Details

sample1.3s

Algorithm

intervals

Results

732.0ms	268×	body	10240	exit
266.0ms	106×	body	2560	valid
104.0ms	640×	body	80	nan
75.0ms	65×	body	1280	valid
32.0ms	50×	body	640	valid
10.0ms	23×	body	320	valid
5.0ms	3×	body	2560	nan
4.0ms	11×	body	160	valid
1.0ms	1×	body	1280	nan
0.0ms	1×	body	80	valid
0.0ms	1×	body	160	nan

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.8b

localize23.0ms

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))

rewrite7.0ms

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:

3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
2.0ms	(fmod (cosh a) (* a a))

series25.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
21.0ms	(fmod (cosh a) (* a a))

simplify3.1s

Counts

21 → 21

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	29	241
1	43	241
2	61	209
3	90	209
4	148	209
5	288	209
6	765	209
7	2920	209
done	5000	209

prune103.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.3b

localize20.0ms

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))

series10.0ms

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))

simplify3.9s

Counts

39 → 39

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	51	463
1	70	410
2	92	359
3	130	359
4	211	359
5	428	359
6	1103	359
7	4017	359
done	5000	359

prune216.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 60.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.4b	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
0.9b	(- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
61.0b	(fmod (cosh a) (pow a 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 31

Calls

3 calls:

1.0ms	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
43.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
1.0ms	(fmod (cosh a) (pow a 2))

series50.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
41.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
5.0ms	(fmod (cosh a) (pow a 2))

simplify2.0s

Counts

40 → 40

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	58	663
1	117	625
2	215	585
3	386	581
4	812	581
5	2140	581
done	5001	581

prune219.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
8.2b	(- (/ PI 2) (* (sqrt (asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))) (sqrt (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
61.0b	(fmod (cosh a) (pow a 2))
61.0b	(fmod (cosh a) (pow a 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
2×	`difference-of-squares`
1×	`sub-neg` `asin-acos` `flip3--` `times-frac` `diff-log` `flip--`

Counts

4 → 36

Calls

4 calls:

1.0ms	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
20.0ms	(- (/ PI 2) (* (sqrt (asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))) (sqrt (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
0.0ms	(fmod (cosh a) (pow a 2))
0.0ms	(fmod (cosh a) (pow a 2))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))
44.0ms	(- (/ PI 2) (* (sqrt (asin (pow (fmod (cosh a) (pow a 2)) (log1p a)))) (sqrt (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))))
3.0ms	(fmod (cosh a) (pow a 2))
3.0ms	(fmod (cosh a) (pow a 2))

simplify3.6s

Counts

48 → 48

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	60	990
1	129	698
2	265	646
3	554	634
4	1307	634
5	3958	634
done	5000	634

prune233.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 59.7b

regimes54.0ms

Accuracy

0% (0.0b remaining)

Error of 59.3b against oracle of 59.3b and baseline of 59.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
done	13	27

end0.0ms

sample31.1s

Algorithm

intervals

Results

18.7s	7885×	body	10240	exit
6.7s	3081×	body	2560	valid
2.5s	2519×	body	1280	valid
980.0ms	16129×	body	80	nan
707.0ms	1308×	body	640	valid
244.0ms	631×	body	320	valid
97.0ms	349×	body	160	valid
21.0ms	7×	body	5120	nan
17.0ms	13×	body	2560	nan
15.0ms	112×	body	80	valid
5.0ms	8×	body	1280	nan
2.0ms	7×	body	160	nan
2.0ms	5×	body	640	nan
2.0ms	6×	body	320	nan