Details

sample212.0ms

Algorithm

intervals

Results

96.0ms	73×	body	1280	valid
36.0ms	82×	body	640	valid
28.0ms	296×	body	80	valid
13.0ms	43×	body	320	valid
6.0ms	25×	body	160	valid

simplify20.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize28.0ms

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)))
6.6b	(- (exp l) (exp (- l)))

rewrite194.0ms

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:

83.0ms	(* J (- (exp l) (exp (- l))))
85.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
23.0ms	(- (exp l) (exp (- l)))

series296.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(* J (- (exp l) (exp (- l))))
143.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
58.0ms	(- (exp l) (exp (- l)))

simplify2.5s

Counts

69 → 69

Iterations

Useful iterations: 3 (954.0ms)

Iter	Nodes	Cost
0	114	899
1	259	874
2	755	738
3	2987	735
done	5000	735

prune280.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
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)))

rewrite222.0ms

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` `add-log-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `sum-log` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `cube-mult` `associate-+r+` `unpow3`

Counts

4 → 89

Calls

4 calls:

26.0ms	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
14.0ms	(* 1/60 (pow l 5))
14.0ms	(* 1/3 (pow l 3))
161.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
67.0ms	(* 1/60 (pow l 5))
52.0ms	(* 1/3 (pow l 3))
245.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	173	1516
1	443	1410
2	1707	1230
done	5000	1229

prune605.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize35.0ms

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))

rewrite716.0ms

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:

13.0ms	(* 1/60 (pow l 5))
570.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
112.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
18.0ms	(* 1/3 (pow l 3))

series512.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* 1/60 (pow l 5))
243.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
145.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
54.0ms	(* 1/3 (pow l 3))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	181	1751
1	447	1661
2	1551	1433
done	5000	1406

prune639.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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)))

rewrite19.0ms

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:

13.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

417.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
215.0ms	(cbrt (cos (/ K 2.0)))
221.0ms	(cbrt (cos (/ K 2.0)))
205.0ms	(cbrt (cos (/ K 2.0)))

simplify1.9s

Counts

85 → 85

Iterations

Useful iterations: done (1.9s)

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

prune681.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes479.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.1s	2659×	body	1280	valid
1.7s	8459×	body	80	valid
1.7s	2604×	body	640	valid
1.3s	1437×	body	320	valid
168.0ms	708×	body	160	valid