Details

sample179.0ms

Algorithm

intervals

Results

79.0ms	674×	body	80	nan
51.0ms	372×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	2792
5	816
4	285
3	114
2	58
1	29
0	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

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	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt k))
1.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite102.0ms

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×	`associate-/r*` `div-exp` `pow-prod-down` `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` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 157

Calls

4 calls:

44.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
15.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
25.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series761.0ms

Counts

4 → 12

Calls

4 calls:

477.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
45.0ms	(/ 1.0 (sqrt k))
203.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.8s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	3343
1	1004
0	361

prune999.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt k))
0.2b	(/ 1.0 (sqrt k))
1.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

17.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
5.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series362.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* 2.0 PI) n)
66.0ms	(/ 1.0 (sqrt k))
52.0ms	(/ 1.0 (sqrt k))
180.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

152 → 152

Iterations

Iter	Nodes
done	5001
2	1862
1	614
0	242

prune984.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.2b	(pow n (/ (- 1.0 k) 2.0))

rewrite68.0ms

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×	`add-cbrt-cube` `prod-exp`
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` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 169

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
13.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
6.0ms	(pow n (/ (- 1.0 k) 2.0))

series593.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1.0 (sqrt k))
349.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
107.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
79.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	5004
2	2846
1	908
0	334

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
1.2b	(pow n (/ (- 1.0 k) 2.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
72×	`times-frac`
66×	`*-un-lft-identity`
54×	`add-cube-cbrt`
38×	`pow-unpow`
24×	`sqrt-prod`
22×	`associate-l`
21×	`add-exp-log`
12×	`unpow-prod-down`
11×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-r`
6×	`pow1` `associate-/r*` `prod-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `div-sub` `div-exp` `pow-exp` `log1p-expm1-u` `div-inv` `pow-sub` `add-log-exp`
3×	`associate-/l*`
2×	`cbrt-undiv` `pow-pow` `cbrt-unprod`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 172

Calls

4 calls:

9.0ms	(/ 1.0 (sqrt k))
40.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
12.0ms	(pow PI (/ (- 1.0 k) 2.0))
9.0ms	(pow n (/ (- 1.0 k) 2.0))

series487.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (sqrt k))
311.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
62.0ms	(pow PI (/ (- 1.0 k) 2.0))
65.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

184 → 184

Iterations

Iter	Nodes
done	5003
2	2867
1	938
0	353

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes462.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.7s	20706×	body	80	nan
2.1s	11897×	body	80	valid
0.0ms	2×	body	160	nan