Details

sample138.0ms

Algorithm

intervals

Results

47.0ms	859×	body	80	nan
23.0ms	326×	body	80	valid
19.0ms	57×	body	1280	nan
12.0ms	46×	body	640	nan
4.0ms	23×	body	320	nan
1.0ms	13×	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	1044	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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:

9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series551.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
335.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
32.0ms	(* (* 2.0 PI) n)
38.0ms	(/ 1.0 (sqrt k))

simplify105.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	981	1502
1	4022	1398
2	5002	1383

prune481.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
50×	`add-sqr-sqrt`
40×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
33×	`prod-exp`
29×	`sqrt-prod`
25×	`add-cbrt-cube`
24×	`associate-l`
18×	`pow1`
17×	`associate-r`
11×	`cbrt-unprod`
9×	`pow-prod-down`
8×	`pow-exp`
7×	`div-exp`
6×	`associate-/r*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`frac-times` `unpow-prod-down` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 150

Calls

4 calls:

16.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
9.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))
6.0ms	(* (* 2.0 PI) (sqrt n))

series497.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0)))
44.0ms	(/ 1.0 (sqrt k))
43.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))
77.0ms	(* (* 2.0 PI) (sqrt n))

simplify110.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	961	1622
1	4077	1445
2	5002	1431

prune620.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-exp-log`
100×	`prod-exp`
51×	`add-sqr-sqrt`
40×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
35×	`pow-exp`
29×	`sqrt-prod`
25×	`add-cbrt-cube`
24×	`associate-l`
21×	`div-exp` `associate-r`
19×	`pow-to-exp`
10×	`div-sub` `cbrt-unprod` `pow-sub`
9×	`pow1`
7×	`unpow-prod-down`
6×	`frac-times` `associate-l/` `associate-/r` `unswap-sqr`
5×	`sqr-pow`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-prod-down` `-commutative` `associate-/l`
2×	`div-inv`
1×	`frac-2neg` `clear-num`

Counts

4 → 186

Calls

4 calls:

12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0)))
14.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0))) (pow (sqrt n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) (sqrt n))

series1.4s

Counts

4 → 12

Calls

4 calls:

559.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0)))
711.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0))) (pow (sqrt n) (/ (- 1.0 k) 2.0)))
41.0ms	(/ 1.0 (sqrt k))
71.0ms	(* (* 2.0 PI) (sqrt n))

simplify56.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1438	2696
1	5001	2500

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-exp-log`
103×	`prod-exp`
38×	`add-sqr-sqrt`
35×	`pow-exp`
28×	`add-cbrt-cube`
27×	`associate-r`
25×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
22×	`times-frac`
20×	`div-exp` `sqrt-prod`
19×	`pow-to-exp`
14×	`pow1`
13×	`cbrt-unprod`
7×	`unpow-prod-down`
6×	`pow-prod-down` `unswap-sqr`
5×	`sqr-pow`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/`
2×	`cbrt-undiv`
1×	`div-inv`

Counts

4 → 160

Calls

4 calls:

6.0ms	(* (* 2.0 PI) (sqrt n))
9.0ms	(* (* 2.0 PI) (sqrt n))
13.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0))) (pow (sqrt n) (/ 1.0 2.0)))
12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (* 2.0 PI) (sqrt n))
70.0ms	(* (* 2.0 PI) (sqrt n))
591.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0))) (pow (sqrt n) (/ 1.0 2.0)))
781.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)))

simplify117.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	906	1896
1	4001	1675
2	5001	1627

prune518.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes138.0ms

Accuracy

0% (0.6b 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	19	11
1	19	11

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	26986×	body	80	nan
693.0ms	2010×	body	1280	nan
655.0ms	10676×	body	80	valid
447.0ms	1620×	body	640	nan
155.0ms	807×	body	320	nan
44.0ms	388×	body	160	nan