Details

sample148.0ms

Algorithm

intervals

Results

52.0ms	584×	body	80	nan
49.0ms	363×	body	80	valid

simplify1.2s

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	1555	16
done	5001	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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

rewrite183.0ms

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:

73.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
13.0ms	(/ 1.0 (sqrt k))
46.0ms	(* (* 2.0 PI) n)
45.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series766.0ms

Counts

4 → 12

Calls

4 calls:

447.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
54.0ms	(/ 1.0 (sqrt k))
48.0ms	(* (* 2.0 PI) n)
217.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.2s

Counts

169 → 169

Iterations

Useful iterations: done (3.1s)

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

prune780.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

28.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
32.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series741.0ms

Counts

3 → 9

Calls

3 calls:

478.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
53.0ms	(* (* 2.0 PI) n)
210.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

101 → 101

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	270	1898
1	771	1770
2	3672	1598
done	5000	1587

prune487.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize33.0ms

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) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
1.1b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.1b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
143×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
122×	`pow-unpow`
103×	`add-cube-cbrt`
91×	`add-exp-log`
64×	`prod-exp`
36×	`pow-exp`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`pow-to-exp` `div-sub`
11×	`add-cbrt-cube`
10×	`pow-prod-down` `sqr-pow`
8×	`associate-r` `div-inv`
6×	`unpow-prod-down` `pow-pow` `associate-l` `pow-sub`
5×	`swap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`*-commutative`
1×	`pow2` `frac-times` `associate-r/` `associate-l/` `pow-sqr` `pow-prod-up`

Counts

4 → 242

Calls

4 calls:

25.0ms	(* (* 2.0 PI) n)
96.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
63.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
32.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series807.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* 2.0 PI) n)
274.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
211.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
251.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify816.0ms

Counts

254 → 254

Iterations

Useful iterations: done (798.0ms)

Iter	Nodes	Cost
0	319	5430
1	1041	4550
done	5000	4056

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
1.1b	(pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2))
1.1b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
136×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
100×	`add-cube-cbrt`
29×	`pow1` `add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`pow-prod-down` `prod-exp`
9×	`pow-pow` `pow-exp`
8×	`div-inv`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `div-sub` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `pow1/3` `pow-sub` `sqr-pow`

Counts

4 → 192

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
189.0ms	(pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2))
48.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series985.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt n)
276.0ms	(cbrt n)
225.0ms	(pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2))
215.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.3s

Counts

204 → 204

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	327	3810
1	1079	3555
2	4039	3142
done	5000	2886

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes193.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	16	16
done	16	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.8s	20706×	body	80	nan
2.1s	11991×	body	80	valid
0.0ms	1×	body	160	nan