Details

sample95.0ms

Algorithm

intervals

Results

41.0ms	693×	body	80	nan
26.0ms	379×	body	80	valid

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

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	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.7b	(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:

18.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series536.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
44.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (85.0ms)

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

prune479.0ms

Filtered

169 candidates to 119 candidates (70.4%)

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))
0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.4b	(pow n (/ (- 1.0 k) 2.0))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`times-frac`
64×	`*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
11×	`prod-exp` `add-cbrt-cube`
8×	`pow1`
7×	`pow-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down` `div-exp` `associate-r`
4×	`expm1-log1p-u` `pow-to-exp` `div-sub` `log1p-expm1-u` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 169

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
15.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
4.0ms	(pow n (/ (- 1.0 k) 2.0))
5.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series461.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt k))
288.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
57.0ms	(pow n (/ (- 1.0 k) 2.0))
78.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	844	1367
1	3255	1284
2	5001	1267

prune563.0ms

Filtered

181 candidates to 131 candidates (72.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
0.4b	(pow n (/ (- 1.0 k) 2.0))
0.5b	(pow PI (/ (- 1.0 k) 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
64×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow` `prod-exp`
22×	`associate-l`
21×	`sqrt-prod`
18×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
11×	`div-exp`
10×	`div-sub` `pow-sub`
8×	`pow1`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-l/` `associate-/l`
2×	`pow-pow` `sqr-pow`
1×	`frac-2neg` `associate-r` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 178

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
29.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
4.0ms	(pow n (/ (- 1.0 k) 2.0))
4.0ms	(pow PI (/ (- 1.0 k) 2.0))

series714.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (sqrt k))
559.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
64.0ms	(pow n (/ (- 1.0 k) 2.0))
47.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1057	1626
1	4206	1464
2	5001	1453

prune614.0ms

Filtered

190 candidates to 129 candidates (67.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))))
0.3b	(/ (sqrt 1.0) (sqrt (sqrt k)))
0.3b	(/ (sqrt 1.0) (sqrt (sqrt k)))
0.4b	(pow n (/ (- 1.0 k) 2.0))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

387×	`add-exp-log`
261×	`prod-exp`
186×	`sqrt-prod`
123×	`times-frac`
102×	`add-sqr-sqrt` `*-un-lft-identity`
96×	`add-cube-cbrt`
74×	`div-exp`
73×	`pow-exp`
44×	`add-cbrt-cube`
37×	`pow-to-exp`
33×	`div-sub`
21×	`cbrt-unprod`
19×	`pow-unpow`
18×	`associate-/r*`
17×	`frac-times` `pow-sub`
12×	`pow1` `associate-/l*`
11×	`associate-r/` `associate-l/`
8×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`sqrt-undiv` `frac-2neg` `clear-num`
1×	`pow2` `pow-pow` `pow-plus` `swap-sqr` `associate-r` `associate-l` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 327

Calls

4 calls:

78.0ms	(* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))))
5.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
9.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
4.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

616.0ms	(* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))))
183.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
183.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
65.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify120.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	1116	4080
1	4374	3489
2	5001	3484

prune772.0ms

Filtered

339 candidates to 139 candidates (41.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes146.0ms

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	17	11
1	17	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	20577×	body	80	nan
745.0ms	11846×	body	80	valid
0.0ms	2×	body	160	nan