Details

sample1.1s

Algorithm

intervals

Results

464.0ms	260×	body	10240	exit
175.0ms	97×	body	2560	valid
62.0ms	85×	body	1280	valid
26.0ms	565×	body	80	nan
19.0ms	41×	body	640	valid
6.0ms	21×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	1×	body	640	nan
0.0ms	3×	body	80	valid
0.0ms	1×	body	320	nan

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	24	10
3	44	10
4	89	10
5	195	10
6	633	10
7	2582	10
done	5000	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p a)
0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))
1.5b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.6b	(fmod (cosh a) (* a a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

0.0ms	(log1p a)
3.0ms	(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))

series130.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(log1p a)
116.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
9.0ms	(fmod (cosh a) (* a a))

simplify1.5s

Counts

51 → 51

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	55	543
1	95	528
2	205	482
3	489	482
4	1375	482
done	5000	482

prune152.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p a)
1.5b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
11.5b	(log (exp (fmod (cosh a) (* a a))))
59.6b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 37

Calls

4 calls:

0.0ms	(log1p a)
1.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))

series10.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(log1p a)
4.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
3.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify2.7s

Counts

49 → 49

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	58	499
1	78	446
2	101	391
3	141	391
4	225	391
5	443	391
6	1167	391
7	4306	391
done	5000	391

prune164.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 58.7b

localize17.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (cbrt (exp (fmod (cosh a) (* a a)))))
2.9b	(log (cbrt (exp (fmod (cosh a) (* a a)))))
59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod`
4×	`log-pow` `add-cbrt-cube` `add-log-exp`
2×	`pow1/3` `rem-log-exp`

Counts

4 → 46

Calls

4 calls:

3.0ms	(log (cbrt (exp (fmod (cosh a) (* a a)))))
3.0ms	(log (cbrt (exp (fmod (cosh a) (* a a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series420.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(log (cbrt (exp (fmod (cosh a) (* a a)))))
207.0ms	(log (cbrt (exp (fmod (cosh a) (* a a)))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify1.2s

Counts

58 → 58

Iterations

Useful iterations: 5 (52.0ms)

Iter	Nodes	Cost
0	42	702
1	56	688
2	70	612
3	83	602
4	101	602
5	132	598
6	199	598
7	422	598
8	1362	598
done	5001	598

prune246.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 58.6b

localize20.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (cbrt (sqrt (exp (fmod (cosh a) (* a a))))))
59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
2×	`log-pow`
1×	`pow1/3` `rem-log-exp`

Counts

4 → 40

Calls

4 calls:

3.0ms	(log (cbrt (sqrt (exp (fmod (cosh a) (* a a))))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series221.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(log (cbrt (sqrt (exp (fmod (cosh a) (* a a))))))
3.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify1.1s

Counts

52 → 52

Iterations

Useful iterations: 5 (59.0ms)

Iter	Nodes	Cost
0	54	618
1	69	601
2	83	536
3	96	530
4	114	530
5	145	528
6	212	528
7	435	528
8	1396	528
done	5000	528

prune228.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 58.6b

regimes253.0ms

Accuracy

75.2% (0.4b remaining)

Error of 58.9b against oracle of 58.5b and baseline of 60.2b

bsearch155.0ms

Steps

Iters	Range		Point
9	5.5548132533506025e-168	4.2147044714608302e-162	1.5819252110031022e-162

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
done	16	30

end0.0ms

sample22.8s

Algorithm

intervals

Results

13.6s	7784×	body	10240	exit
5.1s	3188×	body	2560	valid
1.8s	2482×	body	1280	valid
731.0ms	16233×	body	80	nan
513.0ms	1270×	body	640	valid
175.0ms	628×	body	320	valid
60.0ms	305×	body	160	valid
13.0ms	127×	body	80	valid
9.0ms	4×	body	5120	nan
9.0ms	9×	body	2560	nan
7.0ms	13×	body	1280	nan
4.0ms	11×	body	640	nan
2.0ms	9×	body	320	nan
1.0ms	4×	body	160	nan