Details

sample172.0ms

Algorithm

intervals

Results

66.0ms	829×	body	80	nan
28.0ms	335×	body	80	valid
15.0ms	25×	body	1280	nan
14.0ms	71×	body	80	overflowed
11.0ms	26×	body	640	nan
4.0ms	13×	body	320	nan
2.0ms	10×	body	160	nan

simplify39.0ms

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: 0.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 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×	`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:

15.0ms	(* (/ 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)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series549.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (* 2.0 PI) n)
143.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (88.0ms)

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

prune432.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Merged error: 0.0b

Counts

170 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
105×	`prod-exp`
39×	`pow-exp`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`times-frac` `cbrt-unprod`
9×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
11.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.4s

Counts

4 → 12

Calls

4 calls:

419.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
913.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
31.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)

simplify103.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	935	1406
1	4012	1247
2	5001	1237

prune264.0ms

Filtered

138 candidates to 67 candidates (48.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	136	12	148

Merged error: 0.0b

Counts

148 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
118×	`prod-exp`
85×	`add-sqr-sqrt`
83×	`times-frac`
77×	`div-exp`
60×	`pow-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-r`
28×	`add-cbrt-cube`
26×	`sqrt-prod`
24×	`associate-l`
22×	`sqr-pow`
20×	`pow-to-exp`
16×	`pow1`
15×	`unswap-sqr`
10×	`unpow-prod-down` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 217

Calls

4 calls:

25.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series861.0ms

Counts

4 → 12

Calls

4 calls:

756.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
38.0ms	(/ 1.0 (sqrt k))
35.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)

simplify55.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1308	2682
1	5001	2469

prune513.0ms

Filtered

229 candidates to 135 candidates (59.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	230	11	241

Merged error: 0b

Counts

241 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log` `add-cbrt-cube`
19×	`pow1`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-r` `pow-prod-down`
6×	`times-frac` `associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
7.0ms	(/ (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt k))

series666.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
38.0ms	(* (* 2.0 PI) n)
556.0ms	(/ (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt k))

simplify53.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	409	636
1	1841	537
2	5002	522

prune267.0ms

Filtered

101 candidates to 68 candidates (67.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	101	11	112

Merged error: 0b

Counts

112 → 11

regimes181.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.2s	26816×	body	80	nan
942.0ms	10678×	body	80	valid
627.0ms	1019×	body	1280	nan
376.0ms	837×	body	640	nan
330.0ms	2357×	body	80	overflowed
125.0ms	392×	body	320	nan
35.0ms	202×	body	160	nan

Details

sample172.0ms

simplify39.0ms

prune3.0ms

localize14.0ms

rewrite38.0ms

series549.0ms

simplify105.0ms

prune432.0ms

localize18.0ms

rewrite33.0ms

series1.4s

simplify103.0ms

prune264.0ms

localize19.0ms

rewrite50.0ms

series861.0ms

simplify55.0ms

prune513.0ms

localize21.0ms

rewrite25.0ms

series666.0ms

simplify53.0ms

prune267.0ms

regimes181.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.5s

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