Details

sample161.0ms

Algorithm

intervals

Results

67.0ms	665×	body	80	nan
46.0ms	398×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	2792
5	816
4	285
3	114
2	58
1	29
0	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

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:

23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
43.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
28.0ms	(* (* 2.0 PI) n)
10.0ms	(/ 1.0 (sqrt k))

series768.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
476.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
45.0ms	(* (* 2.0 PI) n)
70.0ms	(/ 1.0 (sqrt k))

simplify3.4s

Counts

169 → 169

Iterations

Iter	Nodes
done	5002
2	3424
1	1003
0	361

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 3 expressions with local error:

0.1b	(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)

rewrite64.0ms

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×	`associate-/r*` `div-exp` `pow-prod-down` `pow-exp` `sqrt-prod`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `cbrt-undiv` `div-sub` `div-inv` `pow-sub`
1×	`clear-num` `unpow-prod-down` `frac-2neg` `associate-l` `associate-r/` `-commutative` `associate-/l*` `sqr-pow` `associate-/l/`

Counts

3 → 92

Calls

3 calls:

25.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
17.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
19.0ms	(* (* 2.0 PI) n)

series631.0ms

Counts

3 → 9

Calls

3 calls:

201.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
382.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
48.0ms	(* (* 2.0 PI) n)

simplify3.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2480
1	761
0	268

prune715.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

70×	`sqrt-prod`
42×	`add-sqr-sqrt`
35×	`add-exp-log`
34×	`times-frac`
29×	`pow1`
26×	`*-un-lft-identity` `add-cube-cbrt`
21×	`add-cbrt-cube`
19×	`associate-r`
17×	`swap-sqr`
15×	`associate-l` `prod-exp`
9×	`pow-prod-down`
8×	`sqrt-pow1` `pow1/2` `cbrt-unprod`
6×	`associate-/r*` `div-exp`
5×	`pow-prod-up` `div-inv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-exp` `pow-sqr` `*-commutative`
2×	`cbrt-undiv` `associate-*r/`
1×	`pow2` `frac-times` `pow-to-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-sub` `associate-l/` `associate-/l` `pow-sub` `associate-/l/`

Counts

4 → 151

Calls

4 calls:

17.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
42.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
20.0ms	(* (* 2.0 PI) n)
14.0ms	(* (* 2.0 PI) n)

series991.0ms

Counts

4 → 12

Calls

4 calls:

390.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
490.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
47.0ms	(* (* 2.0 PI) n)
63.0ms	(* (* 2.0 PI) n)

simplify3.8s

Counts

163 → 163

Iterations

Iter	Nodes
done	5004
2	3199
1	941
0	346

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
0.5b	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

200×	`sqrt-prod`
159×	`add-sqr-sqrt`
136×	`times-frac`
95×	`*-un-lft-identity` `add-cube-cbrt`
33×	`swap-sqr`
28×	`associate-r`
26×	`associate-l`
24×	`pow1`
16×	`unswap-sqr`
15×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-prod-down` `div-inv` `associate-/l*`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `*-commutative`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/`

Counts

4 → 231

Calls

4 calls:

26.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt k))
5.0ms	(/ 1.0 (sqrt k))
63.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* 2.0 PI) n)
56.0ms	(/ 1.0 (sqrt k))
61.0ms	(/ 1.0 (sqrt k))
134.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))

simplify3.1s

Counts

243 → 243

Iterations

Iter	Nodes
done	5000
3	4705
2	1518
1	595
0	291

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes271.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.0s	20549×	body	80	nan
2.0s	11990×	body	80	valid
0.0ms	2×	body	160	nan