Details

sample172.0ms

Algorithm

intervals

Results

64.0ms	846×	body	80	nan
33.0ms	363×	body	80	valid
19.0ms	33×	body	1280	nan
11.0ms	78×	body	80	overflowed
8.0ms	20×	body	640	nan
3.0ms	9×	body	320	nan
2.0ms	11×	body	160	nan

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

rewrite35.0ms

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)))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series759.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
260.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5003	1344

prune404.0ms

Filtered

161 candidates to 107 candidates (66.5%)

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

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
118×	`prod-exp`
85×	`add-sqr-sqrt`
83×	`times-frac`
77×	`div-exp`
60×	`pow-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-r`
28×	`add-cbrt-cube`
26×	`sqrt-prod`
24×	`associate-l`
22×	`sqr-pow`
20×	`pow-to-exp`
16×	`pow1`
15×	`unswap-sqr`
10×	`unpow-prod-down` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 209

Calls

4 calls:

23.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series896.0ms

Counts

4 → 12

Calls

4 calls:

782.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
45.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)

simplify63.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1271	2638
1	5001	2478

prune485.0ms

Filtered

221 candidates to 127 candidates (57.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	221	10	231

Merged error: 0.0b

Counts

231 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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

series1.2s

Counts

4 → 12

Calls

4 calls:

258.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
913.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
38.0ms	(* (* 2.0 PI) n)
33.0ms	(* (* 2.0 PI) n)

simplify106.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	916	1358
1	3952	1199
2	5002	1199

prune252.0ms

Filtered

130 candidates to 59 candidates (45.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	132	8	140

Merged error: 0b

Counts

140 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log` `add-cbrt-cube`
19×	`pow1`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-r` `pow-prod-down`
6×	`times-frac` `associate-/r*` `sqrt-prod`
4×	`add-log-exp`
3×	`associate-l` `*-commutative`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

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

series679.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
577.0ms	(/ (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt k))

simplify55.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	399	600
1	1813	501
2	5002	488

prune240.0ms

Filtered

93 candidates to 60 candidates (64.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 0b

Counts

101 → 8

regimes111.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.1s	27633×	body	80	nan
878.0ms	10709×	body	80	valid
612.0ms	1033×	body	1280	nan
356.0ms	826×	body	640	nan
341.0ms	2562×	body	80	overflowed
121.0ms	409×	body	320	nan
36.0ms	217×	body	160	nan

Details

sample172.0ms

simplify46.0ms

prune3.0ms

localize13.0ms

rewrite35.0ms

series759.0ms

simplify104.0ms

prune404.0ms

localize19.0ms

rewrite48.0ms

series896.0ms

simplify63.0ms

prune485.0ms

localize19.0ms

rewrite32.0ms

series1.2s

simplify106.0ms

prune252.0ms

localize21.0ms

rewrite25.0ms

series679.0ms

simplify55.0ms

prune240.0ms

regimes111.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.3s

Profiling