Details

sample228.0ms

Algorithm

intervals

Results

75.0ms	81×	body	1280	valid
42.0ms	69×	body	640	valid
34.0ms	264×	body	80	valid
19.0ms	45×	body	320	valid
4.0ms	16×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	15
1	23	15
2	41	15
3	82	15
4	198	15
5	537	15
6	2607	15
done	5001	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize24.0ms

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)))
5.9b	(- (exp l) (exp (- l)))

rewrite149.0ms

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:

64.0ms	(* J (- (exp l) (exp (- l))))
68.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
14.0ms	(- (exp l) (exp (- l)))

series321.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* J (- (exp l) (exp (- l))))
174.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
68.0ms	(- (exp l) (exp (- l)))

simplify1.0s

Counts

69 → 69

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	114	899
1	288	874
2	1360	748
done	5000	738

prune319.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

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)))

rewrite306.0ms

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:

108.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
12.0ms	(* 1/60 (pow l 5))
20.0ms	(* 1/3 (pow l 3))
161.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

524.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
76.0ms	(* 1/60 (pow l 5))
69.0ms	(* 1/3 (pow l 3))
222.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify1.5s

Counts

110 → 110

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	184	1706
1	512	1614
2	2430	1404
done	5001	1397

prune627.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 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))

rewrite248.0ms

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:

12.0ms	(* 1/60 (pow l 5))
113.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
99.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
21.0ms	(* 1/3 (pow l 3))

series491.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* 1/60 (pow l 5))
236.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
121.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
45.0ms	(* 1/3 (pow l 3))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	181	1751
1	478	1661
2	2073	1439
done	5000	1432

prune615.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))))
15.5b	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
15.5b	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
15.5b	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

55.0ms	(* (cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))))
22.0ms	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
42.0ms	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
35.0ms	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

469.0ms	(* (cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))))
437.0ms	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
472.0ms	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
392.0ms	(cbrt (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))

simplify874.0ms

Counts

84 → 84

Iterations

Useful iterations: done (868.0ms)

Iter	Nodes	Cost
0	152	3298
1	386	3009
2	1409	2681
done	5000	2411

prune745.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes485.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b 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

sample8.4s

Algorithm

intervals

Results

2.8s	2675×	body	1280	valid
1.9s	2563×	body	640	valid
1.2s	8238×	body	80	valid
1.0s	1416×	body	320	valid
361.0ms	743×	body	160	valid