Details

sample192.0ms

Algorithm

intervals

Results

68.0ms	870×	body	80	nan
33.0ms	341×	body	80	valid
21.0ms	35×	body	1280	nan
11.0ms	26×	body	640	nan
10.0ms	75×	body	80	overflowed
4.0ms	13×	body	320	nan
1.0ms	7×	body	160	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

prune4.0ms

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: 0.6b

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

11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
13.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series689.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
180.0ms	(/ 1.0 (sqrt k))
33.0ms	(* (* 2.0 PI) n)
131.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	947	1443
1	4226	1340
2	5001	1327

prune571.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	152	9	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	9	162

Merged error: 0.0b

Counts

162 → 9

localize19.0ms

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))

rewrite40.0ms

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))

series1.2s

Counts

4 → 12

Calls

4 calls:

589.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
185.0ms	(/ 1.0 (sqrt k))
382.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
73.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1119	2024
1	5001	1849

prune654.0ms

Filtered

192 candidates to 119 candidates (62.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	190	11	201

Merged error: 0b

Counts

201 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow n (/ (- 1.0 k) 2.0))
0.2b	(/ (* (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt k))
0.3b	(* (* 1.0 (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))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
61×	`prod-exp`
41×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`pow-unpow`
36×	`times-frac`
29×	`add-cube-cbrt`
25×	`pow-exp`
18×	`pow-to-exp` `add-cbrt-cube`
16×	`div-exp`
10×	`div-sub` `pow-sub`
8×	`pow1`
7×	`unpow-prod-down` `associate-r`
6×	`associate-r/` `associate-/r` `sqrt-prod` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-pow` `div-inv` `associate-/l/` `sqr-pow`
2×	`frac-times` `associate-*l/`
1×	`frac-2neg` `associate-l` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 149

Calls

4 calls:

6.0ms	(pow n (/ (- 1.0 k) 2.0))
10.0ms	(/ (* (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt k))
8.0ms	(* (* 1.0 (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))

series1.1s

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow n (/ (- 1.0 k) 2.0))
650.0ms	(/ (* (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt k))
308.0ms	(* (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
69.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	1014	1748
1	4718	1549
2	5001	1543

prune550.0ms

Filtered

161 candidates to 98 candidates (60.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	161	11	172

Merged error: 0b

Counts

172 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

594×	`sqrt-prod`
591×	`times-frac`
328×	`add-sqr-sqrt` `*-un-lft-identity`
322×	`add-cube-cbrt`
34×	`associate-/l*`
22×	`add-exp-log`
19×	`pow-unpow`
18×	`associate-/r*`
16×	`add-cbrt-cube`
15×	`pow1`
13×	`div-inv`
6×	`pow-prod-down` `prod-exp`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 439

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt (sqrt k)))
5.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
16.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ 1.0 (sqrt (sqrt k)))
32.0ms	(* (* 2.0 PI) n)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
193.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

simplify74.0ms

Algorithm

egg-herbie

Counts

451 → 451

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1321	5782
1	5001	5005

prune883.0ms

Filtered

451 candidates to 170 candidates (37.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	450	1	451
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	451	11	462

Merged error: 0b

Counts

462 → 11

regimes416.0ms

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	17	11
1	17	11

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.1s	26400×	body	80	nan
912.0ms	10626×	body	80	valid
582.0ms	933×	body	1280	nan
358.0ms	776×	body	640	nan
346.0ms	2485×	body	80	overflowed
122.0ms	396×	body	320	nan
39.0ms	206×	body	160	nan

Details

sample192.0ms

simplify35.0ms

prune4.0ms

localize14.0ms

rewrite38.0ms

series689.0ms

simplify107.0ms

prune571.0ms

localize19.0ms

rewrite40.0ms

series1.2s

simplify50.0ms

prune654.0ms

localize17.0ms

rewrite42.0ms

series1.1s

simplify122.0ms

prune550.0ms

localize16.0ms

rewrite66.0ms

series558.0ms

simplify74.0ms

prune883.0ms

regimes416.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.6s

Profiling