Details

sample156.0ms

Algorithm

intervals

Results

78.0ms	689×	body	80	nan
51.0ms	372×	body	80	valid

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite45.0ms

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:

20.0ms	(* (/ 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))

series545.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
39.0ms	(/ 1.0 (sqrt k))
35.0ms	(* (* 2.0 PI) n)
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344

prune416.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
136×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
100×	`add-cube-cbrt`
26×	`pow1` `add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`div-inv`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`div-sub` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 192

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)
13.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
13.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series347.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
143.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify79.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	696	1678
1	2767	1618
2	5001	1608

prune667.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
0.6b	(cbrt n)
1.4b	(pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log`
22×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`pow-unpow`
16×	`add-cube-cbrt`
15×	`times-frac`
13×	`pow-prod-down` `prod-exp`
9×	`cbrt-prod`
6×	`pow-pow` `pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

0.0ms	(cbrt n)
0.0ms	(cbrt n)
1.0ms	(cbrt n)
55.0ms	(pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))

series696.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt n)
180.0ms	(cbrt n)
177.0ms	(cbrt n)
166.0ms	(pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	406	669
1	1327	628
2	5001	574

prune284.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* 2.0 PI) n))
0.5b	(cbrt (* (* 2.0 PI) n))
0.6b	(* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
1.4b	(pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`pow-unpow`
17×	`add-cube-cbrt` `pow1/3`
15×	`pow-pow` `times-frac`
12×	`add-exp-log`
11×	`pow-prod-up`
7×	`pow-plus` `pow-prod-down`
6×	`cbrt-prod`
5×	`pow-sqr`
4×	`swap-sqr` `associate-r` `associate-l` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow2` `pow-exp` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `pow3` `*-commutative` `cbrt-unprod` `div-inv` `pow-sub` `unswap-sqr` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

5.0ms	(cbrt (* (* 2.0 PI) n))
8.0ms	(cbrt (* (* 2.0 PI) n))
8.0ms	(* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
21.0ms	(pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (* (* 2.0 PI) n))
241.0ms	(cbrt (* (* 2.0 PI) n))
344.0ms	(* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
198.0ms	(pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	517	1053
1	1976	831
2	5001	798

prune300.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes157.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.4s	21052×	body	80	nan
1.6s	11941×	body	80	valid
1.0ms	3×	body	160	nan