Details

sample273.0ms

Algorithm

intervals

Results

143.0ms	607×	body	80	nan
89.0ms	382×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	2026
6	2026
5	970
4	328
3	124
2	62
1	31
0	13

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
0.3b	(* n (* 2 PI))
0.9b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite99.0ms

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-l` `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-r` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

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

series654.0ms

Counts

3 → 9

Calls

3 calls:

359.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
60.0ms	(* n (* 2 PI))
235.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.4s

Counts

445 → 445

Iterations

Iter	Nodes
done	2001
2	2001
1	1526
0	695

prune3.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
0.5b	(pow (* 2 PI) (- 1/2 (/ k 2)))
0.6b	(pow n (- 1/2 (/ k 2)))

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

43085×	`times-frac`
25423×	`add-sqr-sqrt`
25417×	`*-un-lft-identity`
25413×	`add-cube-cbrt`
23985×	`unpow-prod-up`
22815×	`prod-diff`
6903×	`sqrt-prod`
1806×	`div-inv`
1151×	`unpow-prod-down`
585×	`sub-neg` `sqr-pow`
327×	`associate-/r*`
54×	`associate-/l*`
53×	`add-exp-log` `pow-sub`
51×	`associate-/r/`
31×	`div-exp`
16×	`pow-exp`
12×	`pow-unpow`
11×	`pow-to-exp` `add-cbrt-cube`
8×	`pow1`
5×	`prod-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-pow`
2×	`clear-num` `frac-2neg` `distribute-lft-out--`
1×	`pow-prod-down` `associate-/l/`

Counts

4 → 14326

Calls

4 calls:

48.0ms	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))
20.0ms	(/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
19.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
13.0ms	(pow n (- 1/2 (/ k 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

550.0ms	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))
735.0ms	(/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
109.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
121.0ms	(pow n (- 1/2 (/ k 2)))

simplify1.1m

Counts

14338 → 14338

Iterations

Iter	Nodes
done	13509
0	13509

prune2.4m

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
0.5b	(/ 1 (pow 2 (- 1/2 (/ k 2))))
0.5b	(pow PI (- 1/2 (/ k 2)))
0.6b	(pow n (- 1/2 (/ k 2)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

1067×	`times-frac`
882×	`add-sqr-sqrt`
764×	`*-un-lft-identity`
739×	`add-cube-cbrt`
615×	`unpow-prod-up`
585×	`prod-diff`
293×	`associate-r`
165×	`sqrt-prod`
149×	`associate-l`
115×	`add-exp-log`
73×	`unpow-prod-down`
60×	`div-exp`
49×	`unswap-sqr`
48×	`associate-/r*` `div-inv`
43×	`sqr-pow`
40×	`prod-exp`
27×	`pow-to-exp` `pow-exp`
18×	`add-cbrt-cube`
15×	`rec-exp` `sub-neg` `1-exp`
12×	`pow-unpow`
8×	`pow1`
5×	`cbrt-undiv` `pow-sub`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-/r/` `associate-/l*`
2×	`pow-pow` `distribute-lft-out--`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 901

Calls

4 calls:

50.0ms	(* (/ 1 (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
9.0ms	(/ 1 (pow 2 (- 1/2 (/ k 2))))
6.0ms	(pow PI (- 1/2 (/ k 2)))
10.0ms	(pow n (- 1/2 (/ k 2)))

series848.0ms

Counts

4 → 12

Calls

4 calls:

636.0ms	(* (/ 1 (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
97.0ms	(/ 1 (pow 2 (- 1/2 (/ k 2))))
44.0ms	(pow PI (- 1/2 (/ k 2)))
71.0ms	(pow n (- 1/2 (/ k 2)))

simplify3.0s

Counts

913 → 913

Iterations

Iter	Nodes
done	2000
1	2000
0	1339

prune4.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))
0.2b	(/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2))))
0.5b	(pow PI (- 1/2 (/ k 2)))
0.6b	(pow n (- 1/2 (/ k 2)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

1460×	`times-frac`
1100×	`add-sqr-sqrt`
1094×	`*-un-lft-identity`
1090×	`add-cube-cbrt`
902×	`unpow-prod-up`
882×	`sqrt-prod`
858×	`prod-diff`
96×	`associate-/r*`
68×	`div-inv`
66×	`unpow-prod-down`
22×	`sub-neg` `sqr-pow`
18×	`associate-/l*`
16×	`add-exp-log`
12×	`pow-unpow`
8×	`add-cbrt-cube`
6×	`pow1` `div-exp`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `insert-posit16` `log1p-expm1-u` `pow-sub` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `pow-pow` `frac-2neg` `associate-/r/` `distribute-lft-out--`

Counts

4 → 1144

Calls

4 calls:

10.0ms	(/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))
14.0ms	(/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2))))
6.0ms	(pow PI (- 1/2 (/ k 2)))
6.0ms	(pow n (- 1/2 (/ k 2)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))
195.0ms	(/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2))))
47.0ms	(pow PI (- 1/2 (/ k 2)))
64.0ms	(pow n (- 1/2 (/ k 2)))

simplify1.6s

Counts

1156 → 1156

Iterations

Iter	Nodes
done	2004
1	2004
0	1459

prune6.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes78.0ms

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	19
1	19
0	16

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.7s	20747×	body	80	nan
1.9s	11976×	body	80	valid
0.0ms	1×	body	160	nan