Details

sample195.0ms

Algorithm

intervals

Results

87.0ms	1021×	body	80	nan
30.0ms	347×	body	80	valid
18.0ms	30×	body	1280	nan
14.0ms	31×	body	640	nan
10.0ms	71×	body	80	overflowed
4.0ms	13×	body	320	nan
1.0ms	4×	body	160	nan

simplify38.0ms

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

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: 0.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite34.0ms

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:

4.0ms	(/ 1.0 (sqrt k))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series767.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ 1.0 (sqrt k))
375.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
33.0ms	(* (* 2.0 PI) n)
149.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	947	1443
1	4226	1340
2	5002	1328

prune420.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	148	13	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	13	162

Merged error: 0.0b

Counts

162 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.3b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 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)
6.0ms	(* (* 2.0 PI) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

273.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
998.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
35.0ms	(* (* 2.0 PI) n)
39.0ms	(* (* 2.0 PI) n)

simplify103.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	893	1334
1	3988	1147
2	5001	1147

prune269.0ms

Filtered

130 candidates to 59 candidates (45.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	123	7	130
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	130	13	143

Merged error: 0.0b

Counts

143 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.4b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt k))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms	(* (* 2.0 PI) n)
9.0ms	(* (* 2.0 PI) n)
8.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt k))

series978.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
33.0ms	(* (* 2.0 PI) n)
33.0ms	(* (* 2.0 PI) n)
632.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt k))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	559	700
1	2438	601
2	5002	597

prune267.0ms

Filtered

108 candidates to 65 candidates (60.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Merged error: 0b

Counts

121 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

127×	`add-exp-log`
67×	`prod-exp`
36×	`pow-exp`
30×	`div-exp`
20×	`pow1`
19×	`add-cbrt-cube`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
13×	`pow-unpow`
12×	`pow-to-exp`
9×	`pow-prod-down`
7×	`cbrt-unprod`
6×	`associate-r`
5×	`associate-/r*`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-pow` `sqr-pow`
2×	`cbrt-undiv` `associate-l` `*-commutative` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 118

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
10.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

268.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
927.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
33.0ms	(* (* 2.0 PI) n)
45.0ms	(* (* 2.0 PI) n)

simplify96.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	806	1281
1	3574	1078
2	5001	1078

prune248.0ms

Filtered

130 candidates to 67 candidates (51.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	130	13	143

Merged error: 0b

Counts

143 → 13

regimes238.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	26665×	body	80	nan
933.0ms	10627×	body	80	valid
618.0ms	1004×	body	1280	nan
358.0ms	808×	body	640	nan
342.0ms	2457×	body	80	overflowed
122.0ms	397×	body	320	nan
37.0ms	193×	body	160	nan

Details

sample195.0ms

simplify38.0ms

prune3.0ms

localize14.0ms

rewrite34.0ms

series767.0ms

simplify109.0ms

prune420.0ms

localize18.0ms

rewrite32.0ms

series1.3s

simplify103.0ms

prune269.0ms

localize18.0ms

rewrite32.0ms

series978.0ms

simplify66.0ms

prune267.0ms

localize18.0ms

rewrite31.0ms

series1.3s

simplify96.0ms

prune248.0ms

regimes238.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.4s

Profiling