Details

sample170.0ms

Algorithm

intervals

Results

68.0ms	829×	body	80	nan
28.0ms	335×	body	80	valid
15.0ms	25×	body	1280	nan
11.0ms	26×	body	640	nan
10.0ms	71×	body	80	overflowed
4.0ms	13×	body	320	nan
2.0ms	10×	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

prune2.0ms

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))

rewrite39.0ms

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:

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))

series540.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(* (/ 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)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (84.0ms)

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

prune382.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	151	10	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	10	162

Merged error: 0.0b

Counts

162 → 10

localize19.0ms

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)

rewrite36.0ms

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` `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 → 118

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
9.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

259.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
893.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
37.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)

simplify99.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	916	1358
1	3952	1199
2	5002	1199

prune247.0ms

Filtered

130 candidates to 59 candidates (45.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	128	12	140

Merged error: 0.0b

Counts

140 → 12

localize18.0ms

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)

rewrite51.0ms

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×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 209

Calls

4 calls:

27.0ms	(* (/ 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)

series887.0ms

Counts

4 → 12

Calls

4 calls:

779.0ms	(* (/ 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))
38.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)

simplify52.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1271	2638
1	5001	2478

prune477.0ms

Filtered

221 candidates to 127 candidates (57.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	222	11	233

Merged error: 0b

Counts

233 → 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))

rewrite162.0ms

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×	`add-log-exp`
3×	`associate-l` `*-commutative`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
8.0ms	(/ (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt k))

series639.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
539.0ms	(/ (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt k))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	399	600
1	1813	501
2	5002	488

prune241.0ms

Filtered

93 candidates to 60 candidates (64.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	93	11	104

Merged error: 0b

Counts

104 → 11

regimes180.0ms

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

sample5.4s

Algorithm

intervals

Results

2.2s	26816×	body	80	nan
914.0ms	10678×	body	80	valid
619.0ms	1019×	body	1280	nan
366.0ms	837×	body	640	nan
328.0ms	2357×	body	80	overflowed
125.0ms	392×	body	320	nan
35.0ms	202×	body	160	nan

Details

sample170.0ms

simplify37.0ms

prune2.0ms

localize14.0ms

rewrite39.0ms

series540.0ms

simplify99.0ms

prune382.0ms

localize19.0ms

rewrite36.0ms

series1.2s

simplify99.0ms

prune247.0ms

localize18.0ms

rewrite51.0ms

series887.0ms

simplify52.0ms

prune477.0ms

localize21.0ms

rewrite162.0ms

series639.0ms

simplify52.0ms

prune241.0ms

regimes180.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.4s

Profiling