Details

sample162.0ms

Algorithm

intervals

Results

66.0ms	701×	body	80	nan
43.0ms	408×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1555	16
done	5001	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

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)
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite150.0ms

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:

68.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
13.0ms	(/ 1.0 (sqrt k))
22.0ms	(* (* 2.0 PI) n)
41.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series840.0ms

Counts

4 → 12

Calls

4 calls:

503.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
73.0ms	(/ 1.0 (sqrt k))
73.0ms	(* (* 2.0 PI) n)
191.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.9s

Counts

169 → 169

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	369	2880
1	1037	2720
2	4907	2552
done	5000	2549

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.3b	(pow (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
1.1b	(pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
45×	`times-frac`
36×	`pow-unpow`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
24×	`add-exp-log`
15×	`pow1`
12×	`difference-of-squares`
11×	`pow-exp` `add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down`
6×	`pow-prod-down` `associate-/r*` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-r` `cbrt-unprod` `associate-/l*` `sqr-pow`
2×	`unpow-prod-up` `div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `pow-sub`

Counts

4 → 140

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt k))
26.0ms	(* (* 2.0 PI) n)
29.0ms	(pow (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
28.0ms	(pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k)))

series1.6s

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1.0 (sqrt k))
35.0ms	(* (* 2.0 PI) n)
1.1s	(pow (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
417.0ms	(pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k)))

simplify1.5s

Counts

152 → 152

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	626	6148
1	1971	5708
done	5001	5325

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite178.0ms

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×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 200

Calls

4 calls:

19.0ms	(* (* 2.0 PI) n)
25.0ms	(* (* 2.0 PI) n)
65.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
38.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series515.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* 2.0 PI) n)
64.0ms	(* (* 2.0 PI) n)
190.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
206.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.4s

Counts

212 → 212

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	245	3332
1	796	3098
2	3630	2986
done	5000	2978

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite110.0ms

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:

70.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
7.0ms	(/ 1.0 (sqrt k))
12.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

799.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
57.0ms	(/ 1.0 (sqrt k))
129.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
121.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

181 → 181

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	333	2626
1	927	2468
2	3705	2362
done	5000	2340

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes300.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
done	20	32

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.6s	20612×	body	80	nan
2.1s	11830×	body	80	valid
0.0ms	1×	body	160	nan