Details

sample194.0ms

Algorithm

intervals

Results

79.0ms	975×	body	80	nan
29.0ms	345×	body	80	valid
20.0ms	34×	body	1280	nan
13.0ms	31×	body	640	nan
11.0ms	86×	body	80	overflowed
3.0ms	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	1044	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

localize19.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

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))

series539.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
325.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383

prune447.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	13	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	13	170

Merged error: 0.0b

Counts

170 → 13

localize21.0ms

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×	`expm1-log1p-u` `pow-to-exp` `div-sub` `log1p-expm1-u` `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 → 169

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))

series460.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow n (/ (- 1.0 k) 2.0))
44.0ms	(/ 1.0 (sqrt k))
282.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
77.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	844	1367
1	3255	1284
2	5002	1267

prune477.0ms

Filtered

181 candidates to 131 candidates (72.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Merged error: 0.0b

Counts

194 → 9

localize19.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 178

Calls

4 calls:

5.0ms	(pow n (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))
12.0ms	(* (/ 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))

series907.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow n (/ (- 1.0 k) 2.0))
37.0ms	(/ 1.0 (sqrt k))
755.0ms	(* (/ 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))

simplify106.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1057	1626
1	4206	1464
2	5001	1453

prune517.0ms

Filtered

190 candidates to 129 candidates (67.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	190	9	199

Merged error: 0.0b

Counts

199 → 9

localize23.0ms

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))

rewrite41.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 219

Calls

4 calls:

7.0ms	(/ (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))

series604.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)))
37.0ms	(/ 1.0 (sqrt k))
288.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
71.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	986	2055
1	4138	1958
2	5002	1946

prune652.0ms

Filtered

231 candidates to 163 candidates (70.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	231	9	240

Merged error: 0b

Counts

240 → 9

regimes143.0ms

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

sample5.4s

Algorithm

intervals

Results

2.2s	27557×	body	80	nan
917.0ms	10729×	body	80	valid
587.0ms	987×	body	1280	nan
366.0ms	839×	body	640	nan
326.0ms	2402×	body	80	overflowed
122.0ms	406×	body	320	nan
36.0ms	180×	body	160	nan