Details

sample81.0ms

Algorithm

intervals

Results

32.0ms	649×	body	80	nan
24.0ms	396×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	57	16
3	114	16
4	300	16
5	859	16
6	3256	16
done	5000	16

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))

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×	`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:

17.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
7.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(/ 1.0 (sqrt k))

series528.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
38.0ms	(/ 1.0 (sqrt k))

simplify1.1s

Counts

169 → 169

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	369	2880
1	987	2720
2	3678	2554
done	5001	2539

prune452.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 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))

rewrite27.0ms

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:

6.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(/ 1.0 (sqrt k))
3.0ms	(/ 1.0 (sqrt k))

series249.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
37.0ms	(/ 1.0 (sqrt k))
42.0ms	(/ 1.0 (sqrt k))

simplify647.0ms

Counts

152 → 152

Iterations

Useful iterations: done (643.0ms)

Iter	Nodes	Cost
0	240	1698
1	589	1576
2	2011	1464
done	5000	1454

prune488.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

594×	`sqrt-prod`
591×	`times-frac`
328×	`add-sqr-sqrt` `*-un-lft-identity`
322×	`add-cube-cbrt`
34×	`associate-/l*`
22×	`add-exp-log`
19×	`pow-unpow`
18×	`associate-/r*`
16×	`add-cbrt-cube`
15×	`pow1`
13×	`div-inv`
6×	`pow-prod-down` `prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 447

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt (sqrt k)))
17.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 2.0 PI) n)
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
170.0ms	(/ 1.0 (sqrt (sqrt k)))
39.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

simplify1.3s

Counts

459 → 459

Iterations

Useful iterations: 2 (414.0ms)

Iter	Nodes	Cost
0	566	9021
1	1367	7999
2	4331	7284
done	5000	7284

prune872.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

1527×	`sqrt-prod`
933×	`add-sqr-sqrt`
768×	`times-frac`
339×	`*-un-lft-identity`
333×	`add-cube-cbrt`
196×	`swap-sqr`
81×	`unswap-sqr`
76×	`associate-r` `associate-l`
42×	`add-exp-log`
36×	`add-cbrt-cube`
21×	`associate-/r*`
19×	`pow-unpow`
17×	`pow1`
14×	`cbrt-undiv` `div-exp`
11×	`prod-exp`
8×	`sqrt-undiv` `cbrt-unprod`
7×	`div-inv` `associate-/l*`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-exp` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
2×	`frac-times` `frac-2neg` `sqrt-unprod` `associate-r/` `associate-l/` `clear-num`
1×	`pow2` `pow-to-exp` `unpow-prod-down` `pow-plus` `div-sub` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `pow-sub` `sqr-pow`

Counts

4 → 645

Calls

4 calls:

7.0ms	(/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
27.0ms	(/ (* (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))
119.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
99.0ms	(/ (* (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt k)))
210.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))

simplify503.0ms

Counts

657 → 657

Iterations

Useful iterations: done (478.0ms)

Iter	Nodes	Cost
0	540	17445
1	1642	15839
done	5000	14904

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes232.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	23
1	25	23
done	25	23

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	20532×	body	80	nan
730.0ms	11909×	body	80	valid
1.0ms	5×	body	160	nan