Details

sample172.0ms

Algorithm

intervals

Results

69.0ms	727×	body	80	nan
46.0ms	400×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1545	16
done	5000	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

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

rewrite177.0ms

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:

86.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
36.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
7.0ms	(/ 1.0 (sqrt k))

series777.0ms

Counts

4 → 12

Calls

4 calls:

462.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
42.0ms	(* (* 2.0 PI) n)
209.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
64.0ms	(/ 1.0 (sqrt k))

simplify2.7s

Counts

161 → 161

Iterations

Useful iterations: 2 (853.0ms)

Iter	Nodes	Cost
0	361	2800
1	1009	2643
2	4753	2479
done	5001	2479

prune728.0ms

Pruning

13 alts after pruning (13 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	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

18.0ms	(* (* 2.0 PI) n)
41.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
7.0ms	(/ 1.0 (sqrt k))
7.0ms	(/ 1.0 (sqrt k))

series341.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* 2.0 PI) n)
200.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
52.0ms	(/ 1.0 (sqrt k))
46.0ms	(/ 1.0 (sqrt k))

simplify1.9s

Counts

144 → 144

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	234	1642
1	602	1507
2	2730	1405
done	5000	1401

prune797.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

243×	`add-exp-log`
174×	`prod-exp`
63×	`pow-exp`
26×	`div-exp`
25×	`add-cbrt-cube`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`pow-to-exp`
18×	`times-frac`
16×	`div-sub`
14×	`pow1`
12×	`sqrt-prod`
11×	`associate-r` `cbrt-unprod`
8×	`pow-sub`
6×	`pow-prod-down` `associate-/r*`
5×	`frac-times` `associate-*l/`
4×	`add-log-exp`
3×	`associate-r/` `associate-l` `-commutative` `associate-/l*`
2×	`cbrt-undiv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `div-inv` `sqr-pow`

Counts

4 → 154

Calls

4 calls:

214.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
41.0ms	(* (* 2.0 PI) n)
23.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))

series712.0ms

Counts

4 → 12

Calls

4 calls:

544.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
50.0ms	(* (* 2.0 PI) n)
57.0ms	(* (* 2.0 PI) n)
60.0ms	(/ 1.0 (sqrt k))

simplify3.1s

Counts

166 → 166

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	337	4193
1	934	3027
2	4690	2769
done	5000	2763

prune541.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.2b	(* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))

rewrite527.0ms

Algorithm

rewrite-expression-head

Rules

602×	`add-exp-log`
498×	`prod-exp`
186×	`pow-exp`
120×	`times-frac`
103×	`pow-to-exp`
87×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
61×	`pow-unpow` `div-exp`
50×	`div-sub`
25×	`add-cbrt-cube` `pow-sub`
17×	`frac-times` `associate-*l/`
15×	`pow1`
12×	`sqrt-prod` `cbrt-unprod`
10×	`associate-r`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`associate-*r/`
6×	`pow-prod-down` `associate-/r*`
5×	`div-inv`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `associate-l` `*-commutative` `sqr-pow`
1×	`frac-2neg` `clear-num`

Counts

4 → 305

Calls

4 calls:

43.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
391.0ms	(* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
35.0ms	(* (* 2.0 PI) n)
13.0ms	(/ 1.0 (sqrt k))

series1.9s

Counts

4 → 12

Calls

4 calls:

228.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.6s	(* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
35.0ms	(* (* 2.0 PI) n)
49.0ms	(/ 1.0 (sqrt k))

simplify1.1s

Counts

317 → 317

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	617	10616
1	1916	10084
done	5000	8835

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes232.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	23
1	19	23
done	19	23

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.5s	12068×	body	80	valid
2.5s	21072×	body	80	nan
0.0ms	3×	body	160	nan