Details

sample251.0ms

Algorithm

intervals

Results

125.0ms	744×	body	80	nan
72.0ms	383×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2753
5	970
4	328
3	124
2	62
1	31
0	13

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
0.2b	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
0.2b	(* (* n 2) PI)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

493×	`times-frac`
383×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
378×	`add-cube-cbrt`
328×	`unpow-prod-up`
312×	`prod-diff`
141×	`sqrt-prod`
46×	`associate-/l*`
26×	`add-exp-log`
25×	`div-inv`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-l` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

22.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
15.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
32.0ms	(* (* n 2) PI)

series550.0ms

Counts

3 → 9

Calls

3 calls:

194.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
315.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
41.0ms	(* (* n 2) PI)

simplify3.4s

Counts

445 → 445

Iterations

Iter	Nodes
done	5000
2	4186
1	1539
0	699

prune3.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
0.1b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
0.2b	(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
0.2b	(* (* n 2) PI)

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

3088×	`times-frac`
1878×	`add-sqr-sqrt`
1875×	`*-un-lft-identity`
1873×	`add-cube-cbrt`
1312×	`unpow-prod-up`
1248×	`prod-diff`
693×	`sqrt-prod`
327×	`associate-/r*`
102×	`div-inv`
72×	`add-exp-log`
32×	`sub-neg` `unpow-prod-down` `div-exp` `sqr-pow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
6×	`rec-exp` `pow-unpow` `1-exp` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`associate-l` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 1599

Calls

4 calls:

43.0ms	(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
40.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
26.0ms	(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
29.0ms	(* (* n 2) PI)

series1.4s

Counts

4 → 12

Calls

4 calls:

321.0ms	(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
207.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
798.0ms	(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
66.0ms	(* (* n 2) PI)

simplify6.8s

Counts

1611 → 1611

Iterations

Iter	Nodes
done	5000
1	4740
0	1732

prune11.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
0.2b	(/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
0.2b	(* (* n 2) PI)
0.3b	(/ 1 (sqrt k))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

10821×	`times-frac`
5428×	`add-sqr-sqrt`
5425×	`*-un-lft-identity`
5423×	`add-cube-cbrt`
2870×	`unpow-prod-up`
2730×	`prod-diff`
1308×	`sqrt-prod`
379×	`div-inv`
207×	`add-exp-log`
149×	`associate-/r*`
138×	`div-exp`
70×	`sub-neg` `unpow-prod-down` `sqr-pow`
42×	`prod-exp`
39×	`pow-exp`
37×	`rec-exp` `1-exp`
25×	`associate-/l*`
24×	`associate-/r/` `pow-sub`
23×	`add-cbrt-cube`
17×	`pow1`
13×	`pow-to-exp`
9×	`cbrt-undiv`
6×	`pow-unpow` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod` `pow-flip`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--` `inv-pow` `associate-/l/`

Counts

4 → 3530

Calls

4 calls:

40.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
26.0ms	(/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
15.0ms	(* (* n 2) PI)
6.0ms	(/ 1 (sqrt k))

series623.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
332.0ms	(/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
73.0ms	(* (* n 2) PI)
39.0ms	(/ 1 (sqrt k))

simplify9.3s

Counts

3542 → 3542

Iterations

Iter	Nodes
done	5001
0	4156

prune27.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
0.1b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
0.2b	(/ (pow k (- 1/2)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
0.2b	(* (* n 2) PI)

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

3027×	`times-frac`
1736×	`add-sqr-sqrt`
1733×	`*-un-lft-identity`
1731×	`add-cube-cbrt`
1189×	`unpow-prod-up`
1131×	`prod-diff`
461×	`unpow-prod-down`
189×	`associate-/r*`
173×	`sqr-pow`
154×	`add-exp-log`
97×	`div-inv`
88×	`div-exp`
55×	`pow-exp`
42×	`prod-exp`
29×	`pow-to-exp` `sub-neg`
20×	`rec-exp` `1-exp`
16×	`add-cbrt-cube`
15×	`pow1`
11×	`pow-sub`
10×	`associate-/r/` `associate-/l*`
6×	`pow-unpow` `pow-prod-down`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `difference-of-squares` `associate-/l/`
1×	`neg-sub0` `pow-neg` `associate-l` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 1524

Calls

4 calls:

16.0ms	(/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
35.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
44.0ms	(/ (pow k (- 1/2)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
23.0ms	(* (* n 2) PI)

series850.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
246.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
320.0ms	(/ (pow k (- 1/2)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
74.0ms	(* (* n 2) PI)

simplify5.3s

Counts

1536 → 1536

Iterations

Iter	Nodes
done	5001
0	2099

prune13.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.8s	20633×	body	80	nan
2.5s	11932×	body	80	valid
1.0ms	4×	body	160	nan