Details

sample262.0ms

Algorithm

intervals

Results

110.0ms	103×	body	1280	valid
54.0ms	99×	body	640	valid
32.0ms	274×	body	80	valid
14.0ms	38×	body	320	valid
6.0ms	25×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
6	2572
5	534
4	198
3	82
2	41
1	23
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (exp l) J)
0.0b	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2.0)))
5.9b	(- (* (exp l) J) (/ J (exp l)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

9.0ms	(* (exp l) J)
81.0ms	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2.0)))
13.0ms	(- (* (exp l) J) (/ J (exp l)))

series307.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (exp l) J)
141.0ms	(* (- (* (exp l) J) (/ J (exp l))) (cos (/ K 2.0)))
119.0ms	(- (* (exp l) J) (/ J (exp l)))

simplify1.4s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
2	1003
1	244
0	104

prune384.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ U (* (* 2 (* J l)) (cos (/ K 2.0))))
0.0b	(* 2 (* J l))
0.2b	(* (* 2 (* J l)) (cos (/ K 2.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

6.0ms	(+ U (* (* 2 (* J l)) (cos (/ K 2.0))))
12.0ms	(* 2 (* J l))
39.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

156.0ms	(+ U (* (* 2 (* J l)) (cos (/ K 2.0))))
30.0ms	(* 2 (* J l))
70.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

simplify1.3s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
2	1153
1	246
0	91

prune389.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

rewrite26.0ms

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` `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 → 73

Calls

4 calls:

18.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

461.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
260.0ms	(cbrt (cos (/ K 2.0)))
206.0ms	(cbrt (cos (/ K 2.0)))
254.0ms	(cbrt (cos (/ K 2.0)))

simplify4.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	3811
2	607
1	155
0	70

prune630.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2 (* J l)) (pow (* (cos (/ K 2.0)) (cos (/ K 2.0))) 1/3))
0.2b	(* (* (* 2 (* J l)) (pow (* (cos (/ K 2.0)) (cos (/ K 2.0))) 1/3)) (cbrt (cos (/ K 2.0))))
0.3b	(* (cos (/ K 2.0)) (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log`
68×	`prod-exp`
37×	`add-cbrt-cube`
32×	`cbrt-unprod`
14×	`add-sqr-sqrt` `associate-r`
13×	`pow1`
12×	`*-un-lft-identity` `pow-exp` `add-cube-cbrt`
6×	`cbrt-prod` `pow-to-exp` `unpow1/3`
5×	`associate-l`
4×	`add-log-exp`
3×	`swap-sqr` `*-commutative`
2×	`pow-prod-down`
1×	`pow2` `sqr-cos` `unpow-prod-down` `pow-plus` `pow1/3` `pow-sqr` `cos-mult` `pow-prod-up` `unswap-sqr` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

72.0ms	(* (* 2 (* J l)) (pow (* (cos (/ K 2.0)) (cos (/ K 2.0))) 1/3))
169.0ms	(* (* (* 2 (* J l)) (pow (* (cos (/ K 2.0)) (cos (/ K 2.0))) 1/3)) (cbrt (cos (/ K 2.0))))
9.0ms	(* (cos (/ K 2.0)) (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

636.0ms	(* (* 2 (* J l)) (pow (* (cos (/ K 2.0)) (cos (/ K 2.0))) 1/3))
85.0ms	(* (* (* 2 (* J l)) (pow (* (cos (/ K 2.0)) (cos (/ K 2.0))) 1/3)) (cbrt (cos (/ K 2.0))))
49.0ms	(* (cos (/ K 2.0)) (cos (/ K 2.0)))
234.0ms	(cbrt (cos (/ K 2.0)))

simplify2.7s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	3175
1	503
0	173

prune626.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes624.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	12

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.7s	2716×	body	1280	valid
1.6s	2651×	body	640	valid
1.4s	8432×	body	80	valid
873.0ms	1425×	body	320	valid
208.0ms	711×	body	160	valid