Details

sample199.0ms

Algorithm

intervals

Results

68.0ms	87×	body	1280	valid
42.0ms	81×	body	640	valid
26.0ms	256×	body	80	valid
18.0ms	49×	body	320	valid
3.0ms	17×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	15
1	23	15
2	41	15
3	82	15
4	198	15
5	534	15
6	2572	15
done	5002	15

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize42.0ms

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)))
6.3b	(- (exp l) (exp (- l)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `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:

59.0ms	(* J (- (exp l) (exp (- l))))
92.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
21.0ms	(- (exp l) (exp (- l)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* J (- (exp l) (exp (- l))))
177.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
74.0ms	(- (exp l) (exp (- l)))

simplify837.0ms

Counts

69 → 69

Iterations

Useful iterations: done (834.0ms)

Iter	Nodes	Cost
0	113	899
1	287	874
2	1402	750
done	5002	738

prune622.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

58.0ms	(* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))
10.0ms	(* 1/60 (pow l 5))
141.0ms	(* (* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))
23.0ms	(* 1/3 (pow l 3))

series624.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))))
98.0ms	(* 1/60 (pow l 5))
287.0ms	(* (* J (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))) (cos (/ K 2.0)))
42.0ms	(* 1/3 (pow l 3))

simplify1.3s

Counts

110 → 110

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	183	1706
1	520	1626
2	2489	1410
done	5000	1401

prune727.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
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-+` `pow-exp` `associate-*r/` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 96

Calls

4 calls:

10.0ms	(* 1/60 (pow l 5))
77.0ms	(* J (* (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))) (cos (/ K 2.0))))
105.0ms	(* (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
22.0ms	(* 1/3 (pow l 3))

series486.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* 1/60 (pow l 5))
230.0ms	(* J (* (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))) (cos (/ K 2.0))))
117.0ms	(* (+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
70.0ms	(* 1/3 (pow l 3))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	184	1751
1	490	1673
2	2162	1441
done	5001	1440

prune895.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

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)))

rewrite30.0ms

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:

19.0ms	(* (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:

451.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
199.0ms	(cbrt (cos (/ K 2.0)))
226.0ms	(cbrt (cos (/ K 2.0)))
203.0ms	(cbrt (cos (/ K 2.0)))

simplify4.8s

Counts

85 → 85

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	70	982
1	155	897
2	607	825
3	3811	742
done	5000	737

prune770.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes707.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample7.9s

Algorithm

intervals

Results

2.5s	2673×	body	1280	valid
2.4s	2610×	body	640	valid
1.2s	8566×	body	80	valid
550.0ms	1392×	body	320	valid
171.0ms	774×	body	160	valid