Details

sample1.1s

Algorithm

intervals

Results

471.0ms	268×	body	10240	exit
182.0ms	106×	body	2560	valid
47.0ms	65×	body	1280	valid
40.0ms	50×	body	640	valid
29.0ms	640×	body	80	nan
6.0ms	23×	body	320	valid
3.0ms	3×	body	2560	nan
2.0ms	11×	body	160	valid
1.0ms	1×	body	1280	nan
0.0ms	1×	body	160	nan
0.0ms	1×	body	80	valid

simplify47.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	6
1	24	6
2	43	6
3	91	6
4	257	6
5	1277	6
6	5001	6
done	5001	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.8b

localize18.0ms

Local error

Found 2 expressions with local error:

1.5b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
61.0b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 15

Calls

2 calls:

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

series15.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
11.0ms	(fmod (cosh a) (* a a))

simplify85.0ms

Counts

21 → 21

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	44	144
1	72	124
2	156	124
3	405	124
4	1968	124
5	5002	124
done	5002	124

prune75.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.3b

localize13.0ms

Local error

Found 3 expressions with local error:

1.5b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
10.3b	(log (exp (fmod (cosh a) (* a a))))
61.0b	(fmod (cosh a) (* a a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

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))

series9.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(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))

simplify111.0ms

Counts

39 → 39

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	73	265
1	107	226
2	221	226
3	590	226
4	2934	226
5	5002	226
done	5002	226

prune128.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.3b

localize19.0ms

Local error

Found 4 expressions with local error:

10.3b	(log (exp (fmod (cosh a) (* a a))))
61.0b	(fmod (cosh a) (* a a))
61.0b	(fmod (cosh a) (* a a))
61.0b	(fmod (cosh a) (* a a))

rewrite4.0ms

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×	`rem-log-exp`

Counts

4 → 36

Calls

4 calls:

3.0ms	(log (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))

series10.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(log (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))

simplify83.0ms

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	52	246
1	75	212
2	157	212
3	405	212
4	1946	212
5	5003	212
done	5003	212

prune222.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 60.3b

localize27.0ms

Local error

Found 4 expressions with local error:

61.0b	(fmod (cosh a) (* a a))
61.0b	(fmod (cosh a) (* a a))
61.0b	(fmod (cosh a) (* a a))
61.0b	(fmod (cosh a) (* a a))

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`

Counts

4 → 28

Calls

4 calls:

0.0ms	(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))

series10.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(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))

simplify58.0ms

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	196
1	40	168
2	92	168
3	228	168
4	1044	168
5	5001	168
done	5001	168

prune252.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 60.3b

regimes168.0ms

Accuracy

0% (0.4b remaining)

Error of 60.2b against oracle of 59.8b and baseline of 60.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	19	37
done	19	37

end0.0ms

sample22.8s

Algorithm

intervals

Results

13.8s	7885×	body	10240	exit
4.9s	3081×	body	2560	valid
1.8s	2519×	body	1280	valid
696.0ms	16129×	body	80	nan
515.0ms	1308×	body	640	valid
172.0ms	631×	body	320	valid
69.0ms	349×	body	160	valid
15.0ms	7×	body	5120	nan
12.0ms	13×	body	2560	nan
11.0ms	112×	body	80	valid
4.0ms	8×	body	1280	nan
2.0ms	5×	body	640	nan
1.0ms	6×	body	320	nan
1.0ms	7×	body	160	nan