Details

sample163.0ms

Algorithm

intervals

Results

56.0ms	796×	body	80	nan
26.0ms	62×	body	1280	nan
24.0ms	335×	body	80	valid
15.0ms	47×	body	640	nan
9.0ms	31×	body	320	nan
2.0ms	14×	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: 0.7b

Counts

2 → 1

localize18.0ms

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	(/ 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:

11.0ms	(* (/ 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))

series542.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
39.0ms	(/ 1.0 (sqrt k))
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344

prune403.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	11	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	11	162

Merged error: 0.0b

Counts

162 → 11

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
68×	`prod-exp`
63×	`add-sqr-sqrt`
55×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
27×	`pow-exp`
23×	`associate-l` `sqrt-prod`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`pow-to-exp`
17×	`div-exp`
12×	`associate-r`
11×	`div-sub` `pow-sub`
7×	`pow1` `cbrt-unprod`
6×	`frac-times` `associate-l/` `associate-/r` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down`
4×	`associate-*r/` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num`

Counts

4 → 180

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))
10.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
7.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series994.0ms

Counts

4 → 12

Calls

4 calls:

586.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
39.0ms	(/ 1.0 (sqrt k))
292.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
77.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1125	2057
1	4814	1860
2	5001	1856

prune434.0ms

Filtered

192 candidates to 119 candidates (62.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	193	10	203

Merged error: 0.0b

Counts

203 → 10

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

276×	`add-exp-log`
215×	`prod-exp`
70×	`pow-to-exp` `pow-exp`
51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
41×	`div-exp`
36×	`add-cbrt-cube`
33×	`div-sub` `pow-sub`
23×	`associate-l`
22×	`frac-times`
21×	`sqrt-prod`
19×	`pow-unpow`
17×	`cbrt-unprod`
16×	`associate-r/` `associate-l/`
8×	`associate-r`
7×	`pow1`
6×	`unpow-prod-down` `associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative` `sqr-pow`
1×	`pow-pow` `frac-2neg` `pow-prod-down` `clear-num`

Counts

4 → 235

Calls

4 calls:

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)))
4.0ms	(/ 1.0 (sqrt k))
13.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

865.0ms	(* (* (/ 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)))
38.0ms	(/ 1.0 (sqrt k))
567.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
51.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1485	3321
1	5001	2933

prune549.0ms

Filtered

247 candidates to 130 candidates (52.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	248	9	257

Merged error: 0b

Counts

257 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow PI (/ k 2.0))
0.3b	(/ (* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0))) (* (* (sqrt k) (pow PI (/ k 2.0))) (pow n (/ k 2.0))))
0.3b	(* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0)))
1.0b	(pow PI (/ 1.0 2.0))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

2253×	`add-exp-log`
1974×	`prod-exp`
646×	`pow-to-exp` `pow-exp`
442×	`div-exp`
67×	`add-cbrt-cube`
36×	`cbrt-unprod`
26×	`pow-unpow`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
9×	`unpow-prod-down`
7×	`associate-r`
6×	`pow1`
4×	`associate-*l/` `add-log-exp`
3×	`div-inv` `sqr-pow`
2×	`pow-pow` `div-sub` `associate-*r/` `pow-sub`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l/` `associate-/l*`

Counts

4 → 575

Calls

4 calls:

4.0ms	(pow PI (/ k 2.0))
25.0ms	(/ (* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0))) (* (* (sqrt k) (pow PI (/ k 2.0))) (pow n (/ k 2.0))))
12.0ms	(* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0)))
4.0ms	(pow PI (/ 1.0 2.0))

series1.7s

Counts

4 → 10

Calls

4 calls:

31.0ms	(pow PI (/ k 2.0))
1.3s	(/ (* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0))) (* (* (sqrt k) (pow PI (/ k 2.0))) (pow n (/ k 2.0))))
425.0ms	(* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0)))
0.0ms	(pow PI (/ 1.0 2.0))

simplify128.0ms

Algorithm

egg-herbie

Counts

585 → 585

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1628	10564
1	5001	10285

prune620.0ms

Filtered

585 candidates to 92 candidates (15.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	585	0	585
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	585	9	594

Merged error: 0b

Counts

594 → 9

regimes141.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	18
1	26	18

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.9s	27028×	body	80	nan
886.0ms	2114×	body	1280	nan
811.0ms	10703×	body	80	valid
541.0ms	1669×	body	640	nan
195.0ms	857×	body	320	nan
57.0ms	411×	body	160	nan