Details

sample1.2s

Algorithm

intervals

Results

582.0ms	214×	body	10240	exit
331.0ms	90×	body	2560	valid
102.0ms	86×	body	1280	valid
43.0ms	478×	body	80	nan
30.0ms	45×	body	640	valid
9.0ms	23×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	5×	body	80	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	24	10
3	44	10
4	91	10
5	373	10
6	3269	10
done	5001	10

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
2.0b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.1b	(fmod (cosh a) (* a a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log`
3×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

3 → 32

Calls

3 calls:

4.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
1.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series183.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
7.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
15.0ms	(fmod (cosh a) (* a a))

simplify1.8s

Counts

41 → 41

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	51	507
1	126	492
2	468	450
3	2588	450
done	5000	450

prune276.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.0b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
12.0b	(log (exp (fmod (cosh a) (* a a))))
59.1b	(fmod (cosh a) (* a a))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`log-pow`
7×	`pow1` `unpow-prod-down`
6×	`exp-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod`
1×	`acos-asin` `pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

21.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
5.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(fmod (cosh a) (* a a))

series216.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
8.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
5.0ms	(log (exp (fmod (cosh a) (* a a))))
5.0ms	(fmod (cosh a) (* a a))

simplify601.0ms

Counts

63 → 63

Iterations

Useful iterations: 2 (155.0ms)

Iter	Nodes	Cost
0	78	857
1	192	729
2	714	668
done	5000	668

prune429.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 59.8b

localize27.0ms

Local error

Found 4 expressions with local error:

2.0b	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
59.1b	(fmod (cosh a) (pow a 2))
59.1b	(fmod (cosh a) (pow a 2))
59.1b	(fmod (cosh a) (pow a 2))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
1×	`acos-asin`

Counts

4 → 29

Calls

4 calls:

1.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
0.0ms	(fmod (cosh a) (pow a 2))
0.0ms	(fmod (cosh a) (pow a 2))
0.0ms	(fmod (cosh a) (pow a 2))

series13.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
3.0ms	(fmod (cosh a) (pow a 2))
3.0ms	(fmod (cosh a) (pow a 2))
3.0ms	(fmod (cosh a) (pow a 2))

simplify3.3s

Counts

41 → 41

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	25	417
1	40	417
2	65	361
3	123	361
4	246	361
5	745	361
6	3904	361
done	5001	361

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))) (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))))
2.0b	(acos (* (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))) (sqrt (pow (fmod (cosh a) (* a a)) (log1p a)))))
59.1b	(fmod (cosh a) (* a a))
59.1b	(fmod (cosh a) (* a a))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-prod`
44×	`add-sqr-sqrt`
20×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity` `unswap-sqr`
12×	`swap-sqr` `sqr-pow`
11×	`pow1`
10×	`associate-r` `associate-l`
6×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

27.0ms	(* (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))) (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))))
1.0ms	(acos (* (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))) (sqrt (pow (fmod (cosh a) (* a a)) (log1p a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series176.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))) (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))))
13.0ms	(acos (* (sqrt (pow (fmod (cosh a) (* a a)) (log1p a))) (sqrt (pow (fmod (cosh a) (* a a)) (log1p a)))))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify9.7s

Counts

105 → 105

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	102	2657
1	191	1802
2	606	1680
3	4876	1646
done	5000	1646

prune488.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 59.8b

regimes118.0ms

Accuracy

0% (0.4b remaining)

Error of 60.4b against oracle of 60.0b and baseline of 60.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
done	9	12

end0.0ms

sample33.9s

Algorithm

intervals

Results

20.2s	7748×	body	10240	exit
6.7s	3136×	body	2560	valid
2.8s	2535×	body	1280	valid
1.6s	15889×	body	80	nan
712.0ms	1275×	body	640	valid
636.0ms	652×	body	320	valid
119.0ms	304×	body	160	valid
33.0ms	11×	body	5120	nan
14.0ms	98×	body	80	valid
8.0ms	5×	body	2560	nan
3.0ms	5×	body	1280	nan
2.0ms	4×	body	640	nan
2.0ms	6×	body	320	nan
1.0ms	5×	body	160	nan