Details

sample100.0ms

Algorithm

intervals

Results

31.0ms	81×	body	1280	valid
21.0ms	86×	body	640	valid
14.0ms	283×	body	80	valid
6.0ms	38×	body	320	valid
3.0ms	26×	body	160	valid

simplify376.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	271	9
5	533	9
6	1023	9
7	1395	9
8	4369	9
9	5002	9
done	5002	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

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)))
5.1b	(- (exp l) (exp (- l)))

rewrite118.0ms

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:

43.0ms	(* J (- (exp l) (exp (- l))))
60.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
13.0ms	(- (exp l) (exp (- l)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* J (- (exp l) (exp (- l))))
100.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
38.0ms	(- (exp l) (exp (- l)))

simplify37.0ms

Counts

69 → 69

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	264	566
1	1116	481
2	5002	475
done	5002	475

prune199.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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

rewrite192.0ms

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:

78.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
13.0ms	(* 1/60 (pow l 5))
85.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
13.0ms	(* 1/3 (pow l 3))

series609.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
52.0ms	(* 1/60 (pow l 5))
172.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
39.0ms	(* 1/3 (pow l 3))

simplify69.0ms

Counts

99 → 99

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	465	784
1	2234	701
2	5003	701
done	5003	701

prune318.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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)))

rewrite166.0ms

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))
70.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
13.0ms	(* 1/3 (pow l 3))
68.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* 1/60 (pow l 5))
168.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
37.0ms	(* 1/3 (pow l 3))
92.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify68.0ms

Counts

108 → 108

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	444	856
1	2079	731
2	5001	731
done	5001	731

prune340.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-r`
23×	`add-exp-log`
21×	`add-sqr-sqrt`
20×	`add-cbrt-cube`
19×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`prod-exp`
10×	`cbrt-unprod`
9×	`pow-prod-down` `sqrt-prod`
6×	`associate-*l/`
5×	`associate-l`
4×	`unpow-prod-down` `cube-prod` `associate-*r/` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`flip3-+` `flip-+` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `pow-exp`

Counts

4 → 93

Calls

4 calls:

1.0ms	(sqrt (cos (/ K 2.0)))
292.0ms	(* (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (sqrt (cos (/ K 2.0)))) (sqrt (cos (/ K 2.0))))
87.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (sqrt (cos (/ K 2.0))))
12.0ms	(* 1/3 (pow l 3))

series449.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (cos (/ K 2.0)))
173.0ms	(* (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (sqrt (cos (/ K 2.0)))) (sqrt (cos (/ K 2.0))))
207.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (sqrt (cos (/ K 2.0))))
43.0ms	(* 1/3 (pow l 3))

simplify78.0ms

Counts

105 → 105

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	456	1088
1	2466	877
2	5002	877
done	5002	877

prune335.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12
done	30	12

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2660×	body	1280	valid
630.0ms	2603×	body	640	valid
446.0ms	8399×	body	80	valid
243.0ms	1431×	body	320	valid
81.0ms	771×	body	160	valid