Details

sample1.1s

Algorithm

intervals

Results

358.0ms	137×	body	1280	valid
274.0ms	67×	body	2560	valid
149.0ms	18×	body	5120	valid
147.0ms	98×	body	640	valid
58.0ms	66×	body	80	valid
40.0ms	10×	body	160	valid
29.0ms	26×	body	320	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2 (* (* (/ t l) (/ t l)) t))
2.1b	(* (* (/ t l) (/ t l)) t)
2.1b	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
26.2b	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

rewrite200.0ms

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:

25.0ms	(/ 2 (* (* (/ t l) (/ t l)) t))
51.0ms	(* (* (/ t l) (/ t l)) t)
41.0ms	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
68.0ms	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

series692.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 2 (* (* (/ t l) (/ t l)) t))
56.0ms	(* (* (/ t l) (/ t l)) t)
251.0ms	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
325.0ms	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

simplify1.1s

Counts

332 → 332

Iterations

Iter	Nodes
done	2002
2	2002
1	1294
0	452

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.4b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k))
6.7b	(* (/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ (sqrt 2) t) (tan k)) (/ k t)))
13.1b	(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))
14.8b	(/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

10272×	`times-frac`
4459×	`add-sqr-sqrt`
3937×	`*-un-lft-identity` `add-cube-cbrt`
1020×	`sqrt-prod`
971×	`add-cbrt-cube` `add-exp-log`
928×	`associate-r`
663×	`cbrt-undiv` `div-exp`
564×	`associate-l`
455×	`div-inv`
286×	`associate-/r/`
173×	`prod-exp` `cbrt-unprod`
127×	`associate-/l*`
86×	`frac-times` `associate-l/` `associate-r/`
81×	`unswap-sqr`
29×	`associate-/r*`
27×	`tan-quot`
6×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 3563

Calls

4 calls:

19.0ms	(/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k))
814.0ms	(* (/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ (sqrt 2) t) (tan k)) (/ k t)))
28.0ms	(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))
42.0ms	(/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t))

series1.3s

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k))
625.0ms	(* (/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ (sqrt 2) t) (tan k)) (/ k t)))
224.0ms	(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))
264.0ms	(/ (/ (/ (sqrt 2) (* (/ t l) (/ t l))) (sin k)) (/ k t))

simplify4.8s

Counts

3575 → 3575

Iterations

Iter	Nodes
done	4315
0	4315

prune31.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.8b

localize60.0ms

Local error

Found 4 expressions with local error:

2.5b	(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
4.6b	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
11.8b	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))
13.1b	(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

48508×	`times-frac`
19366×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10908×	`sqrt-prod`
5124×	`cbrt-prod`
1787×	`div-inv`
1055×	`associate-/l*`
135×	`add-exp-log`
106×	`associate-/r/`
94×	`div-exp`
89×	`add-cbrt-cube`
70×	`cbrt-undiv`
30×	`associate-/r*`
14×	`tan-quot`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

4 → 12188

Calls

4 calls:

31.0ms	(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
38.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
49.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))
18.0ms	(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))

series1.0s

Counts

4 → 12

Calls

4 calls:

271.0ms	(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
308.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
195.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))
240.0ms	(/ (/ (/ (sqrt 2) t) (tan k)) (/ k t))

simplify18.7s

Counts

12200 → 12200

Iterations

Iter	Nodes
done	13640
0	13640

prune2.0m

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 4.9b

localize90.0ms

Local error

Found 4 expressions with local error:

2.5b	(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
4.6b	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
5.5b	(/ (/ (/ (sqrt (cbrt 2)) (cbrt t)) (tan k)) (/ k (cbrt t)))
11.8b	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

60163×	`times-frac`
24244×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13014×	`sqrt-prod`
9849×	`cbrt-prod`
1931×	`div-inv`
1163×	`associate-/l*`
135×	`add-exp-log`
115×	`associate-/r/`
94×	`div-exp`
84×	`add-cbrt-cube`
70×	`cbrt-undiv`
39×	`associate-/r*`
23×	`tan-quot`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

4 → 15320

Calls

4 calls:

24.0ms	(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
28.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
36.0ms	(/ (/ (/ (sqrt (cbrt 2)) (cbrt t)) (tan k)) (/ k (cbrt t)))
38.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))

series743.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k))))
238.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (* (cbrt (sin k)) (cbrt (sin k)))) k)
173.0ms	(/ (/ (/ (sqrt (cbrt 2)) (cbrt t)) (tan k)) (/ k (cbrt t)))
160.0ms	(/ (/ (/ (sqrt (sqrt 2)) (/ t l)) (cbrt (sin k))) (/ 1 t))

simplify20.2s

Counts

15332 → 15332

Iterations

Iter	Nodes
done	17097
0	17097

prune2.4m

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.8b

regimes641.0ms

Accuracy

0% (3.1b remaining)

Error of 7.8b against oracle of 4.7b and baseline of 7.8b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	52
1	52
0	46

end0.0ms

sample25.6s

Algorithm

intervals

Results

8.1s	4090×	body	1280	valid
7.0s	2193×	body	2560	valid
4.8s	920×	body	5120	valid
3.7s	2589×	body	640	valid
902.0ms	1023×	body	320	valid
535.0ms	1990×	body	80	valid
210.0ms	387×	body	160	valid