Details

sample251.0ms

Algorithm

intervals

Results

79.0ms	269×	body	80	valid
63.0ms	87×	body	1280	valid
42.0ms	89×	body	640	valid
22.0ms	65×	body	320	valid
4.0ms	20×	body	160	valid

simplify21.0s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize32.0ms

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)))
4.6b	(- (exp l) (exp (- l)))

rewrite179.0ms

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:

60.0ms	(* J (- (exp l) (exp (- l))))
76.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
41.0ms	(- (exp l) (exp (- l)))

series278.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* J (- (exp l) (exp (- l))))
156.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
43.0ms	(- (exp l) (exp (- l)))

simplify2.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (1.1s)

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

prune347.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

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)
0.1b	(* 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))

rewrite331.0ms

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:

110.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
23.0ms	(* 1/60 (pow l 5))
165.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
28.0ms	(* 1/3 (pow l 3))

series884.0ms

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)
72.0ms	(* 1/60 (pow l 5))
227.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
49.0ms	(* 1/3 (pow l 3))

simplify1.3s

Counts

99 → 99

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	180	1661
1	468	1533
2	1741	1379
done	5001	1378

prune524.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 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))

rewrite259.0ms

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))
134.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
94.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
16.0ms	(* 1/3 (pow l 3))

series567.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* 1/60 (pow l 5))
286.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
129.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
51.0ms	(* 1/3 (pow l 3))

simplify1.2s

Counts

108 → 108

Iterations

Useful iterations: done (1.2s)

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

prune555.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))))
14.6b	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
14.6b	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
14.6b	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-r/` `associate-l/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

127.0ms	(* (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))))
159.0ms	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
94.0ms	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
119.0ms	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

series2.1s

Counts

4 → 12

Calls

4 calls:

589.0ms	(* (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))))
493.0ms	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
501.0ms	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
482.0ms	(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

simplify931.0ms

Counts

84 → 84

Iterations

Useful iterations: done (924.0ms)

Iter	Nodes	Cost
0	174	4042
1	426	3713
2	1330	3313
done	5000	2960

prune717.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes359.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b 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

sample8.0s

Algorithm

intervals

Results

2.7s	2682×	body	1280	valid
1.5s	1444×	body	320	valid
1.4s	2606×	body	640	valid
1.0s	8289×	body	80	valid
358.0ms	785×	body	160	valid