Details

sample169.0ms

Algorithm

intervals

Results

65.0ms	814×	body	80	nan
28.0ms	330×	body	80	valid
19.0ms	26×	body	1280	nan
11.0ms	80×	body	80	overflowed
10.0ms	23×	body	640	nan
3.0ms	9×	body	320	nan
1.0ms	4×	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: 0.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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)
13.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))

series559.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 2.0 PI) n)
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
337.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
41.0ms	(/ 1.0 (sqrt k))

simplify107.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5001	1383

prune470.0ms

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

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

1128×	`times-frac`
1122×	`sqrt-prod`
653×	`add-sqr-sqrt`
572×	`*-un-lft-identity`
566×	`add-cube-cbrt`
284×	`associate-l`
71×	`add-exp-log`
31×	`associate-/l*`
30×	`prod-exp`
26×	`unswap-sqr`
23×	`add-cbrt-cube`
22×	`div-inv`
19×	`pow-unpow`
18×	`div-exp`
15×	`pow1` `sqr-pow`
12×	`pow-exp`
9×	`associate-/r*`
8×	`associate-r`
6×	`cbrt-undiv` `pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-sub` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l/`

Counts

4 → 739

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
66.0ms	(* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
17.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 2.0 PI) n)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
340.0ms	(* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
49.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

simplify133.0ms

Algorithm

egg-herbie

Counts

751 → 751

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1971	10743
1	5001	9651

prune1.7s

Filtered

751 candidates to 380 candidates (50.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	749	2	751
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	751	10	761

Merged error: 0b

Counts

761 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (sqrt k)))
0.2b	(* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
75×	`times-frac`
69×	`sqrt-prod`
62×	`*-un-lft-identity`
56×	`add-cube-cbrt`
48×	`add-exp-log`
32×	`associate-l`
22×	`prod-exp`
19×	`pow-unpow`
18×	`pow1`
16×	`add-cbrt-cube`
9×	`pow-exp` `associate-/r*`
8×	`associate-r` `unswap-sqr`
7×	`div-exp`
6×	`pow-prod-down` `sqr-pow`
5×	`pow-flip` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `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` `pow1/2` `*-commutative`
1×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-r/` `associate-l/` `clear-num` `inv-pow`

Counts

4 → 188

Calls

4 calls:

6.0ms	(/ 1 (sqrt (sqrt k)))
19.0ms	(* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series638.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ 1 (sqrt (sqrt k)))
295.0ms	(* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
41.0ms	(* (* 2.0 PI) n)
149.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	983	1821
1	4056	1684
2	5001	1673

prune512.0ms

Filtered

200 candidates to 122 candidates (61.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	200	10	210

Merged error: 0b

Counts

210 → 10

localize18.0ms

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))

rewrite48.0ms

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×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `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 → 188

Calls

4 calls:

13.0ms	(* (* (/ 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))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
8.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

617.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
41.0ms	(/ 1.0 (sqrt k))
303.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
83.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify133.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	1162	2113
1	4931	1915
2	5001	1887

prune489.0ms

Filtered

200 candidates to 127 candidates (63.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	201	9	210

Merged error: 0b

Counts

210 → 9

regimes214.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.4s	26505×	body	80	nan
932.0ms	10581×	body	80	valid
650.0ms	1029×	body	1280	nan
386.0ms	836×	body	640	nan
350.0ms	2440×	body	80	overflowed
122.0ms	397×	body	320	nan
35.0ms	189×	body	160	nan