Details

sample189.0ms

Algorithm

intervals

Results

96.0ms	727×	body	80	nan
41.0ms	400×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

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))

rewrite157.0ms

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:

71.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms	(* (* 2.0 PI) n)
37.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
19.0ms	(/ 1.0 (sqrt k))

series762.0ms

Counts

4 → 12

Calls

4 calls:

420.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
62.0ms	(* (* 2.0 PI) n)
211.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
69.0ms	(/ 1.0 (sqrt k))

simplify2.9s

Counts

169 → 169

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	369	2880
1	1038	2720
2	4964	2556
done	5000	2555

prune840.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

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))

rewrite81.0ms

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×	`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` `frac-2neg` `div-exp` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

24.0ms	(* (* 2.0 PI) n)
27.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
13.0ms	(/ 1.0 (sqrt k))
12.0ms	(/ 1.0 (sqrt k))

series343.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* 2.0 PI) n)
194.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
54.0ms	(/ 1.0 (sqrt k))
42.0ms	(/ 1.0 (sqrt k))

simplify1.9s

Counts

152 → 152

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	240	1698
1	617	1560
2	2789	1462
done	5000	1455

prune894.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow n (/ (- 1.0 k) 2.0))
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))

rewrite135.0ms

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:

15.0ms	(pow n (/ (- 1.0 k) 2.0))
61.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
13.0ms	(/ 1.0 (sqrt k))
30.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series729.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(pow n (/ (- 1.0 k) 2.0))
452.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
53.0ms	(/ 1.0 (sqrt k))
145.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

181 → 181

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	333	2626
1	922	2474
2	3791	2362
done	5000	2340

prune874.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
64×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow` `prod-exp`
22×	`associate-l`
21×	`sqrt-prod`
18×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
11×	`div-exp`
10×	`div-sub` `pow-sub`
8×	`pow1`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-l/` `associate-/l`
2×	`pow-pow` `sqr-pow`
1×	`frac-2neg` `associate-r` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 178

Calls

4 calls:

9.0ms	(pow n (/ (- 1.0 k) 2.0))
119.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
13.0ms	(/ 1.0 (sqrt k))
15.0ms	(pow PI (/ (- 1.0 k) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

105.0ms	(pow n (/ (- 1.0 k) 2.0))
800.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
48.0ms	(/ 1.0 (sqrt k))
466.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

190 → 190

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	384	3225
1	1143	2900
2	4674	2698
done	5000	2694

prune985.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	28
1	18	28
done	18	28

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.9s	21072×	body	80	nan
1.8s	12068×	body	80	valid
1.0ms	3×	body	160	nan