Details

sample81.0ms

Algorithm

intervals

Results

35.0ms	706×	body	80	nan
21.0ms	359×	body	80	valid

simplify41.0ms

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	1034	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	(* (/ 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)
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite44.0ms

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:

17.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series549.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
38.0ms	(* (* 2.0 PI) n)
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify113.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (98.0ms)

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

prune430.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
19×	`pow-unpow`
17×	`add-cube-cbrt`
14×	`pow1` `prod-exp`
13×	`add-cbrt-cube`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `sqrt-prod`
4×	`cbrt-unprod`
3×	`pow-pow` `associate-r` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`unpow-prod-down` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

3 → 86

Calls

3 calls:

7.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series482.0ms

Counts

3 → 9

Calls

3 calls:

302.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
32.0ms	(* (* 2.0 PI) n)
147.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	709	938
1	2966	838
2	5002	830

prune258.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
143×	`add-sqr-sqrt` `*-un-lft-identity`
137×	`add-cube-cbrt`
78×	`sqrt-prod`
46×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `sqr-pow`
19×	`pow-unpow`
16×	`div-exp` `add-cbrt-cube`
15×	`pow1`
12×	`prod-exp`
9×	`pow-exp` `associate-/l*`
7×	`div-inv`
6×	`div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`associate-l` `*-commutative`

Counts

4 → 274

Calls

4 calls:

16.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
5.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

475.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
420.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(* (* 2.0 PI) n)
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1543	4220
1	5001	4048

prune756.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
64×	`sqrt-prod`
58×	`times-frac`
51×	`*-un-lft-identity`
39×	`add-cube-cbrt`
38×	`pow-unpow`
36×	`pow1`
23×	`add-exp-log`
17×	`swap-sqr`
16×	`associate-r`
14×	`associate-l`
12×	`pow-prod-down`
11×	`add-cbrt-cube`
10×	`prod-exp`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-pow` `pow-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`
5×	`pow-prod-up`
4×	`sqrt-div` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `*-commutative` `pow-sub` `sqr-pow`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 165

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
26.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series718.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
403.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
138.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	788	2022
1	3711	1824
2	5001	1763

prune516.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes108.0ms

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	15	8
1	15	8

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	20603×	body	80	nan
687.0ms	11703×	body	80	valid
0.0ms	3×	body	160	nan