Details

sample9.0s

Algorithm

intervals

Results

29.0ms	345×	body	80	valid
21.0ms	34×	body	1280	nan
14.0ms	32×	body	640	nan
10.0ms	73×	body	80	overflowed
10.0ms	175×	body	80	nan
2.0ms	8×	body	320	nan
2.0ms	9×	body	160	nan

simplify35.0ms

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

localize16.0ms

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

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

series91.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(* (* 2.0 PI) n)
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
8.0ms	(/ 1.0 (sqrt k))

simplify103.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	953	1493
1	4233	1364
2	5001	1350

prune300.0ms

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

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)

rewrite31.0ms

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))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series178.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
147.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)

simplify105.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	939	1410
1	4082	1188
2	5001	1188

prune204.0ms

Filtered

59 candidates to 130 candidates (-120.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	130	12	142

Merged error: 0b

Counts

142 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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:

23.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series150.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))

simplify51.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1280	2683
1	5001	2479

prune407.0ms

Filtered

126 candidates to 221 candidates (-75.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	223	10	233

Merged error: 0b

Counts

233 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

594×	`sqrt-prod`
576×	`times-frac`
314×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
34×	`associate-/l*`
21×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
14×	`pow1`
12×	`div-inv`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 421

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt (sqrt k)))
16.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
17.0ms	(/ 1.0 (sqrt (sqrt k)))
8.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

simplify112.0ms

Algorithm

egg-herbie

Counts

433 → 433

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	1055	5531
1	4267	4749
2	5001	4743

prune382.0ms

Filtered

159 candidates to 433 candidates (-172.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	433	0	433
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	433	10	443

Merged error: 0b

Counts

443 → 10

regimes199.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b 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

sample11.9s

Algorithm

intervals

Results

927.0ms	10739×	body	80	valid
626.0ms	1027×	body	1280	nan
366.0ms	828×	body	640	nan
349.0ms	2415×	body	80	overflowed
337.0ms	5878×	body	80	nan
125.0ms	418×	body	320	nan
41.0ms	232×	body	160	nan

Details

sample9.0s

simplify35.0ms

prune3.0ms

localize16.0ms

rewrite35.0ms

series91.0ms

simplify103.0ms

prune300.0ms

localize18.0ms

rewrite31.0ms

series178.0ms

simplify105.0ms

prune204.0ms

localize18.0ms

rewrite49.0ms

series150.0ms

simplify51.0ms

prune407.0ms

localize21.0ms

rewrite61.0ms

series32.0ms

simplify112.0ms

prune382.0ms

regimes199.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample11.9s

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