Details

sample213.0ms

Algorithm

intervals

Results

57.0ms	291×	body	80	valid
56.0ms	79×	body	1280	valid
39.0ms	84×	body	640	valid
16.0ms	49×	body	320	valid
5.0ms	24×	body	160	valid

simplify20.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	15
1	23	15
2	41	15
3	81	15
4	168	15
5	230	15
6	285	15
7	395	15
8	483	15
9	800	15
10	1301	15
11	1948	15
12	2455	15
13	2758	15
14	2840	15
done	2840	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.0b	(- (exp l) (exp (- l)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

74.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
23.0ms	(- (exp l) (exp (- l)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
61.0ms	(- (exp l) (exp (- l)))

simplify2.8s

Counts

40 → 40

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	96	588
1	221	571
2	701	473
3	2985	471
done	5002	471

prune192.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 76

Calls

3 calls:

25.0ms	(* 1/60 (pow l 5))
20.0ms	(* 1/3 (pow l 3))
140.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series450.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(* 1/60 (pow l 5))
70.0ms	(* 1/3 (pow l 3))
282.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify979.0ms

Counts

85 → 85

Iterations

Useful iterations: done (975.0ms)

Iter	Nodes	Cost
0	159	1153
1	405	1072
2	1565	922
done	5002	921

prune382.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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

rewrite228.0ms

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:

22.0ms	(* 1/60 (pow l 5))
105.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
14.0ms	(* 1/3 (pow l 3))
81.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* 1/60 (pow l 5))
213.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
56.0ms	(* 1/3 (pow l 3))
116.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	181	1751
1	446	1663
2	1561	1433
done	5000	1406

prune626.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

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)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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:

25.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

421.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
209.0ms	(cbrt (cos (/ K 2.0)))
210.0ms	(cbrt (cos (/ K 2.0)))
214.0ms	(cbrt (cos (/ K 2.0)))

simplify2.0s

Counts

85 → 85

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	70	982
1	132	897
2	295	825
3	651	742
4	1599	735
done	5001	695

prune610.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes476.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.4s	2697×	body	1280	valid
2.1s	8369×	body	80	valid
1.9s	2569×	body	640	valid
747.0ms	1382×	body	320	valid
161.0ms	756×	body	160	valid