Details

sample104.0ms

Algorithm

intervals

Results

35.0ms	84×	body	1280	valid
21.0ms	84×	body	640	valid
17.0ms	249×	body	80	valid
7.0ms	40×	body	320	valid
3.0ms	26×	body	160	valid

simplify12.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	15
1	23	15
2	41	15
3	72	15
4	121	15
5	184	15
6	260	15
7	367	15
8	500	15
9	916	15
10	2263	15
11	2919	15
12	3279	15
13	4205	15
14	4488	15
done	4488	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.7b	(- (exp l) (exp (- l)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `flip3--` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

21.0ms	(* J (- (exp l) (exp (- l))))
26.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
9.0ms	(- (exp l) (exp (- l)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* J (- (exp l) (exp (- l))))
93.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
40.0ms	(- (exp l) (exp (- l)))

simplify1.8s

Counts

69 → 69

Iterations

Useful iterations: 3 (593.0ms)

Iter	Nodes	Cost
0	114	899
1	266	874
2	765	738
3	2728	735
done	5000	735

prune213.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
0.0b	(* 1/60 (pow l 5))
0.1b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `prod-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `cube-mult` `unpow3` `sum-log`

Counts

4 → 87

Calls

4 calls:

37.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
5.0ms	(* 1/60 (pow l 5))
41.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
7.0ms	(* 1/3 (pow l 3))

series600.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
55.0ms	(* 1/60 (pow l 5))
160.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
40.0ms	(* 1/3 (pow l 3))

simplify725.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (205.0ms)

Iter	Nodes	Cost
0	180	1661
1	474	1533
2	1613	1379
done	5001	1379

prune349.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/60 (pow l 5))
0.1b	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
0.1b	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
11×	`pow1`
10×	`prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `pow-prod-down` `associate-l/` `-commutative` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 96

Calls

4 calls:

5.0ms	(* 1/60 (pow l 5))
30.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
33.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
11.0ms	(* 1/3 (pow l 3))

series345.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 1/60 (pow l 5))
166.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
90.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
40.0ms	(* 1/3 (pow l 3))

simplify733.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (186.0ms)

Iter	Nodes	Cost
0	181	1751
1	454	1661
2	1513	1431
done	5001	1431

prune389.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))) (cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
0.6b	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
0.6b	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
0.6b	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`associate-*r/` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

15.0ms	(* (cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))) (cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
10.0ms	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
9.0ms	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
10.0ms	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))

series858.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(* (cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))) (cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
205.0ms	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
204.0ms	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
207.0ms	(cbrt (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))

simplify597.0ms

Counts

84 → 84

Iterations

Useful iterations: done (593.0ms)

Iter	Nodes	Cost
0	160	3708
1	376	3403
2	1182	3043
done	5000	2784

prune459.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes407.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	24
1	30	24
done	30	24

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2677×	body	1280	valid
695.0ms	2657×	body	640	valid
459.0ms	8332×	body	80	valid
240.0ms	1397×	body	320	valid
96.0ms	816×	body	160	valid