Details

sample328.0ms

Algorithm

intervals

Results

151.0ms	99×	body	1280	valid
63.0ms	95×	body	640	valid
37.0ms	272×	body	80	valid
17.0ms	37×	body	320	valid
4.0ms	16×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	45	14
3	91	14
4	222	14
5	600	14
6	2862	14
done	5000	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize38.0ms

Local error

Found 1 expressions with local error:

6.1b	(- (exp l) (exp (- l)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

31.0ms

(- (exp l) (exp (- l)))

series71.0ms

Counts

1 → 3

Calls

1 calls:

71.0ms

(- (exp l) (exp (- l)))

simplify928.0ms

Counts

31 → 31

Iterations

Useful iterations: done (927.0ms)

Iter	Nodes	Cost
0	73	547
1	170	404
2	671	308
done	5000	254

prune231.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

13.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series673.0ms

Counts

2 → 6

Calls

2 calls:

240.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
434.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify3.2s

Counts

38 → 38

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	82	824
1	180	815
2	612	706
3	3651	696
done	5001	690

prune405.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

25.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
6.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
6.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
7.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

885.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
506.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
489.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
484.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

simplify990.0ms

Counts

78 → 78

Iterations

Useful iterations: done (985.0ms)

Iter	Nodes	Cost
0	132	2272
1	317	2080
2	1117	1843
done	5001	1589

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt J)
0.6b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
13.4b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 48

Calls

4 calls:

2.0ms	(cbrt J)
2.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
7.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
7.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

400.0ms	(cbrt J)
287.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
573.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
543.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

simplify3.4s

Counts

60 → 60

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	131	1154
1	284	1127
2	823	1023
3	4043	947
done	5000	945

prune980.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes963.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	21
1	21	21
done	21	21

end0.0ms

sample10.3s

Algorithm

intervals

Results

4.3s	2690×	body	1280	valid
2.0s	2534×	body	640	valid
1.9s	8411×	body	80	valid
686.0ms	1376×	body	320	valid
187.0ms	711×	body	160	valid