Details

sample105.0ms

Algorithm

intervals

Results

31.0ms	80×	body	1280	valid
20.0ms	81×	body	640	valid
16.0ms	250×	body	80	valid
10.0ms	57×	body	320	valid
2.0ms	19×	body	160	valid

simplify12.5s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize19.0ms

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)))
5.0b	(- (exp l) (exp (- l)))

rewrite127.0ms

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:

48.0ms	(* J (- (exp l) (exp (- l))))
64.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
14.0ms	(- (exp l) (exp (- l)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* J (- (exp l) (exp (- l))))
99.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
39.0ms	(- (exp l) (exp (- l)))

simplify1.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (698.0ms)

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

prune209.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
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)))
0.2b	(* 1/3 (pow l 3))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`associate-l` `prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `associate-r/` `pow-prod-down` `-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:

71.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
14.0ms	(* 1/60 (pow l 5))
94.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
13.0ms	(* 1/3 (pow l 3))

series393.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
51.0ms	(* 1/60 (pow l 5))
170.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
38.0ms	(* 1/3 (pow l 3))

simplify680.0ms

Counts

110 → 110

Iterations

Useful iterations: done (677.0ms)

Iter	Nodes	Cost
0	184	1706
1	466	1616
2	1628	1390
done	5002	1389

prune573.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 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)))
0.2b	(* 1/3 (pow l 3))

rewrite183.0ms

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:

12.0ms	(* 1/60 (pow l 5))
77.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
76.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
14.0ms	(* 1/3 (pow l 3))

series352.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/60 (pow l 5))
167.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
92.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
40.0ms	(* 1/3 (pow l 3))

simplify717.0ms

Counts

108 → 108

Iterations

Useful iterations: done (714.0ms)

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

prune372.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize22.0ms

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)))

rewrite17.0ms

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:

12.0ms	(* (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)))

series701.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
141.0ms	(cbrt (cos (/ K 2.0)))
142.0ms	(cbrt (cos (/ K 2.0)))
141.0ms	(cbrt (cos (/ K 2.0)))

simplify1.2s

Counts

85 → 85

Iterations

Useful iterations: done (1.2s)

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

prune346.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes415.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b 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

sample3.2s

Algorithm

intervals

Results

1.1s	2652×	body	1280	valid
636.0ms	2568×	body	640	valid
448.0ms	8463×	body	80	valid
246.0ms	1426×	body	320	valid
81.0ms	762×	body	160	valid