Details

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 68.103681%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

27.0ms	44×	body	1280	nan
22.0ms	256×	body	80	valid
12.0ms	87×	body	80	overflowed
11.0ms	26×	body	640	nan
5.0ms	15×	body	320	nan
1.0ms	16×	body	80	nan
1.0ms	4×	body	160	nan
0.0ms	4×	body	80	invalid

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

prune7.0ms

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

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

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:

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

series91.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms	(/ 1.0 (sqrt k))
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(* (* 2.0 PI) n)

simplify106.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	953	1493
1	4234	1364
2	5001	1351

prune304.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	153	8	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	8	162

Merged error: 0.0b

Counts

162 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.3b	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
61×	`prod-exp`
30×	`pow-exp`
29×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `add-cbrt-cube`
14×	`pow1`
12×	`sqrt-prod`
11×	`associate-r`
10×	`pow-to-exp`
8×	`div-sub` `sqr-pow`
7×	`associate-l` `pow-prod-down` `cbrt-unprod`
6×	`associate-/r*`
5×	`swap-sqr`
4×	`unpow-prod-down` `pow-sub` `add-log-exp` `unswap-sqr`
3×	`-commutative` `associate-/l`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 135

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
10.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))

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 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))

simplify72.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	582	1161
1	2543	1023
2	5001	990

prune238.0ms

Filtered

82 candidates to 147 candidates (-79.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	147	8	155

Merged error: 0.0b

Counts

155 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

12.0ms	(/ (* 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)
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series181.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
25.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	939	1410
1	4081	1188
2	5002	1188

prune196.0ms

Filtered

60 candidates to 130 candidates (-116.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	129	9	138

Merged error: 0b

Counts

138 → 9

localize21.0ms

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
40×	`add-sqr-sqrt`
31×	`times-frac`
27×	`add-cube-cbrt` `*-un-lft-identity`
25×	`prod-exp`
24×	`associate-l`
20×	`pow1`
19×	`add-cbrt-cube`
13×	`pow-unpow`
11×	`associate-r` `sqrt-prod`
9×	`pow-prod-down` `pow-exp`
8×	`cbrt-unprod`
6×	`unswap-sqr`
5×	`div-exp` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `*-commutative`
2×	`unpow-prod-down` `div-inv`
1×	`cbrt-undiv` `associate-*l/`

Counts

4 → 119

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series118.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
86.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
25.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	655	982
1	2615	870
2	5001	870

prune209.0ms

Filtered

82 candidates to 131 candidates (-59.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	131	9	140

Merged error: 0b

Counts

140 → 9

regimes316.0ms

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	19	16
1	19	16

end0.0ms

sample3.9s

Algorithm

intervals

sampling

Space saved by range analysis: 68.103681%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

716.0ms	8000×	body	80	valid
631.0ms	1013×	body	1280	nan
379.0ms	841×	body	640	nan
339.0ms	2383×	body	80	overflowed
145.0ms	440×	body	320	nan
40.0ms	221×	body	160	nan
31.0ms	553×	body	80	nan
11.0ms	118×	body	80	invalid

Details

sample1.7s

simplify38.0ms

prune7.0ms

localize14.0ms

rewrite35.0ms

series91.0ms

simplify106.0ms

prune304.0ms

localize16.0ms

rewrite29.0ms

series40.0ms

simplify72.0ms

prune238.0ms

localize18.0ms

rewrite35.0ms

series181.0ms

simplify103.0ms

prune196.0ms

localize21.0ms

rewrite32.0ms

series118.0ms

simplify71.0ms

prune209.0ms

regimes316.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.9s

Profiling