Details

sample888.0ms

Algorithm

intervals

Results

236.0ms	67×	body	2560	valid
219.0ms	138×	body	1280	valid
206.0ms	26×	body	5120	valid
123.0ms	85×	body	640	valid
28.0ms	34×	body	320	valid
17.0ms	69×	body	80	valid
5.0ms	10×	body	160	valid

simplify6.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5174
4	3622
3	689
2	142
1	44
0	19

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize119.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (pow t 3.0))
0.4b	(* (pow (/ k t) 2.0) (tan k))
19.1b	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
33.2b	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

410×	`add-exp-log`
181×	`div-exp`
173×	`prod-exp`
144×	`times-frac`
89×	`add-cbrt-cube`
80×	`add-sqr-sqrt`
72×	`*-un-lft-identity` `add-cube-cbrt`
55×	`pow-exp`
54×	`unpow-prod-down`
47×	`associate-l`
38×	`pow-to-exp`
34×	`cbrt-unprod`
30×	`cbrt-undiv`
28×	`associate-/l*`
15×	`sqr-pow`
9×	`pow1`
8×	`associate-/r*`
7×	`div-inv`
4×	`associate-r` `associate-*r/` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-*l/` `tan-quot`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-/l/`

Counts

4 → 296

Calls

4 calls:

10.0ms	(/ 2.0 (pow t 3.0))
43.0ms	(* (pow (/ k t) 2.0) (tan k))
187.0ms	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
81.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

series4.5s

Counts

4 → 12

Calls

4 calls:

822.0ms	(/ 2.0 (pow t 3.0))
635.0ms	(* (pow (/ k t) 2.0) (tan k))
2.0s	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
993.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

simplify7.8s

Counts

308 → 308

Iterations

Iter	Nodes
done	5003
2	4993
1	1267
0	437

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.6b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.1b	(* (pow k 2.0) (pow t 1.0))
16.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

1298×	`add-exp-log`
790×	`prod-exp`
466×	`div-exp`
367×	`pow-exp`
157×	`pow-to-exp`
80×	`rec-exp` `1-exp`
62×	`add-cbrt-cube`
27×	`add-sqr-sqrt`
23×	`cbrt-unprod`
20×	`cbrt-undiv`
19×	`unpow-prod-down`
18×	`associate-l`
15×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac` `unswap-sqr` `sqr-pow`
8×	`associate-r`
6×	`associate-/l*`
5×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r/` `div-inv`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-r/` `-commutative`
1×	`frac-times` `pow-flip` `inv-pow`

Counts

4 → 385

Calls

4 calls:

31.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
31.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
26.0ms	(* (pow k 2.0) (pow t 1.0))
318.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

series4.6s

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
1.3s	(/ 1 (* (pow k 2.0) (pow t 1.0)))
1.3s	(* (pow k 2.0) (pow t 1.0))
1.8s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

simplify9.0s

Counts

397 → 397

Iterations

Iter	Nodes
done	5031
2	3347
1	1112
0	448

prune2.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.0b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.3b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.6b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.7b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

rewrite910.0ms

Algorithm

rewrite-expression-head

Rules

4232×	`add-exp-log`
3008×	`prod-exp`
1373×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
76×	`add-cbrt-cube`
51×	`add-sqr-sqrt`
49×	`times-frac`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`cbrt-unprod`
25×	`cbrt-undiv`
24×	`associate-l`
14×	`associate-r`
13×	`swap-sqr`
12×	`pow1`
7×	`unpow-prod-down` `div-inv`
6×	`associate-/l*`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-r/` `associate-/r/`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `-commutative`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `pow-flip` `inv-pow` `sqr-pow`

Counts

4 → 916

Calls

4 calls:

39.0ms	(* (/ (sin k) l) (/ (sin k) l))
51.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
96.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
395.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

series3.6s

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (/ (sin k) l) (/ (sin k) l))
244.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
1.4s	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.8s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

simplify9.7s

Counts

928 → 928

Iterations

Iter	Nodes
done	5001
1	1747
0	653

prune2.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.3b

localize144.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.3b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
5.2b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) 2.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))))
10.2b	(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) 2.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

17407×	`add-exp-log`
9462×	`prod-exp`
8965×	`div-exp`
6565×	`pow-exp`
2380×	`pow-to-exp`
1317×	`rec-exp` `1-exp`
160×	`add-cbrt-cube`
73×	`cbrt-unprod`
67×	`times-frac`
63×	`add-sqr-sqrt`
51×	`*-un-lft-identity` `add-cube-cbrt`
49×	`cbrt-undiv`
43×	`associate-l`
34×	`unpow-prod-down`
24×	`associate-r`
13×	`pow1` `swap-sqr`
7×	`div-inv`
6×	`associate-*r/` `associate-/r/`
4×	`insert-posit16` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`frac-times` `associate-l/` `-commutative` `associate-/l*`
2×	`pow-prod-down`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 2850

Calls

4 calls:

51.0ms	(* (/ (sin k) l) (/ (sin k) l))
27.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
1.4s	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) 2.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))))
512.0ms	(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) 2.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))))

series4.0s

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (sin k) l) (/ (sin k) l))
272.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
1.9s	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) 2.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))))
1.7s	(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) 2.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))))

simplify19.7s

Counts

2862 → 2862

Iterations

Iter	Nodes
done	5355
1	3591
0	1354

prune3.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.2b

regimes2.0s

Accuracy

0% (2.4b remaining)

Error of 8.3b against oracle of 5.8b and baseline of 8.3b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample32.3s

Algorithm

intervals

Results

10.4s	4083×	body	1280	valid
8.1s	2252×	body	2560	valid
7.6s	992×	body	5120	valid
3.4s	2539×	body	640	valid
933.0ms	993×	body	320	valid
759.0ms	1986×	body	80	valid
316.0ms	430×	body	160	valid