Details

sample217.0ms

Algorithm

intervals

Results

124.0ms	654×	body	80	nan
63.0ms	362×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite367.0ms

Algorithm

rewrite-expression-head

Rules

619×	`times-frac`
531×	`add-sqr-sqrt`
465×	`*-un-lft-identity`
463×	`add-cube-cbrt`
328×	`unpow-prod-up`
312×	`prod-diff`
204×	`sqrt-prod`
176×	`unpow-prod-down`
135×	`associate-l`
67×	`associate-/l*`
54×	`associate-r`
36×	`unswap-sqr`
26×	`add-exp-log`
25×	`div-inv`
18×	`*-commutative`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `sqr-pow`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`expm1-log1p-u` `pow-pow` `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` `distribute-lft-out--` `associate-/l/`

Counts

3 → 617

Calls

3 calls:

186.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
55.0ms	(* (* n 2) PI)
87.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series588.0ms

Counts

3 → 9

Calls

3 calls:

348.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
56.0ms	(* (* n 2) PI)
184.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.5s

Counts

626 → 626

Iterations

Iter	Nodes
done	5000
1	1952
0	920

prune3.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* n 2) (sqrt PI))
0.7b	(pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
52×	`add-cube-cbrt`
41×	`unpow-prod-up`
39×	`prod-diff`
30×	`associate-l`
28×	`times-frac`
27×	`unpow-prod-down`
18×	`associate-r`
17×	`pow1`
16×	`sqrt-prod`
15×	`add-exp-log`
14×	`unswap-sqr`
9×	`add-cbrt-cube`
6×	`pow-unpow` `pow-prod-down` `prod-exp`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-exp` `cbrt-unprod` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 164

Calls

4 calls:

52.0ms	(* (* n 2) (sqrt PI))
81.0ms	(pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
3.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series401.0ms

Counts

4 → 8

Calls

4 calls:

109.0ms	(* (* n 2) (sqrt PI))
291.0ms	(pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify2.3s

Counts

172 → 172

Iterations

Iter	Nodes
done	5003
2	3085
1	1170
0	361

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (* n (sqrt 2)) (- 1/2 (* k 1/2))) (/ (pow (* (sqrt 2) PI) (- 1/2 (* k 1/2))) (sqrt k)))
0.2b	(/ (pow (* (sqrt 2) PI) (- 1/2 (* k 1/2))) (sqrt k))
0.4b	(* n (sqrt 2))
0.7b	(pow (* n (sqrt 2)) (- 1/2 (* k 1/2)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1050×	`add-sqr-sqrt`
746×	`times-frac`
696×	`*-un-lft-identity`
690×	`add-cube-cbrt`
646×	`unpow-prod-up`
612×	`prod-diff`
571×	`associate-r`
475×	`sqrt-prod`
335×	`unpow-prod-down`
311×	`associate-l`
185×	`unswap-sqr`
175×	`associate-/l*`
73×	`add-exp-log` `pow-sub`
70×	`*-commutative`
68×	`frac-times` `associate-*r/`
38×	`sqr-pow`
32×	`prod-exp`
22×	`pow-exp`
20×	`div-exp`
18×	`associate-/r*`
17×	`sub-neg`
13×	`add-cbrt-cube`
11×	`pow-to-exp` `pow1` `pow-unpow`
4×	`expm1-log1p-u` `clear-num` `distribute-rgt-out--` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `cbrt-unprod` `associate-/l/`
2×	`cbrt-undiv` `pow-pow` `un-div-inv` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate-*l/`

Counts

4 → 1176

Calls

4 calls:

859.0ms	(* (pow (* n (sqrt 2)) (- 1/2 (* k 1/2))) (/ (pow (* (sqrt 2) PI) (- 1/2 (* k 1/2))) (sqrt k)))
80.0ms	(/ (pow (* (sqrt 2) PI) (- 1/2 (* k 1/2))) (sqrt k))
17.0ms	(* n (sqrt 2))
34.0ms	(pow (* n (sqrt 2)) (- 1/2 (* k 1/2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (pow (* n (sqrt 2)) (- 1/2 (* k 1/2))) (/ (pow (* (sqrt 2) PI) (- 1/2 (* k 1/2))) (sqrt k)))
290.0ms	(/ (pow (* (sqrt 2) PI) (- 1/2 (* k 1/2))) (sqrt k))
63.0ms	(* n (sqrt 2))
218.0ms	(pow (* n (sqrt 2)) (- 1/2 (* k 1/2)))

simplify6.7s

Counts

1188 → 1188

Iterations

Iter	Nodes
done	5000
1	3810
0	1397

prune6.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
0.2b	(/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
0.2b	(* n PI)
0.7b	(pow (* n PI) (- 1/2 (/ k 2)))

rewrite927.0ms

Algorithm

rewrite-expression-head

Rules

1194×	`times-frac`
1086×	`add-sqr-sqrt`
909×	`*-un-lft-identity`
891×	`add-cube-cbrt`
697×	`unpow-prod-up`
663×	`prod-diff`
486×	`associate-r`
414×	`associate-l`
369×	`sqrt-prod`
212×	`unpow-prod-down`
130×	`unswap-sqr`
122×	`associate-/l*`
73×	`sqr-pow`
63×	`add-exp-log`
52×	`div-inv`
32×	`prod-exp`
26×	`pow-unpow`
22×	`pow-exp`
19×	`pow-prod-down`
18×	`*-commutative`
17×	`sub-neg`
16×	`pow1`
15×	`pow-to-exp`
13×	`add-cbrt-cube` `div-exp`
9×	`pow-sub`
7×	`distribute-lft-out--`
6×	`associate-/r*` `pow-pow` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-unprod` `associate-/l/`
2×	`frac-times` `cbrt-undiv` `associate-l/` `associate-r/`
1×	`clear-num` `frac-2neg`

Counts

4 → 1148

Calls

4 calls:

259.0ms	(* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
515.0ms	(/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
14.0ms	(* n PI)
44.0ms	(pow (* n PI) (- 1/2 (/ k 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

294.0ms	(* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
608.0ms	(/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
26.0ms	(* n PI)
157.0ms	(pow (* n PI) (- 1/2 (/ k 2)))

simplify4.2s

Counts

1160 → 1160

Iterations

Iter	Nodes
done	5000
1	3813
0	1480

prune6.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes81.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	15

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.8s	21069×	body	80	nan
2.4s	11971×	body	80	valid
1.0ms	2×	body	160	nan