Details

analyze392.0ms

Algorithm: search

sample91.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
21.0ms	35×	body	1280	nan
12.0ms	84×	body	80	overflowed
12.0ms	27×	body	640	nan
6.0ms	10×	body	160	nan
3.0ms	10×	body	320	nan
1.0ms	19×	body	80	nan
1.0ms	11×	body	80	invalid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1034	8
5	5001	8

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: 0.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:

9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
8.0ms	(* (* 2.0 PI) n)
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))

series88.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
6.0ms	(* (* 2.0 PI) n)
58.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms	(/ 1.0 (sqrt k))

simplify102.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	953	1493
1	4234	1364
2	5001	1350

prune298.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

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

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.3b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
105×	`prod-exp`
39×	`pow-exp`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`times-frac` `cbrt-unprod`
9×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
145.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify101.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	939	1410
1	4082	1188
2	5002	1188

prune187.0ms

Filtered

60 candidates to 130 candidates (-116.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	130	10	140

Merged error: 0b

Counts

140 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`add-exp-log`
40×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
23×	`sqrt-prod`
22×	`prod-exp`
21×	`add-cbrt-cube`
14×	`pow1`
11×	`associate-r`
8×	`cbrt-unprod`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow-to-exp` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 129

Calls

4 calls:

4.0ms	(* (* 2.0 PI) n)
4.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
10.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
83.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	621	1038
1	2688	925
2	5001	915

prune242.0ms

Filtered

93 candidates to 141 candidates (-51.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	141	10	151

Merged error: 0b

Counts

151 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
50×	`add-sqr-sqrt`
40×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
33×	`prod-exp`
29×	`sqrt-prod`
25×	`add-cbrt-cube`
24×	`associate-l`
18×	`pow1`
17×	`associate-r`
11×	`cbrt-unprod`
9×	`pow-prod-down`
8×	`pow-exp`
7×	`div-exp`
6×	`associate-/r*` `unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`frac-times` `unpow-prod-down` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 142

Calls

4 calls:

11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) (sqrt n))
4.0ms	(/ 1.0 (sqrt k))
9.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series78.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) (sqrt n))
10.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify115.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1001	1633
1	4720	1437
2	5001	1424

prune227.0ms

Filtered

105 candidates to 154 candidates (-46.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	154	10	164

Merged error: 0b

Counts

164 → 10

regimes195.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms

analyze396.0ms

Algorithm: search

sample2.5s

Algorithm

intervals

Results

704.0ms	8000×	body	80	valid
618.0ms	1002×	body	1280	nan
384.0ms	840×	body	640	nan
337.0ms	2392×	body	80	overflowed
127.0ms	421×	body	320	nan
41.0ms	751×	body	80	nan
39.0ms	221×	body	160	nan
19.0ms	205×	body	80	invalid

Details

analyze392.0ms

sample91.0ms

simplify35.0ms

prune3.0ms

localize13.0ms

rewrite37.0ms

series88.0ms

simplify102.0ms

prune298.0ms

localize18.0ms

rewrite31.0ms

series174.0ms

simplify101.0ms

prune187.0ms

localize18.0ms

rewrite28.0ms

series97.0ms

simplify69.0ms

prune242.0ms

localize16.0ms

rewrite35.0ms

series78.0ms

simplify115.0ms

prune227.0ms

regimes195.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze396.0ms

sample2.5s

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