Details

sample86.0ms

Algorithm

intervals

Results

33.0ms	651×	body	80	nan
27.0ms	398×	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	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)))
0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite46.0ms

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:

21.0ms	(* (/ 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:

329.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (* 2.0 PI) n)
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (85.0ms)

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

prune461.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

741×	`sqrt-prod`
583×	`add-sqr-sqrt`
501×	`times-frac`
245×	`*-un-lft-identity`
239×	`add-cube-cbrt`
124×	`swap-sqr`
61×	`associate-r`
59×	`associate-l`
49×	`unswap-sqr`
29×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`pow1`
19×	`pow-unpow`
10×	`prod-exp`
9×	`associate-/r*`
7×	`pow-prod-down` `cbrt-unprod`
6×	`div-inv` `associate-/l*`
5×	`cbrt-undiv` `sqrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-pow` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative`
1×	`pow2` `frac-times` `pow-to-exp` `unpow-prod-down` `frac-2neg` `pow-plus` `sqrt-unprod` `div-sub` `associate-r/` `associate-l/` `clear-num` `rem-square-sqrt` `pow-sqr` `pow-prod-up` `pow-sub` `sqr-pow`

Counts

4 → 451

Calls

4 calls:

8.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
81.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
32.0ms	(* (* 2.0 PI) n)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
102.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))))

simplify78.0ms

Algorithm

egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1331	6940
1	5002	6404

prune918.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
13.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series356.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	399	798
1	1625	738
2	5001	694

prune429.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt k) (cbrt k))
0.6b	(cbrt k)
0.6b	(cbrt k)
0.6b	(cbrt k)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt k) (cbrt k))
0.0ms	(cbrt k)
1.0ms	(cbrt k)
1.0ms	(cbrt k)

series745.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt k) (cbrt k))
182.0ms	(cbrt k)
178.0ms	(cbrt k)
183.0ms	(cbrt k)

simplify89.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune477.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes176.0ms

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	19	15
1	19	15

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	20676×	body	80	nan
723.0ms	11905×	body	80	valid