Details

sample174.0ms

Algorithm

intervals

Results

67.0ms	810×	body	80	nan
28.0ms	344×	body	80	valid
22.0ms	37×	body	1280	nan
12.0ms	28×	body	640	nan
11.0ms	81×	body	80	overflowed
2.0ms	8×	body	320	nan
1.0ms	8×	body	160	nan

simplify37.0ms

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: 0.5b

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

rewrite38.0ms

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)))
5.0ms	(* (* 2.0 PI) n)
13.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))

series547.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
39.0ms	(/ 1.0 (sqrt k))

simplify101.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5003	1344

prune412.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	147	14	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	14	162

Merged error: 0.0b

Counts

162 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
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)

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:

7.0ms	(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)
5.0ms	(* (* 2.0 PI) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

268.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
905.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
31.0ms	(* (* 2.0 PI) n)
36.0ms	(* (* 2.0 PI) n)

simplify101.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	916	1358
1	3952	1199
2	5002	1199

prune252.0ms

Filtered

130 candidates to 59 candidates (45.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	132	12	144

Merged error: 0.0b

Counts

144 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
118×	`prod-exp`
85×	`add-sqr-sqrt`
83×	`times-frac`
77×	`div-exp`
60×	`pow-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-r`
28×	`add-cbrt-cube`
26×	`sqrt-prod`
24×	`associate-l`
22×	`sqr-pow`
20×	`pow-to-exp`
16×	`pow1`
15×	`unswap-sqr`
10×	`unpow-prod-down` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 209

Calls

4 calls:

22.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series876.0ms

Counts

4 → 12

Calls

4 calls:

768.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
38.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
39.0ms	(/ 1.0 (sqrt k))

simplify60.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1271	2638
1	5001	2478

prune468.0ms

Filtered

221 candidates to 128 candidates (57.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	221	12	233

Merged error: 0b

Counts

233 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

260×	`add-exp-log`
122×	`prod-exp`
91×	`div-exp`
66×	`pow-exp`
52×	`times-frac`
28×	`add-cbrt-cube`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`pow-to-exp`
14×	`pow1` `associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`unpow-prod-down` `associate-r` `pow-prod-down` `div-inv` `sqr-pow`
4×	`associate-/l*` `add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`associate-/r/`

Counts

4 → 173

Calls

4 calls:

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

series1.8s

Counts

4 → 12

Calls

4 calls:

903.0ms	(/ 1.0 (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
796.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
31.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)

simplify52.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1276	2747
1	5001	2525

prune344.0ms

Filtered

185 candidates to 99 candidates (53.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	185	12	197

Merged error: 0b

Counts

197 → 12

regimes134.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.1s	27049×	body	80	nan
906.0ms	10638×	body	80	valid
606.0ms	1006×	body	1280	nan
362.0ms	828×	body	640	nan
334.0ms	2447×	body	80	overflowed
117.0ms	406×	body	320	nan
39.0ms	207×	body	160	nan

Details

sample174.0ms

simplify37.0ms

prune3.0ms

localize13.0ms

rewrite38.0ms

series547.0ms

simplify101.0ms

prune412.0ms

localize18.0ms

rewrite32.0ms

series1.2s

simplify101.0ms

prune252.0ms

localize18.0ms

rewrite50.0ms

series876.0ms

simplify60.0ms

prune468.0ms

localize19.0ms

rewrite38.0ms

series1.8s

simplify52.0ms

prune344.0ms

regimes134.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.3s

Profiling