Details

sample171.0ms

Algorithm

intervals

Results

67.0ms	849×	body	80	nan
33.0ms	343×	body	80	valid
17.0ms	28×	body	1280	nan
9.0ms	22×	body	640	nan
9.0ms	69×	body	80	overflowed
3.0ms	9×	body	320	nan
1.0ms	5×	body	160	nan

simplify39.0ms

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

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: 0.4b

Counts

2 → 1

localize19.0ms

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

rewrite36.0ms

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:

12.0ms	(* (/ 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)

series539.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
44.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)

simplify104.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	950	1461
1	3925	1358
2	5003	1344

prune408.0ms

Filtered

161 candidates to 107 candidates (66.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	11	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	11	162

Merged error: 0.0b

Counts

162 → 11

localize23.0ms

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))))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite33.0ms

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:

7.0ms	(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)

series1.2s

Counts

4 → 12

Calls

4 calls:

255.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
891.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
36.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)

simplify102.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

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

prune249.0ms

Filtered

130 candidates to 59 candidates (45.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	130	11	141

Merged error: 0b

Counts

141 → 11

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

rewrite53.0ms

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)

series881.0ms

Counts

4 → 12

Calls

4 calls:

775.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
37.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 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

prune473.0ms

Filtered

221 candidates to 127 candidates (57.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	221	11	232

Merged error: 0b

Counts

232 → 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	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
27×	`add-sqr-sqrt`
26×	`sqrt-prod`
21×	`add-exp-log` `add-cbrt-cube`
17×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow-prod-down`
11×	`associate-l`
10×	`swap-sqr` `prod-exp` `cbrt-unprod`
8×	`sqrt-pow1` `pow1/2`
5×	`pow-prod-up`
4×	`times-frac` `sqrt-div` `*-commutative` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 112

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
978.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	641	1639
1	3302	1386
2	5001	1325

prune315.0ms

Filtered

124 candidates to 68 candidates (54.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	124	11	135

Merged error: 0b

Counts

135 → 11

regimes181.0ms

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

sample5.6s

Algorithm

intervals

Results

2.3s	26999×	body	80	nan
921.0ms	10689×	body	80	valid
638.0ms	1047×	body	1280	nan
366.0ms	817×	body	640	nan
336.0ms	2382×	body	80	overflowed
125.0ms	419×	body	320	nan
30.0ms	175×	body	160	nan