Details

sample107.0ms

Algorithm

intervals

Results

34.0ms	86×	body	1280	valid
24.0ms	90×	body	640	valid
13.0ms	261×	body	80	valid
7.0ms	46×	body	320	valid
3.0ms	30×	body	160	valid

simplify12.8s

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: 19.9b

localize18.0ms

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)))
6.2b	(- (exp l) (exp (- l)))

rewrite115.0ms

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:

42.0ms	(* J (- (exp l) (exp (- l))))
58.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
13.0ms	(- (exp l) (exp (- l)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* J (- (exp l) (exp (- l))))
95.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
39.0ms	(- (exp l) (exp (- l)))

simplify1.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (711.0ms)

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

prune204.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

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))))
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))

rewrite182.0ms

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:

66.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
13.0ms	(* 1/60 (pow l 5))
87.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
13.0ms	(* 1/3 (pow l 3))

series384.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
48.0ms	(* 1/60 (pow l 5))
166.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
37.0ms	(* 1/3 (pow l 3))

simplify710.0ms

Counts

110 → 110

Iterations

Useful iterations: done (707.0ms)

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

prune381.0ms

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)))
0.1b	(* 1/3 (pow l 3))

rewrite167.0ms

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:

11.0ms	(* 1/60 (pow l 5))
71.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
70.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
13.0ms	(* 1/3 (pow l 3))

series352.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/60 (pow l 5))
170.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
92.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
38.0ms	(* 1/3 (pow l 3))

simplify743.0ms

Counts

108 → 108

Iterations

Useful iterations: done (739.0ms)

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

prune372.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize22.0ms

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)))))
0.6b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.6b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.6b	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

rewrite182.0ms

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:

130.0ms	(* (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)))))
17.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
16.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
16.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

series662.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (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)))))
167.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
153.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
159.0ms	(cbrt (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

simplify2.3s

Counts

99 → 99

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	166	4010
1	395	3731
2	1205	3441
3	4707	2928
done	5001	2844

prune475.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes405.0ms

Accuracy

0% (0.3b 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

sample3.1s

Algorithm

intervals

Results

1.1s	2693×	body	1280	valid
643.0ms	2631×	body	640	valid
440.0ms	8408×	body	80	valid
255.0ms	1454×	body	320	valid
85.0ms	809×	body	160	valid