Details

sample1.0s

Algorithm

intervals

Results

431.0ms	248×	body	10240	exit
160.0ms	98×	body	2560	valid
58.0ms	81×	body	1280	valid
38.0ms	436×	body	80	nan
17.0ms	44×	body	640	valid
4.0ms	15×	body	320	valid
3.0ms	15×	body	160	valid
0.0ms	1×	body	640	nan
0.0ms	3×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.6b

localize13.0ms

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)))
58.5b	(fmod (cosh a) (* a a))

rewrite14.0ms

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:

10.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series133.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
10.0ms	(fmod (cosh a) (* a a))

simplify137.0ms

Counts

41 → 41

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	91	291
1	249	265
2	805	265
3	3873	265
4	5001	265
done	5001	265

prune140.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fmod (cosh a) (* a a)))
2.0b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
12.7b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

2.0ms	(exp (fmod (cosh a) (* a 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))

series43.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (fmod (cosh a) (* a a)))
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))

simplify120.0ms

Counts

53 → 53

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	80	339
1	125	292
2	248	292
3	665	292
4	3272	292
5	5002	292
done	5002	292

prune208.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 59.3b

localize18.0ms

Local error

Found 4 expressions with local error:

12.7b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))
58.5b	(fmod (cosh a) (* a a))
58.5b	(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:

3.0ms	(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))

simplify81.0ms

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

prune269.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.1b	(- (/ PI 2) (asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
12.7b	(log (exp (fmod (cosh a) (* a a))))
58.5b	(fmod (cosh a) (* a a))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube`
3×	`log-prod` `exp-prod`
2×	`asin-acos` `difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 46

Calls

4 calls:

1.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
20.0ms	(- (/ PI 2) (asin (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))

series42.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(asin (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
33.0ms	(- (/ PI 2) (asin (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))

simplify137.0ms

Counts

58 → 58

Iterations

Useful iterations: 4 (131.0ms)

Iter	Nodes	Cost
0	148	533
1	295	476
2	702	474
3	2899	474
4	5001	472
done	5001	472

prune202.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.3b

regimes210.0ms

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	24	36
1	24	36
done	24	36

end0.0ms

sample22.5s

Algorithm

intervals

Results

13.5s	7785×	body	10240	exit
5.0s	3180×	body	2560	valid
1.8s	2510×	body	1280	valid
684.0ms	15577×	body	80	nan
489.0ms	1252×	body	640	valid
167.0ms	628×	body	320	valid
59.0ms	309×	body	160	valid
25.0ms	12×	body	5120	nan
12.0ms	121×	body	80	valid
4.0ms	7×	body	1280	nan
3.0ms	3×	body	2560	nan
2.0ms	9×	body	320	nan
1.0ms	4×	body	640	nan
1.0ms	5×	body	160	nan