Details

sample174.0ms

Algorithm

intervals

Results

57.0ms	773×	body	80	nan
27.0ms	329×	body	80	valid
15.0ms	26×	body	1280	nan
14.0ms	33×	body	640	nan
13.0ms	72×	body	80	overflowed
5.0ms	16×	body	320	nan
1.0ms	8×	body	160	nan

simplify33.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.9b

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)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite33.0ms

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:

10.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series92.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	953	1493
1	4233	1364
2	5001	1351

prune1.2s

Filtered

161 candidates to 107 candidates (33.5%)

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

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.5b	(pow (* (* 2.0 PI) n) (/ k 2.0))
0.6b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite25.0ms

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:

4.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
6.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
16.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
26.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	453	528
1	1774	479
2	5002	473

prune535.0ms

Filtered

106 candidates to 67 candidates (36.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* (* 2.0 PI) n) (/ k 2.0))
0.6b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
26×	`pow-unpow`
23×	`add-exp-log`
21×	`pow1`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `pow-exp` `associate-/r*`
4×	`add-log-exp`
3×	`associate-r` `cbrt-unprod` `div-inv` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 115

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
6.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series52.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
14.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
27.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	612	691
1	2480	645
2	5001	631

prune773.0ms

Filtered

127 candidates to 85 candidates (33.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 0.0b

Counts

138 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.6b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
68×	`prod-exp`
63×	`add-sqr-sqrt`
55×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
27×	`pow-exp`
23×	`associate-l` `sqrt-prod`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`pow-to-exp`
17×	`div-exp`
12×	`associate-r`
11×	`div-sub` `pow-sub`
7×	`pow1` `cbrt-unprod`
6×	`frac-times` `associate-l/` `associate-/r` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down`
4×	`associate-*r/` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num`

Counts

4 → 180

Calls

4 calls:

13.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
9.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
7.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series151.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
8.0ms	(/ 1.0 (sqrt k))
24.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
5.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1222	2175
1	5001	1958

prune1.5s

Filtered

192 candidates to 119 candidates (38.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	4	4	8
Picked	0	1	1
Done	1	1	2
Total	193	10	203

Merged error: 0b

Counts

203 → 10

regimes274.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.1s	27182×	body	80	nan
893.0ms	10711×	body	80	valid
554.0ms	931×	body	1280	nan
368.0ms	846×	body	640	nan
338.0ms	2434×	body	80	overflowed
112.0ms	371×	body	320	nan
37.0ms	218×	body	160	nan

Details

sample174.0ms

simplify33.0ms

prune4.0ms

localize13.0ms

rewrite33.0ms

series92.0ms

simplify102.0ms

prune1.2s

localize18.0ms

rewrite25.0ms

series50.0ms

simplify49.0ms

prune535.0ms

localize18.0ms

rewrite24.0ms

series52.0ms

simplify58.0ms

prune773.0ms

localize16.0ms

rewrite41.0ms

series151.0ms

simplify48.0ms

prune1.5s

regimes274.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.6s

Profiling