Details

sample153.0ms

Algorithm

intervals

Results

63.0ms	656×	body	80	nan
38.0ms	358×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1541
4	328
3	120
2	59
1	29
0	13

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize25.0ms

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)
1.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite134.0ms

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×	`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 → 149

Calls

4 calls:

58.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (* 2.0 PI) n)
25.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series775.0ms

Counts

4 → 12

Calls

4 calls:

462.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
47.0ms	(/ 1.0 (sqrt k))
63.0ms	(* (* 2.0 PI) n)
202.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.2s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	4735
1	986
0	353

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 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))
1.2b	(pow n (/ (- 1.0 k) 2.0))

rewrite70.0ms

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×	`pow-to-exp` `div-sub` `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 → 161

Calls

4 calls:

31.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
5.0ms	(/ 1.0 (sqrt k))
13.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
12.0ms	(pow n (/ (- 1.0 k) 2.0))

series671.0ms

Counts

4 → 12

Calls

4 calls:

387.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
63.0ms	(/ 1.0 (sqrt k))
130.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
90.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	3720
1	900
0	326

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 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))

rewrite59.0ms

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×	`pow-to-exp` `div-sub` `div-exp` `pow-exp` `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 → 164

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))
6.0ms	(pow n (/ (- 1.0 k) 2.0))

series451.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1.0 (sqrt k))
253.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
74.0ms	(pow PI (/ (- 1.0 k) 2.0))
70.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

176 → 176

Iterations

Iter	Nodes
done	5001
2	4043
1	952
0	345

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow-unpow`
50×	`add-sqr-sqrt` `pow1` `*-un-lft-identity`
45×	`times-frac`
32×	`sqrt-div` `add-cube-cbrt`
26×	`pow-prod-down`
23×	`add-exp-log`
19×	`div-sub` `pow-sub`
17×	`frac-times`
16×	`add-cbrt-cube`
12×	`pow1/2`
11×	`associate-l/` `associate-r/`
10×	`prod-exp`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`cbrt-unprod`
5×	`unpow-prod-down` `pow-pow` `sqrt-unprod` `pow-exp` `pow-sqr` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-to-exp` `div-inv` `sqr-pow`
2×	`pow-plus`
1×	`pow2` `rem-square-sqrt` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 156

Calls

4 calls:

147.0ms	(* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))))
14.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
6.0ms	(pow n (/ (- 1.0 k) 2.0))

series876.0ms

Counts

4 → 12

Calls

4 calls:

594.0ms	(* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))))
103.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
95.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
83.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

168 → 168

Iterations

Iter	Nodes
done	5001
2	3458
1	823
0	275

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes370.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.0s	20122×	body	80	nan
1.8s	11872×	body	80	valid