Details

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 68.07251%

Guaranteed chance to sample good point: 58.105525%

Results

23.0ms	256×	body	80	valid
20.0ms	34×	body	1280	nan
16.0ms	29×	body	640	nan
13.0ms	96×	body	80	overflowed
3.0ms	10×	body	320	nan
1.0ms	7×	body	160	nan
1.0ms	18×	body	80	nan
0.0ms	3×	body	80	invalid

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

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: 0.4b

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

rewrite34.0ms

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

series90.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
11.0ms	(/ 1.0 (sqrt k))
3.0ms	(* (* 2.0 PI) n)

simplify108.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	953	1493
1	4234	1364
2	5002	1350

prune305.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	149	12	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	12	162

Merged error: 0.0b

Counts

162 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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:

9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt (sqrt k)))
15.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(* (* 2.0 PI) n)
16.0ms	(/ 1.0 (sqrt (sqrt k)))
7.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

simplify77.0ms

Algorithm

egg-herbie

Counts

451 → 451

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1340	5786
1	5002	5005

prune395.0ms

Filtered

170 candidates to 451 candidates (-165.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	447	4	451
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	452	11	463

Merged error: 0.0b

Counts

463 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* (pow (/ 1 k) 1/4) 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ (* (pow (/ 1 k) 1/4) 1.0) (sqrt (sqrt k)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-exp-log`
106×	`prod-exp`
54×	`div-exp`
51×	`pow-exp`
34×	`add-sqr-sqrt`
33×	`times-frac`
31×	`*-un-lft-identity`
27×	`sqrt-prod`
25×	`add-cube-cbrt`
23×	`add-cbrt-cube`
19×	`pow-unpow`
15×	`pow1` `pow-to-exp`
14×	`associate-l`
9×	`associate-/r*`
8×	`associate-r` `cbrt-unprod`
6×	`rec-exp` `1-exp` `pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-pow` `div-sub` `div-inv` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`
2×	`unpow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l*`

Counts

4 → 166

Calls

4 calls:

15.0ms	(* (/ (* (pow (/ 1 k) 1/4) 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
5.0ms	(* (* 2.0 PI) n)
10.0ms	(/ (* (pow (/ 1 k) 1/4) 1.0) (sqrt (sqrt k)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (/ (* (pow (/ 1 k) 1/4) 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ (* (pow (/ 1 k) 1/4) 1.0) (sqrt (sqrt k)))

simplify121.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1156	2083
1	4813	1894
2	5002	1890

prune295.0ms

Filtered

95 candidates to 178 candidates (-87.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	179	10	189

Merged error: 0.0b

Counts

189 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.2b	(* (* (pow (/ 1 k) 1/4) 1.0) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))
0.2b	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
0.3b	(* (* 2.0 PI) n)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-exp-log`
108×	`prod-exp`
105×	`times-frac`
99×	`sqrt-prod`
73×	`add-sqr-sqrt` `*-un-lft-identity`
67×	`add-cube-cbrt`
52×	`div-exp` `associate-r`
51×	`pow-exp`
23×	`add-cbrt-cube`
20×	`unpow-prod-down` `sqr-pow`
19×	`pow-unpow`
17×	`pow1`
15×	`pow-to-exp`
9×	`associate-/r*` `cbrt-unprod`
7×	`pow-prod-down`
6×	`rec-exp` `1-exp`
5×	`associate-/l*`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-pow` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`div-sub` `associate-l` `*-commutative` `pow-sub`
1×	`frac-2neg` `associate-*r/` `clear-num` `associate-/l/`

Counts

4 → 236

Calls

4 calls:

9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
19.0ms	(* (* (pow (/ 1 k) 1/4) 1.0) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))
11.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
5.0ms	(* (* 2.0 PI) n)

series115.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
68.0ms	(* (* (pow (/ 1 k) 1/4) 1.0) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))
28.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
3.0ms	(* (* 2.0 PI) n)

simplify65.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1432	3486
1	5002	3262

prune448.0ms

Filtered

146 candidates to 248 candidates (-69.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	248	10	258

Merged error: 0.0b

Counts

258 → 10

regimes204.0ms

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	25	12
1	25	12

end0.0ms

sample4.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 68.07251%

Guaranteed chance to sample good point: 58.105525%

Results

727.0ms	8000×	body	80	valid
604.0ms	1009×	body	1280	nan
393.0ms	858×	body	640	nan
344.0ms	2484×	body	80	overflowed
146.0ms	453×	body	320	nan
37.0ms	210×	body	160	nan
30.0ms	536×	body	80	nan
9.0ms	100×	body	80	invalid

Details

sample1.5s

simplify37.0ms

prune3.0ms

localize14.0ms

rewrite34.0ms

series90.0ms

simplify108.0ms

prune305.0ms

localize15.0ms

rewrite64.0ms

series42.0ms

simplify77.0ms

prune395.0ms

localize22.0ms

rewrite48.0ms

series94.0ms

simplify121.0ms

prune295.0ms

localize22.0ms

rewrite57.0ms

series115.0ms

simplify65.0ms

prune448.0ms

regimes204.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.1s

Profiling