Details

analyze386.0ms

Algorithm: search

sample79.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
15.0ms	76×	body	80	overflowed
15.0ms	26×	body	1280	nan
6.0ms	15×	body	640	nan
4.0ms	15×	body	320	nan
2.0ms	10×	body	160	nan
2.0ms	28×	body	80	nan
0.0ms	5×	body	80	invalid

simplify36.0ms

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

prune4.0ms

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: 0.5b

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

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×	`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))

series87.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ 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))

simplify107.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (89.0ms)

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

prune328.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	148	13	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	13	162

Merged error: 0.0b

Counts

162 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 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)
0.4b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite32.0ms

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:

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)
6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series176.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
6.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	939	1410
1	4081	1188
2	5002	1188

prune210.0ms

Filtered

59 candidates to 130 candidates (-120.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	131	12	143

Merged error: 0.0b

Counts

143 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

127×	`add-exp-log`
67×	`prod-exp`
36×	`pow-exp`
30×	`div-exp`
20×	`pow1`
19×	`add-cbrt-cube`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
13×	`pow-unpow`
12×	`pow-to-exp`
9×	`pow-prod-down`
7×	`cbrt-unprod`
6×	`associate-r`
5×	`associate-/r*`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-pow` `sqr-pow`
2×	`cbrt-undiv` `associate-l` `*-commutative` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 118

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
9.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series149.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
119.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
24.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	833	1353
1	3633	1121
2	5002	1121

prune228.0ms

Filtered

67 candidates to 130 candidates (-94.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	130	12	142

Merged error: 0.0b

Counts

142 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
18×	`pow-prod-down` `prod-exp`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
13×	`pow-unpow`
12×	`cbrt-unprod`
9×	`times-frac`
6×	`sqrt-prod`
4×	`pow-pow` `pow-exp` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`pow-to-exp` `unpow-prod-down` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))
5.0ms	(* (* 2.0 PI) (sqrt n))
23.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	592	627
1	2812	518
2	5001	514

prune148.0ms

Filtered

61 candidates to 106 candidates (-73.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

regimes235.0ms

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

analyze385.0ms

Algorithm: search

sample2.5s

Algorithm

intervals

Results

706.0ms	8000×	body	80	valid
578.0ms	981×	body	1280	nan
369.0ms	830×	body	640	nan
326.0ms	2419×	body	80	overflowed
117.0ms	377×	body	320	nan
45.0ms	747×	body	80	nan
37.0ms	191×	body	160	nan
22.0ms	249×	body	80	invalid

Details

analyze386.0ms

sample79.0ms

simplify36.0ms

prune4.0ms

localize14.0ms

rewrite38.0ms

series87.0ms

simplify107.0ms

prune328.0ms

localize19.0ms

rewrite32.0ms

series176.0ms

simplify102.0ms

prune210.0ms

localize18.0ms

rewrite33.0ms

series149.0ms

simplify90.0ms

prune228.0ms

localize25.0ms

rewrite34.0ms

series36.0ms

simplify73.0ms

prune148.0ms

regimes235.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze385.0ms

sample2.5s

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