Details

sample197.0ms

Algorithm

intervals

Results

81.0ms	975×	body	80	nan
29.0ms	345×	body	80	valid
20.0ms	34×	body	1280	nan
14.0ms	31×	body	640	nan
12.0ms	86×	body	80	overflowed
4.0ms	12×	body	320	nan
2.0ms	9×	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: 0.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

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

5.0ms	(* (* 2.0 PI) n)
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series549.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* 2.0 PI) n)
332.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (85.0ms)

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

prune415.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	148	13	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	13	162

Merged error: 0.0b

Counts

162 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow n (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.4b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.7b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`times-frac`
64×	`*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
11×	`prod-exp` `add-cbrt-cube`
8×	`pow1`
7×	`pow-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down` `div-exp` `associate-r`
4×	`pow-to-exp` `div-sub` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 161

Calls

4 calls:

6.0ms	(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))

series471.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow n (/ (- 1.0 k) 2.0))
37.0ms	(/ 1.0 (sqrt k))
291.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
78.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	819	1327
1	3182	1246
2	5001	1236

prune587.0ms

Filtered

173 candidates to 123 candidates (71.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	177	9	186

Merged error: 0.0b

Counts

186 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow n (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.4b	(* (/ 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))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
64×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow` `prod-exp`
22×	`associate-l`
21×	`sqrt-prod`
18×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
11×	`div-exp`
10×	`div-sub` `pow-sub`
8×	`pow1`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*r/`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-l/` `associate-/l`
2×	`pow-pow` `sqr-pow`
1×	`frac-2neg` `associate-r` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 170

Calls

4 calls:

5.0ms	(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))

series730.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow n (/ (- 1.0 k) 2.0))
39.0ms	(/ 1.0 (sqrt k))
574.0ms	(* (/ 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))

simplify103.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1026	1582
1	4112	1443
2	5002	1436

prune477.0ms

Filtered

182 candidates to 121 candidates (66.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	182	9	191

Merged error: 0.0b

Counts

191 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.4b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.7b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
93×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
74×	`add-cube-cbrt`
50×	`unpow-prod-down`
41×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
21×	`sqr-pow`
19×	`pow-unpow`
14×	`div-exp`
13×	`associate-/r*` `add-cbrt-cube`
12×	`pow-exp`
11×	`prod-exp`
10×	`associate-/l*`
9×	`pow-to-exp`
7×	`pow1`
6×	`unswap-sqr`
5×	`associate-r`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `div-sub` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`pow-pow` `frac-2neg` `clear-num` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `pow-div`

Counts

4 → 211

Calls

4 calls:

6.0ms	(/ (pow n (/ 1.0 2.0)) (pow n (/ 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))

series599.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)))
43.0ms	(/ 1.0 (sqrt k))
280.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
78.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	959	2011
1	4062	1915
2	5002	1910

prune615.0ms

Filtered

223 candidates to 155 candidates (69.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	223	9	232

Merged error: 0b

Counts

232 → 9

regimes139.0ms

Accuracy

0% (0.5b 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	21	13
1	21	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.2s	27557×	body	80	nan
928.0ms	10729×	body	80	valid
606.0ms	987×	body	1280	nan
372.0ms	839×	body	640	nan
336.0ms	2402×	body	80	overflowed
131.0ms	406×	body	320	nan
31.0ms	180×	body	160	nan