Details

sample1.4s

Algorithm

intervals

Results

783.0ms	270×	body	10240	exit
281.0ms	99×	body	2560	valid
95.0ms	516×	body	80	nan
87.0ms	78×	body	1280	valid
28.0ms	44×	body	640	valid
11.0ms	24×	body	320	valid
3.0ms	10×	body	160	valid
2.0ms	1×	body	2560	nan
1.0ms	1×	body	1280	nan
0.0ms	1×	body	80	valid

simplify4.3s

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	91	10
5	373	10
6	3269	10
done	5001	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.7b

localize13.0ms

Local error

Found 2 expressions with local error:

1.7b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
60.4b	(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:

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

series15.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
11.0ms	(fmod (cosh a) (* a a))

simplify3.3s

Counts

21 → 21

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	29	241
1	52	241
2	101	209
3	172	209
4	301	209
5	807	209
6	3981	209
done	5000	209

prune123.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.3b

localize15.0ms

Local error

Found 3 expressions with local error:

1.7b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
10.4b	(log (exp (fmod (cosh a) (* a a))))
60.4b	(fmod (cosh a) (* a a))

rewrite7.0ms

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:

2.0ms	(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))

series26.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
13.0ms	(log (exp (fmod (cosh a) (* a a))))
5.0ms	(fmod (cosh a) (* a a))

simplify3.3s

Counts

39 → 39

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	51	463
1	83	410
2	148	359
3	235	359
4	387	359
5	984	359
6	4616	359
done	5001	359

prune199.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 60.3b

localize16.0ms

Local error

Found 3 expressions with local error:

1.0b	(log (exp (acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))))
1.7b	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
60.4b	(fmod (cosh a) (pow a 2))

rewrite9.0ms

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`
2×	`acos-asin`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

3 → 31

Calls

3 calls:

7.0ms	(log (exp (acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))))
1.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
0.0ms	(fmod (cosh a) (pow a 2))

series19.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(log (exp (acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))))
7.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
5.0ms	(fmod (cosh a) (pow a 2))

simplify3.5s

Counts

40 → 40

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	51	550
1	77	515
2	113	452
3	187	452
4	355	452
5	969	452
6	4926	452
done	5001	452

prune215.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 60.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
1.0b	(log (exp (- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
1.0b	(- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
60.4b	(fmod (cosh a) (pow a 2))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

2.0ms	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
68.0ms	(log (exp (- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
31.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
0.0ms	(fmod (cosh a) (pow a 2))

series106.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
33.0ms	(log (exp (- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
64.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
5.0ms	(fmod (cosh a) (pow a 2))

simplify658.0ms

Counts

65 → 65

Iterations

Useful iterations: 3 (235.0ms)

Iter	Nodes	Cost
0	92	1161
1	180	1064
2	401	981
3	1139	977
done	5000	977

prune359.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 59.6b

regimes44.0ms

Accuracy

0% (0.0b remaining)

Error of 59.4b against oracle of 59.4b and baseline of 59.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
done	15	29

end0.0ms

sample37.3s

Algorithm

intervals

Results

21.8s	8061×	body	10240	exit
8.1s	3142×	body	2560	valid
2.8s	2499×	body	1280	valid
1.8s	16376×	body	80	nan
883.0ms	1295×	body	640	valid
664.0ms	637×	body	320	valid
94.0ms	314×	body	160	valid
20.0ms	6×	body	5120	nan
17.0ms	113×	body	80	valid
13.0ms	11×	body	2560	nan
6.0ms	12×	body	640	nan
2.0ms	3×	body	1280	nan
2.0ms	8×	body	160	nan
2.0ms	5×	body	320	nan