Details

sample143.0ms

Algorithm

intervals

Results

79.0ms	656×	body	80	nan
32.0ms	358×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	495
1	29	495
2	59	495
3	120	495
4	328	495
5	1551	495
done	5000	495

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize22.0ms

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))

rewrite105.0ms

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:

37.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(/ 1.0 (sqrt k))
30.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series652.0ms

Counts

4 → 12

Calls

4 calls:

362.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
42.0ms	(/ 1.0 (sqrt k))
54.0ms	(* (* 2.0 PI) n)
193.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify4.4s

Counts

169 → 169

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	361	75851
1	1013	69294
2	4865	67966
done	5000	67956

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite109.0ms

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:

56.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
10.0ms	(/ 1.0 (sqrt k))
18.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
13.0ms	(pow n (/ (- 1.0 k) 2.0))

series733.0ms

Counts

4 → 12

Calls

4 calls:

431.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
64.0ms	(/ 1.0 (sqrt k))
139.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
98.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify3.1s

Counts

181 → 181

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	334	80749
1	928	73443
2	3775	72315
done	5000	71996

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

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))

rewrite103.0ms

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))
48.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
22.0ms	(pow PI (/ (- 1.0 k) 2.0))
13.0ms	(pow n (/ (- 1.0 k) 2.0))

series498.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1.0 (sqrt k))
255.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
72.0ms	(pow PI (/ (- 1.0 k) 2.0))
115.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify3.1s

Counts

184 → 184

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	353	80084
1	973	72499
2	4088	71801
done	5000	71562

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize90.0ms

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))

rewrite212.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 164

Calls

4 calls:

148.0ms	(* (* (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)))))
16.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
16.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
18.0ms	(pow n (/ (- 1.0 k) 2.0))

series799.0ms

Counts

4 → 12

Calls

4 calls:

480.0ms	(* (* (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)))))
99.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
135.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
85.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify3.3s

Counts

176 → 176

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	281	87494
1	842	76830
2	3531	74400
done	5001	73140

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes399.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	915
1	18	915
done	18	915

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.9s	20122×	body	80	nan
2.0s	11872×	body	80	valid