Details

sample1.1s

Algorithm

intervals

Results

457.0ms	260×	body	10240	exit
155.0ms	97×	body	2560	valid
61.0ms	85×	body	1280	valid
44.0ms	565×	body	80	nan
18.0ms	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

simplify1.9s

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	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` `expm1-log1p-u`
4×	`add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
1×	`acos-asin` `pow-to-exp` `log1p-udef` `pow-pow` `log1p-expm1` `pow-exp` `sqr-pow`

Counts

4 → 49

Calls

4 calls:

0.0ms	(log1p a)
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))

series87.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(log1p a)
52.0ms	(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))

simplify1.6s

Counts

61 → 61

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	120	866
1	271	831
2	739	784
3	2508	727
done	5000	721

prune205.0ms

Pruning

9 alts after pruning (9 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` `expm1-log1p-u`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`acos-asin` `log1p-udef` `log1p-expm1` `rem-log-exp`

Counts

4 → 47

Calls

4 calls:

0.0ms	(log1p a)
1.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
3.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))

series32.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(log1p a)
6.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
3.0ms	(log (exp (fmod (cosh a) (* a a))))
3.0ms	(fmod (cosh a) (* a a))

simplify2.7s

Counts

59 → 59

Iterations

Useful iterations: 4 (333.0ms)

Iter	Nodes	Cost
0	88	608
1	144	539
2	259	483
3	503	482
4	1091	475
5	2704	475
done	5000	475

prune220.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 58.7b

localize16.0ms

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×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `rem-log-exp`

Counts

4 → 54

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))

series436.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(log (cbrt (exp (fmod (cosh a) (* a a)))))
215.0ms	(log (cbrt (exp (fmod (cosh a) (* a a)))))
2.0ms	(fmod (cosh a) (* a a))
5.0ms	(fmod (cosh a) (* a a))

simplify1.1s

Counts

66 → 66

Iterations

Useful iterations: 5 (61.0ms)

Iter	Nodes	Cost
0	46	770
1	60	756
2	74	680
3	87	670
4	105	670
5	136	666
6	203	666
7	425	666
8	1375	666
done	5000	666

prune284.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 58.6b

localize24.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`log-pow`
1×	`pow1/3` `rem-log-exp`

Counts

4 → 48

Calls

4 calls:

4.0ms	(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))

series231.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(log (cbrt (sqrt (exp (fmod (cosh a) (* a a))))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify1.2s

Counts

60 → 60

Iterations

Useful iterations: 5 (68.0ms)

Iter	Nodes	Cost
0	58	682
1	73	665
2	87	600
3	100	594
4	118	594
5	149	592
6	216	592
7	443	592
8	1330	592
done	5000	592

prune291.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 58.6b

regimes251.0ms

Accuracy

75.2% (0.4b remaining)

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

bsearch156.0ms

Steps

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

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	30
1	20	30
done	20	30

end0.0ms

sample22.6s

Algorithm

intervals

Results

13.5s	7784×	body	10240	exit
5.1s	3188×	body	2560	valid
1.8s	2482×	body	1280	valid
698.0ms	16233×	body	80	nan
489.0ms	1270×	body	640	valid
167.0ms	628×	body	320	valid
58.0ms	305×	body	160	valid
13.0ms	127×	body	80	valid
9.0ms	9×	body	2560	nan
9.0ms	4×	body	5120	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