Details

analyze389.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

sample90.0ms

Algorithm

intervals

Results

24.0ms	35×	body	1280	nan
21.0ms	256×	body	80	valid
14.0ms	33×	body	640	nan
9.0ms	68×	body	80	overflowed
6.0ms	18×	body	320	nan
1.0ms	26×	body	80	nan
1.0ms	8×	body	80	invalid
1.0ms	6×	body	160	nan

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4987	16
1	4987	16

prune10.0ms

Filtered

1 candidates to 1 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: 0.6b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.3b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

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:

4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
14.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series92.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
3.0ms	(* (* 2.0 PI) n)
64.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4953	2442
1	4953	2442

prune329.0ms

Filtered

108 candidates to 161 candidates (-49.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	149	12	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	151	12	163

Merged error: 0.0b

Counts

163 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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:

4.0ms	(/ 1.0 (sqrt k))
12.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
7.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
7.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series179.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
114.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
52.0ms	(* (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))

simplify57.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6004	3796

prune438.0ms

Filtered

124 candidates to 197 candidates (-58.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Merged error: 0.0b

Counts

209 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (/ 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	(* (* (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))

rewrite51.0ms

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:

4.0ms	(/ 1.0 (sqrt k))
17.0ms	(* (/ 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))))
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))

series294.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
192.0ms	(* (/ 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))))
90.0ms	(* (* (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))

simplify66.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5173	5368

prune497.0ms

Filtered

128 candidates to 256 candidates (-100.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	256	9	265

Merged error: 0.0b

Counts

265 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

235×	`add-exp-log`
189×	`prod-exp`
73×	`add-sqr-sqrt`
64×	`pow-to-exp` `pow-exp`
57×	`times-frac`
52×	`*-un-lft-identity`
46×	`add-cube-cbrt`
31×	`div-exp`
29×	`associate-r`
27×	`div-sub` `pow-sub`
25×	`add-cbrt-cube`
24×	`sqrt-prod`
19×	`pow-unpow`
18×	`frac-times`
14×	`associate-*l/`
12×	`unpow-prod-down` `associate-*r/`
11×	`cbrt-unprod`
9×	`unswap-sqr`
8×	`associate-l`
6×	`associate-/r*` `sqr-pow`
5×	`pow1`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `clear-num`

Counts

4 → 231

Calls

4 calls:

16.0ms	(* (* (pow PI (/ (- 1.0 k) 2.0)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (pow n (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
11.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))

series223.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* (pow PI (/ (- 1.0 k) 2.0)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (pow n (/ (- 1.0 k) 2.0)))
11.0ms	(/ 1.0 (sqrt k))
20.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
4.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4952	4970
1	4952	4970

prune472.0ms

Filtered

129 candidates to 243 candidates (-88.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	243	9	252

Merged error: 0.0b

Counts

252 → 9

regimes200.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	28	28
1	28	28

end0.0ms

sample2.6s

Algorithm

intervals

Results

694.0ms	8000×	body	80	valid
553.0ms	835×	body	640	nan
553.0ms	952×	body	1280	nan
318.0ms	2398×	body	80	overflowed
126.0ms	415×	body	320	nan
43.0ms	794×	body	80	nan
35.0ms	211×	body	160	nan
25.0ms	253×	body	80	invalid

Details

analyze389.0ms

sample90.0ms

simplify42.0ms

prune10.0ms

localize14.0ms

rewrite38.0ms

series92.0ms

simplify68.0ms

prune329.0ms

localize17.0ms

rewrite38.0ms

series179.0ms

simplify57.0ms

prune438.0ms

localize21.0ms

rewrite51.0ms

series294.0ms

simplify66.0ms

prune497.0ms

localize22.0ms

rewrite49.0ms

series223.0ms

simplify86.0ms

prune472.0ms

regimes200.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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