Details

sample246.0ms

Algorithm

intervals

Results

67.0ms	90×	body	1280	valid
64.0ms	257×	body	80	valid
47.0ms	96×	body	640	valid
16.0ms	45×	body	320	valid
5.0ms	24×	body	160	valid

simplify21.2s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize22.0ms

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))))
5.6b	(- (exp l) (exp (- l)))

rewrite248.0ms

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:

125.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
79.0ms	(* J (- (exp l) (exp (- l))))
41.0ms	(- (exp l) (exp (- l)))

series264.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
73.0ms	(* J (- (exp l) (exp (- l))))
53.0ms	(- (exp l) (exp (- l)))

simplify3.1s

Counts

69 → 69

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	114	899
1	259	874
2	746	738
3	2934	735
done	5002	735

prune316.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.1b	(* 1/60 (pow l 5))
0.1b	(* 1/3 (pow l 3))
0.2b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

rewrite339.0ms

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:

154.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
26.0ms	(* 1/60 (pow l 5))
17.0ms	(* 1/3 (pow l 3))
136.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
102.0ms	(* 1/60 (pow l 5))
73.0ms	(* 1/3 (pow l 3))
258.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify979.0ms

Counts

110 → 110

Iterations

Useful iterations: done (975.0ms)

Iter	Nodes	Cost
0	184	1706
1	466	1616
2	1640	1390
done	5000	1389

prune558.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

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)))

rewrite18.0ms

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:

13.0ms	(* (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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

437.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
220.0ms	(cbrt (cos (/ K 2.0)))
209.0ms	(cbrt (cos (/ K 2.0)))
218.0ms	(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

prune599.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (pow (cos (* 0.5 K)) 2)))
0.2b	(pow (cos (* 0.5 K)) 2)
0.3b	(cbrt (pow (cos (* 0.5 K)) 2))
0.3b	(cbrt (cos (/ K 2.0)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

19×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r`
10×	`pow1` `add-exp-log`
9×	`unpow-prod-down`
7×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `pow-prod-down` `prod-exp` `cbrt-unprod` `unpow2` `sqr-pow`
2×	`pow1/3` `associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `flip3-+` `associate-l` `pow-exp` `*-commutative` `flip-+`

Counts

4 → 73

Calls

4 calls:

173.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (pow (cos (* 0.5 K)) 2)))
12.0ms	(pow (cos (* 0.5 K)) 2)
8.0ms	(cbrt (pow (cos (* 0.5 K)) 2))
2.0ms	(cbrt (cos (/ K 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

476.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cbrt (pow (cos (* 0.5 K)) 2)))
37.0ms	(pow (cos (* 0.5 K)) 2)
477.0ms	(cbrt (pow (cos (* 0.5 K)) 2))
207.0ms	(cbrt (cos (/ K 2.0)))

simplify1.1s

Counts

85 → 85

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	153	1490
1	389	1417
2	1578	1196
done	5000	1185

prune578.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes523.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b 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

sample8.4s

Algorithm

intervals

Results

2.8s	2675×	body	1280	valid
1.6s	8311×	body	80	valid
1.4s	2587×	body	640	valid
1.2s	1476×	body	320	valid
294.0ms	748×	body	160	valid