Details

sample1.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 62.112427%

Guaranteed chance to sample good point: 65.984696%

Results

30.0ms	346×	body	80	valid
27.0ms	40×	body	1280	nan
14.0ms	32×	body	640	nan
14.0ms	97×	body	80	overflowed
5.0ms	16×	body	320	nan
2.0ms	9×	body	160	nan
1.0ms	14×	body	80	nan

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: 0.7b

Counts

2 → 1

localize14.0ms

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

11.0ms	(* (/ 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))

series88.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms	(/ 1.0 (sqrt k))
3.0ms	(* (* 2.0 PI) n)
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	953	1493
1	4233	1364
2	5002	1351

prune295.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	152	9	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	9	162

Merged error: 0.0b

Counts

162 → 9

localize19.0ms

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)
0.4b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite26.0ms

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:

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

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

prune183.0ms

Filtered

67 candidates to 106 candidates (-58.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Merged error: 0.0b

Counts

115 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
18×	`pow-prod-down` `prod-exp`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
13×	`pow-unpow`
12×	`cbrt-unprod`
9×	`times-frac`
6×	`sqrt-prod`
4×	`pow-pow` `pow-exp` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`pow-to-exp` `unpow-prod-down` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) (sqrt n))
10.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))
9.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series38.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) (sqrt n))
25.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))
5.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify73.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	592	627
1	2811	518
2	5002	514

prune163.0ms

Filtered

61 candidates to 106 candidates (-73.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	106	9	115

Merged error: 0.0b

Counts

115 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
26.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	558
1	1703	505
2	5001	495

prune161.0ms

Filtered

73 candidates to 116 candidates (-58.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	116	9	125

Merged error: 0.0b

Counts

125 → 9

regimes183.0ms

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	19	12
1	19	12

end0.0ms

sample4.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 62.112427%

Guaranteed chance to sample good point: 65.984696%

Results

951.0ms	10596×	body	80	valid
597.0ms	984×	body	1280	nan
363.0ms	816×	body	640	nan
351.0ms	2508×	body	80	overflowed
136.0ms	421×	body	320	nan
33.0ms	184×	body	160	nan
32.0ms	555×	body	80	nan

Details

sample1.3s

simplify35.0ms

prune3.0ms

localize14.0ms

rewrite33.0ms

series88.0ms

simplify106.0ms

prune295.0ms

localize19.0ms

rewrite26.0ms

series44.0ms

simplify48.0ms

prune183.0ms

localize22.0ms

rewrite33.0ms

series38.0ms

simplify73.0ms

prune163.0ms

localize19.0ms

rewrite23.0ms

series40.0ms

simplify48.0ms

prune161.0ms

regimes183.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.4s

Profiling