 → 10

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))

rewrite29.0ms

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))
6.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series49.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
27.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify499.0ms

Counts

106 → 106

Iterations

Useful iterations: done (494.0ms)

Iter	Nodes	Cost
0	173	1115
1	455	1061
2	1654	975
done	5000	959

prune228.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Merged error: 0.0b

Counts

116 → 10

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))

rewrite27.0ms

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
27.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify1.4s

Counts

116 → 116

Iterations

Useful iterations: 3 (654.0ms)

Iter	Nodes	Cost
0	190	1106
1	448	1042
2	1443	955
3	4853	937
done	5000	937

prune235.0ms

Filtered

78 candidates to 116 candidates (-48.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

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)))

rewrite34.0ms

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)))

series131.0ms

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))
93.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify637.0ms

Counts

152 → 152

Iterations

Useful iterations: done (632.0ms)

Iter	Nodes	Cost
0	282	2219
1	748	2109
2	2597	1923
done	5000	1898

prune287.0ms

Filtered

102 candidates to 152 candidates (-49.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Merged error: 0.0b

Counts

162 → 10

regimes353.0ms

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

sample5.9s

Algorithm

intervals

Results

2.1s	26913×	body	80	nan
849.0ms	10648×	body	80	valid
647.0ms	1054×	body	1280	nan
400.0ms	879×	body	640	nan
359.0ms	2518×	body	80	overflowed
151.0ms	457×	body	320	nan
39.0ms	210×	body	160	nan

Details

sample188.0ms

simplify1.1s

prune4.0ms

localize12.0ms

rewrite38.0ms

series97.0ms

simplify902.0ms

prune359.0ms

localize16.0ms

rewrite29.0ms

series49.0ms

simplify499.0ms

prune228.0ms

localize16.0ms

rewrite27.0ms

series45.0ms

simplify1.4s

prune235.0ms

localize16.0ms

rewrite34.0ms

series131.0ms

simplify637.0ms

prune287.0ms

regimes353.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.9s

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