Details

sample102.0ms

Algorithm

intervals

Results

36.0ms	87×	body	1280	valid
24.0ms	92×	body	640	valid
14.0ms	263×	body	80	valid
6.0ms	36×	body	320	valid
2.0ms	17×	body	160	valid

simplify16.2s

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	264	15
7	373	15
8	525	15
9	945	15
10	2266	15
11	2975	15
12	3329	15
13	4284	15
14	4567	15
done	4567	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize13.0ms

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)))
5.2b	(- (exp l) (exp (- l)))

rewrite57.0ms

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:

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

series182.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* J (- (exp l) (exp (- l))))
90.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
38.0ms	(- (exp l) (exp (- l)))

simplify1.4s

Counts

69 → 69

Iterations

Useful iterations: 3 (444.0ms)

Iter	Nodes	Cost
0	114	899
1	266	874
2	765	738
3	2728	735
done	5000	735

prune199.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

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)
0.1b	(* 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)))

rewrite94.0ms

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:

40.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
6.0ms	(* 1/60 (pow l 5))
6.0ms	(* 1/3 (pow l 3))
39.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series770.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
241.0ms	(* 1/60 (pow l 5))
37.0ms	(* 1/3 (pow l 3))
164.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify652.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (193.0ms)

Iter	Nodes	Cost
0	180	1661
1	473	1533
2	1610	1379
done	5000	1379

prune332.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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:

5.0ms	(* 1/60 (pow l 5))
9.0ms	(* 1/3 (pow l 3))
32.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
33.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/60 (pow l 5))
41.0ms	(* 1/3 (pow l 3))
161.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
90.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify588.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (178.0ms)

Iter	Nodes	Cost
0	181	1751
1	454	1663
2	1507	1431
done	5000	1431

prune371.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))
0.1b	(* J (/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
29.8b	(/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`add-exp-log`
24×	`associate-r`
22×	`add-cbrt-cube`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l` `prod-exp`
8×	`pow1`
7×	`cbrt-unprod`
6×	`times-frac` `unswap-sqr`
4×	`cbrt-undiv` `unpow-prod-down` `flip3--` `cube-prod` `div-exp` `associate-*l/` `associate-/r/` `flip--` `add-log-exp`
3×	`associate-/r` `-commutative`
2×	`pow-prod-down` `div-inv` `associate-/l/` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `frac-2neg` `unpow3` `associate-r/` `pow-exp` `clear-num` `associate-/l`

Counts

4 → 105

Calls

4 calls:

12.0ms	(* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
7.0ms	(* 1/3 (pow l 3))
38.0ms	(* J (/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
22.0ms	(/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
36.0ms	(* 1/3 (pow l 3))
365.0ms	(* J (/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
160.0ms	(/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

simplify836.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (274.0ms)

Iter	Nodes	Cost
0	222	4635
1	604	4520
2	2488	3686
done	5000	3686

prune501.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

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

1.1s	2639×	body	1280	valid
706.0ms	2682×	body	640	valid
481.0ms	8405×	body	80	valid
243.0ms	1415×	body	320	valid
92.0ms	775×	body	160	valid