Details

sample91.0ms

Algorithm

intervals

Results

38.0ms	754×	body	80	nan
26.0ms	407×	body	80	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1044	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize13.0ms

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)
0.2b	(/ 1.0 (sqrt k))
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite42.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

19.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) n)
3.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series528.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
42.0ms	(/ 1.0 (sqrt k))
138.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383

prune465.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.9b	(pow n (/ (- 1.0 k) 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
16×	`prod-exp`
13×	`pow-exp`
12×	`sqrt-prod`
10×	`unpow-prod-down`
9×	`pow-to-exp` `sqr-pow`
8×	`pow1` `add-cbrt-cube`
7×	`associate-r`
6×	`div-sub` `associate-/r*` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l*`
2×	`pow-prod-down`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
9.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
5.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
4.0ms	(pow n (/ (- 1.0 k) 2.0))

series451.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (sqrt k))
278.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
73.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
60.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	788	1258
1	3048	1181
2	5001	1165

prune507.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
0.9b	(pow n (/ (- 1.0 k) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
57×	`prod-exp`
53×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`pow-to-exp` `pow-exp`
14×	`div-sub` `pow-sub`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`unpow-prod-down`
7×	`associate-r`
6×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `cbrt-unprod` `div-inv` `associate-/l` `sqr-pow`
2×	`pow-pow` `pow-prod-down`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 171

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
19.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
4.0ms	(pow PI (/ (- 1.0 k) 2.0))
4.0ms	(pow n (/ (- 1.0 k) 2.0))

series552.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt k))
396.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
50.0ms	(pow PI (/ (- 1.0 k) 2.0))
62.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	961	1523
1	3925	1313
2	5003	1304

prune527.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
0.9b	(pow n (/ (/ (- 1.0 k) 2.0) 2))
0.9b	(pow n (/ (/ (- 1.0 k) 2.0) 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

237×	`times-frac`
167×	`add-sqr-sqrt` `*-un-lft-identity`
141×	`pow-unpow`
125×	`add-cube-cbrt`
21×	`distribute-lft-out--` `difference-of-squares`
12×	`sqrt-prod`
10×	`div-inv`
9×	`add-exp-log` `unpow-prod-down`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube`
5×	`div-sub`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/l*` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 233

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
4.0ms	(pow PI (/ (- 1.0 k) 2.0))
11.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
8.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (sqrt k))
52.0ms	(pow PI (/ (- 1.0 k) 2.0))
58.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
65.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))

simplify84.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	884	1585
1	3409	1541
2	5001	1531

prune958.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes122.0ms

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	17	11
1	17	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	20896×	body	80	nan
723.0ms	11936×	body	80	valid