Details

sample203.0ms

Algorithm

intervals

Results

55.0ms	82×	body	1280	valid
42.0ms	270×	body	80	valid
42.0ms	92×	body	640	valid
16.0ms	52×	body	320	valid
7.0ms	37×	body	160	valid

simplify19.6s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.9b	(- (exp l) (exp (- l)))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r` `add-log-exp`
7×	`add-cube-cbrt`
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×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

51.0ms	(* J (- (exp l) (exp (- l))))
97.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
105.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
16.0ms	(- (exp l) (exp (- l)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* J (- (exp l) (exp (- l))))
314.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
129.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
54.0ms	(- (exp l) (exp (- l)))

simplify4.2s

Counts

83 → 83

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	146	1240
1	349	1185
2	994	1031
3	3910	1016
done	5000	1016

prune429.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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

rewrite272.0ms

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:

95.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
15.0ms	(* 1/60 (pow l 5))
13.0ms	(* 1/3 (pow l 3))
143.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series967.0ms

Counts

4 → 12

Calls

4 calls:

536.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
98.0ms	(* 1/60 (pow l 5))
72.0ms	(* 1/3 (pow l 3))
261.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify1.2s

Counts

99 → 99

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	180	1661
1	467	1533
2	1748	1379
done	5002	1378

prune418.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

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)))

rewrite296.0ms

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:

14.0ms	(* 1/60 (pow l 5))
124.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
23.0ms	(* 1/3 (pow l 3))
132.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* 1/60 (pow l 5))
225.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
68.0ms	(* 1/3 (pow l 3))
119.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

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

prune661.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize69.0ms

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:

24.0ms	(* (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)))

series1.2s

Counts

4 → 12

Calls

4 calls:

482.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
242.0ms	(cbrt (cos (/ K 2.0)))
225.0ms	(cbrt (cos (/ K 2.0)))
240.0ms	(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

prune658.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes330.0ms

Accuracy

0% (0.3b 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

sample8.2s

Algorithm

intervals

Results

3.2s	2590×	body	1280	valid
1.5s	2599×	body	640	valid
1.2s	8345×	body	80	valid
700.0ms	762×	body	160	valid
556.0ms	1501×	body	320	valid