Details

sample207.0ms

Algorithm

intervals

Results

99.0ms	705×	body	80	nan
49.0ms	375×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1545	16
done	5000	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)

rewrite172.0ms

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×	`div-exp` `pow-prod-down` `associate-/r*` `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` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 149

Calls

4 calls:

37.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
84.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
10.0ms	(/ 1.0 (sqrt k))
30.0ms	(* (* 2.0 PI) n)

series879.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
527.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
62.0ms	(/ 1.0 (sqrt k))
60.0ms	(* (* 2.0 PI) n)

simplify3.3s

Counts

161 → 161

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	361	2800
1	1008	2643
2	4879	2473
done	5001	2473

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.3b	(* (* 2.0 PI) n)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
19×	`pow-unpow`
17×	`add-cube-cbrt`
14×	`pow1` `prod-exp`
13×	`add-cbrt-cube`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `sqrt-prod`
4×	`cbrt-unprod`
3×	`pow-pow` `associate-r` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`unpow-prod-down` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

3 → 86

Calls

3 calls:

43.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
49.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
35.0ms	(* (* 2.0 PI) n)

series784.0ms

Counts

3 → 9

Calls

3 calls:

234.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
488.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
62.0ms	(* (* 2.0 PI) n)

simplify2.4s

Counts

95 → 95

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	264	1828
1	748	1703
2	3500	1535
done	5001	1531

prune628.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k))
0.2b	(pow (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
0.3b	(* n PI)
1.7b	(pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`add-exp-log`
41×	`*-un-lft-identity`
36×	`pow-unpow`
33×	`times-frac`
26×	`sqrt-prod`
25×	`add-cube-cbrt`
19×	`pow-exp`
17×	`prod-exp`
12×	`pow1` `difference-of-squares`
11×	`add-cbrt-cube`
8×	`unpow-prod-down` `div-exp`
6×	`associate-/r*` `distribute-lft-out--`
5×	`pow-to-exp`
4×	`pow-pow` `pow-prod-down` `add-log-exp`
3×	`associate-r` `associate-l` `sqr-pow`
2×	`cbrt-undiv` `unpow-prod-up` `div-sub` `cbrt-unprod` `div-inv` `distribute-lft-out` `pow-sub`
1×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

52.0ms	(/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k))
33.0ms	(pow (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
12.0ms	(* n PI)
48.0ms	(pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k)))

series6.0s

Counts

4 → 12

Calls

4 calls:

4.1s	(/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k))
1.3s	(pow (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
34.0ms	(* n PI)
474.0ms	(pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k)))

simplify1.7s

Counts

139 → 139

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	735	10001
1	2262	9339
done	5000	8603

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.2b	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
143×	`add-sqr-sqrt` `*-un-lft-identity`
137×	`add-cube-cbrt`
78×	`sqrt-prod`
46×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `sqr-pow`
19×	`pow-unpow`
16×	`div-exp` `add-cbrt-cube`
15×	`pow1`
12×	`prod-exp`
9×	`pow-exp` `associate-/l*`
7×	`div-inv`
6×	`div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`associate-l` `*-commutative`

Counts

4 → 274

Calls

4 calls:

39.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
38.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
23.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
43.0ms	(* (* 2.0 PI) n)

series1.7s

Counts

4 → 12

Calls

4 calls:

615.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
258.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
768.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
60.0ms	(* (* 2.0 PI) n)

simplify1.5s

Counts

286 → 286

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	602	8036
1	1714	7688
done	5000	7412

prune2.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes486.0ms

Accuracy

0% (0.9b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 1.0b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	24
1	20	24
done	20	24

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.6s	20541×	body	80	nan
2.6s	11881×	body	80	valid
0.0ms	1×	body	160	nan