Details

sample1.3s

Algorithm

intervals

Results

525.0ms	36×	body	5120	valid
324.0ms	131×	body	1280	valid
221.0ms	65×	body	2560	valid
107.0ms	82×	body	640	valid
36.0ms	36×	body	320	valid
16.0ms	57×	body	80	valid
16.0ms	23×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
4	2005
3	1013
2	173
1	51
0	19

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2 (* (* (/ t l) (/ t l)) t))
1.5b	(* (* (/ t l) (/ t l)) t)
3.2b	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
31.3b	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

685×	`add-cbrt-cube` `add-exp-log`
353×	`cbrt-undiv` `div-exp`
228×	`prod-exp` `cbrt-unprod`
60×	`times-frac`
28×	`associate-/l*`
25×	`associate-*l/`
21×	`associate-/r/`
18×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-*r/`
9×	`pow1` `div-inv`
7×	`frac-times`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `associate-/r` `frac-2neg` `associate-r*` `pow-prod-down` `tan-quot`
2×	`associate-/l/`
1×	`associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 320

Calls

4 calls:

28.0ms	(/ 2 (* (* (/ t l) (/ t l)) t))
30.0ms	(* (* (/ t l) (/ t l)) t)
44.0ms	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
65.0ms	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 2 (* (* (/ t l) (/ t l)) t))
40.0ms	(* (* (/ t l) (/ t l)) t)
246.0ms	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
334.0ms	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

simplify1.0s

Counts

332 → 332

Iterations

Iter	Nodes
done	2002
2	2002
1	1294
0	452

prune993.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sin k) (sin k))
3.7b	(* (/ (* l l) (* t (* k k))) (/ (cos k) (* (sin k) (sin k))))
7.7b	(* t (* k k))
15.5b	(/ (* l l) (* t (* k k)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

140×	`add-cbrt-cube` `add-exp-log`
68×	`prod-exp` `cbrt-unprod`
38×	`cbrt-undiv` `div-exp`
19×	`add-sqr-sqrt`
18×	`pow1`
12×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
11×	`associate-l`
6×	`times-frac`
5×	`pow-prod-down`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`swap-sqr` `*-commutative` `div-inv`
2×	`sin-mult`
1×	`pow2` `frac-times` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up` `sqr-sin` `associate-/l`

Counts

4 → 144

Calls

4 calls:

14.0ms	(* (sin k) (sin k))
92.0ms	(* (/ (* l l) (* t (* k k))) (/ (cos k) (* (sin k) (sin k))))
18.0ms	(* t (* k k))
28.0ms	(/ (* l l) (* t (* k k)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sin k) (sin k))
220.0ms	(* (/ (* l l) (* t (* k k))) (/ (cos k) (* (sin k) (sin k))))
38.0ms	(* t (* k k))
49.0ms	(/ (* l l) (* t (* k k)))

simplify891.0ms

Counts

156 → 156

Iterations

Iter	Nodes
done	2003
2	2003
1	688
0	226

prune687.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sin k) (sin k))
3.7b	(* (* (/ l t) (/ l (* k k))) (/ (cos k) (* (sin k) (sin k))))
7.2b	(/ l (* k k))
9.3b	(* (/ l t) (/ l (* k k)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

140×	`add-cbrt-cube` `add-exp-log`
62×	`prod-exp` `cbrt-unprod`
44×	`cbrt-undiv` `div-exp`
33×	`add-sqr-sqrt`
22×	`times-frac`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1` `associate-r`
17×	`associate-l`
6×	`frac-times` `associate-*l/`
5×	`pow-prod-down` `unswap-sqr`
4×	`associate-*r/` `insert-posit16` `div-inv` `add-log-exp`
3×	`swap-sqr` `-commutative` `associate-/l`
2×	`sin-mult`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `associate-/r/` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 168

Calls

4 calls:

15.0ms	(* (sin k) (sin k))
81.0ms	(* (* (/ l t) (/ l (* k k))) (/ (cos k) (* (sin k) (sin k))))
7.0ms	(/ l (* k k))
27.0ms	(* (/ l t) (/ l (* k k)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sin k) (sin k))
213.0ms	(* (* (/ l t) (/ l (* k k))) (/ (cos k) (* (sin k) (sin k))))
31.0ms	(/ l (* k k))
50.0ms	(* (/ l t) (/ l (* k k)))

simplify885.0ms

Counts

180 → 180

Iterations

Iter	Nodes
done	2005
2	2005
1	823
0	266

prune960.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 2.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos k) (* (sin k) (sin k)))
0.4b	(* (sin k) (sin k))
3.7b	(* (* (/ (/ l t) k) (/ l k)) (/ (cos k) (* (sin k) (sin k))))
5.8b	(/ (/ l t) k)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-cbrt-cube` `add-exp-log`
81×	`times-frac`
56×	`add-sqr-sqrt`
54×	`*-un-lft-identity` `add-cube-cbrt`
48×	`prod-exp` `cbrt-unprod`
46×	`cbrt-undiv` `div-exp`
16×	`pow1` `associate-/l*`
11×	`associate-r`
7×	`div-inv`
5×	`frac-times` `associate-*l/`
4×	`associate-/r` `associate-l*` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `associate-*r/` `sin-mult`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up` `sqr-sin` `unswap-sqr` `associate-/l/`

Counts

4 → 191

Calls

4 calls:

14.0ms	(/ (cos k) (* (sin k) (sin k)))
12.0ms	(* (sin k) (sin k))
70.0ms	(* (* (/ (/ l t) k) (/ l k)) (/ (cos k) (* (sin k) (sin k))))
13.0ms	(/ (/ l t) k)

series396.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (cos k) (* (sin k) (sin k)))
29.0ms	(* (sin k) (sin k))
279.0ms	(* (* (/ (/ l t) k) (/ l k)) (/ (cos k) (* (sin k) (sin k))))
36.0ms	(/ (/ l t) k)

simplify1.1s

Counts

203 → 203

Iterations

Iter	Nodes
done	2005
2	2005
1	954
0	347

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.7b

regimes453.0ms

Accuracy

8.8% (4.7b remaining)

Error of 5.5b against oracle of 0.9b and baseline of 6.0b

bsearch745.0ms

Steps

Iters	Range		Point
8	3.242417738198925e+154	1.3808723455818043e+157	1.602726285194281e+155

simplify7.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample39.3s

Algorithm

intervals

Results

11.7s	4042×	body	1280	valid
10.5s	2197×	body	2560	valid
8.1s	909×	body	5120	valid
6.0s	2514×	body	640	valid
1.3s	972×	body	320	valid
833.0ms	2000×	body	80	valid
358.0ms	457×	body	160	valid