Details

sample292.0ms

Algorithm

intervals

Results

130.0ms	98×	body	1280	valid
58.0ms	84×	body	640	valid
41.0ms	263×	body	80	valid
23.0ms	42×	body	320	valid
8.0ms	23×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
7	2000
6	1004
5	361
4	183
3	80
2	41
1	23
0	14

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (exp l))
0.0b	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
6.8b	(- (* J (exp l)) (/ J (exp l)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r*` `add-cube-cbrt`
6×	`associate-l` `add-exp-log`
5×	`add-log-exp`
3×	`sub-neg` `insert-posit16`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 59

Calls

3 calls:

9.0ms	(* J (exp l))
63.0ms	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
18.0ms	(- (* J (exp l)) (/ J (exp l)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* J (exp l))
116.0ms	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
72.0ms	(- (* J (exp l)) (/ J (exp l)))

simplify1.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	2000
3	2000
2	795
1	266
0	109

prune396.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
0.0b	(* 2 (* J l))
0.1b	(* (cos (/ K 2)) (* 2 (* J l)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`insert-posit16`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

3 → 53

Calls

3 calls:

9.0ms	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
21.0ms	(* 2 (* J l))
73.0ms	(* (cos (/ K 2)) (* 2 (* J l)))

series233.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
23.0ms	(* 2 (* J l))
70.0ms	(* (cos (/ K 2)) (* 2 (* J l)))

simplify1.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	2004
3	2004
2	790
1	230
0	91

prune324.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

13.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
147.0ms	(cbrt (cos (/ K 2)))
152.0ms	(cbrt (cos (/ K 2)))
119.0ms	(cbrt (cos (/ K 2)))

simplify1.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	2000
4	2000
3	795
2	342
1	154
0	71

prune589.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3) (* (cbrt (cos (/ K 2))) (* 2 (* J l))))
0.1b	(pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3)
0.2b	(* (cos (/ K 2)) (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
46×	`prod-exp`
24×	`add-cbrt-cube`
21×	`cbrt-unprod`
19×	`pow1`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow-exp`
8×	`associate-l`
6×	`pow-pow`
5×	`pow-to-exp` `unpow1/3`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `swap-sqr`
2×	`pow2` `unpow-prod-down` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-pow`
1×	`sqr-cos` `pow1/3` `cos-mult` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

110.0ms	(* (pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3) (* (cbrt (cos (/ K 2))) (* 2 (* J l))))
6.0ms	(pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3)
8.0ms	(* (cos (/ K 2)) (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3) (* (cbrt (cos (/ K 2))) (* 2 (* J l))))
219.0ms	(pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3)
20.0ms	(* (cos (/ K 2)) (cos (/ K 2)))
150.0ms	(cbrt (cos (/ K 2)))

simplify1.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	2014
3	2014
2	1853
1	482
0	175

prune721.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes564.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample10.5s

Algorithm

intervals

Results

4.2s	2704×	body	1280	valid
2.2s	2486×	body	640	valid
2.2s	8518×	body	80	valid
864.0ms	1380×	body	320	valid
328.0ms	794×	body	160	valid