Details

sample132.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 80.57251%

Guaranteed chance to sample good point: 96.481307%

Results

22.0ms	256×	body	80	valid
0.0ms	5×	body	80	invalid
0.0ms	4×	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	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.4b	(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)))
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series87.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify108.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (89.0ms)

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

prune500.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

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

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
72×	`prod-exp`
57×	`add-sqr-sqrt`
51×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
32×	`pow-exp`
27×	`associate-l`
22×	`pow-to-exp`
21×	`sqrt-prod`
20×	`add-cbrt-cube`
19×	`pow-unpow`
14×	`div-exp`
13×	`div-sub` `pow-sub`
9×	`pow1`
8×	`associate-r` `sqr-pow`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`frac-times` `associate-r/` `associate-/r` `unswap-sqr`
4×	`associate-*l/` `add-log-exp`
3×	`cbrt-undiv` `pow-prod-down` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `clear-num`

Counts

4 → 185

Calls

4 calls:

12.0ms	(* (/ 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))
7.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series166.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
11.0ms	(/ 1.0 (sqrt k))
45.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
5.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1272	2366
1	5001	2113

prune389.0ms

Filtered

121 candidates to 197 candidates (-62.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	198	9	207

Merged error: 0b

Counts

207 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.7b	(pow PI (/ (- 1.0 k) 2.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

279×	`add-exp-log`
233×	`prod-exp`
85×	`pow-to-exp` `pow-exp`
51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
37×	`div-sub` `pow-sub`
32×	`div-exp` `add-cbrt-cube`
23×	`associate-l`
22×	`frac-times`
21×	`sqrt-prod`
19×	`pow-unpow`
16×	`associate-r/` `associate-l/`
15×	`cbrt-unprod`
8×	`associate-r`
7×	`pow1`
6×	`unpow-prod-down` `associate-/r*`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-prod-down` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative` `sqr-pow`
1×	`pow-pow` `frac-2neg` `clear-num`

Counts

4 → 244

Calls

4 calls:

16.0ms	(* (/ 1.0 (sqrt k)) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))))
4.0ms	(/ 1.0 (sqrt k))
10.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))

series275.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (/ 1.0 (sqrt k)) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))))
8.0ms	(/ 1.0 (sqrt k))
84.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
4.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1665	3794
1	5001	3159

prune490.0ms

Filtered

131 candidates to 256 candidates (-95.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	256	9	265

Merged error: 0b

Counts

265 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
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))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
145.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	939	1410
1	4081	1188
2	5001	1188

prune161.0ms

Filtered

60 candidates to 130 candidates (-116.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	130	9	139

Merged error: 0b

Counts

139 → 9

regimes237.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	11
1	17	11

end0.0ms

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 80.57251%

Guaranteed chance to sample good point: 96.481307%

Results

682.0ms	8000×	body	80	valid
8.0ms	95×	body	80	invalid
8.0ms	140×	body	80	nan

Details

sample132.0ms

simplify35.0ms

prune3.0ms

localize14.0ms

rewrite35.0ms

series87.0ms

simplify108.0ms

prune500.0ms

localize16.0ms

rewrite39.0ms

series166.0ms

simplify52.0ms

prune389.0ms

localize18.0ms

rewrite48.0ms

series275.0ms

simplify68.0ms

prune490.0ms

localize18.0ms

rewrite30.0ms

series175.0ms

simplify105.0ms

prune161.0ms

regimes237.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

Profiling