Details

sample111.0ms

Algorithm

intervals

Results

36.0ms	87×	body	1280	valid
25.0ms	95×	body	640	valid
19.0ms	291×	body	80	valid
8.0ms	47×	body	320	valid
3.0ms	23×	body	160	valid

simplify13.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	15
1	23	15
2	41	15
3	72	15
4	121	15
5	184	15
6	260	15
7	367	15
8	500	15
9	916	15
10	2263	15
11	2919	15
12	3279	15
13	4205	15
14	4488	15
done	4488	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
0.0b	(* J (- (exp l) (exp (- l))))
7.0b	(- (exp l) (exp (- l)))

rewrite59.0ms

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:

26.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
21.0ms	(* J (- (exp l) (exp (- l))))
9.0ms	(- (exp l) (exp (- l)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
54.0ms	(* J (- (exp l) (exp (- l))))
40.0ms	(- (exp l) (exp (- l)))

simplify1.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (614.0ms)

Iter	Nodes	Cost
0	114	899
1	266	874
2	768	738
3	2707	735
done	5001	735

prune196.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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

rewrite90.0ms

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:

35.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
6.0ms	(* 1/60 (pow l 5))
7.0ms	(* 1/3 (pow l 3))
39.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
50.0ms	(* 1/60 (pow l 5))
35.0ms	(* 1/3 (pow l 3))
163.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify759.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (211.0ms)

Iter	Nodes	Cost
0	184	1706
1	470	1616
2	1553	1390
done	5000	1390

prune378.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
0.7b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.7b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.7b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

68.0ms	(* (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
8.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
8.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
11.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

series656.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
155.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
154.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
158.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

simplify512.0ms

Counts

99 → 99

Iterations

Useful iterations: done (508.0ms)

Iter	Nodes	Cost
0	166	4010
1	395	3731
2	1211	3441
done	5001	3264

prune548.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.7b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.7b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.7b	(cbrt (* (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
10×	`cbrt-prod`
9×	`flip3-+` `flip-+`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `associate-l/`

Counts

4 → 56

Calls

4 calls:

8.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
8.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
8.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
21.0ms	(cbrt (* (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
158.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
157.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
210.0ms	(cbrt (* (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))))

simplify1.8s

Counts

68 → 68

Iterations

Useful iterations: 3 (790.0ms)

Iter	Nodes	Cost
0	162	2945
1	372	2801
2	1081	2565
3	4980	2381
done	5000	2381

prune433.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes529.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2729×	body	1280	valid
690.0ms	2575×	body	640	valid
460.0ms	8426×	body	80	valid
254.0ms	1423×	body	320	valid
82.0ms	718×	body	160	valid