Details

sample988.0ms

Algorithm

intervals

Results

464.0ms	260×	body	10240	exit
151.0ms	91×	body	2560	valid
63.0ms	86×	body	1280	valid
23.0ms	550×	body	80	nan
18.0ms	46×	body	640	valid
5.0ms	18×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	1×	body	2560	nan
0.0ms	2×	body	80	valid

simplify3.2s

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	85	10
5	199	10
6	523	10
7	1893	10
done	5000	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.1b

localize12.0ms

Local error

Found 2 expressions with local error:

1.4b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.9b	(fmod (cosh a) (* a a))

rewrite3.0ms

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))

series13.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
10.0ms	(fmod (cosh a) (* a a))

simplify4.7s

Counts

21 → 21

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	29	241
1	45	241
2	63	209
3	92	209
4	144	209
5	278	209
6	711	209
7	2499	209
done	5001	209

prune83.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 59.7b

localize12.0ms

Local error

Found 3 expressions with local error:

1.4b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
9.1b	(log (exp (fmod (cosh a) (* a a))))
59.9b	(fmod (cosh a) (* a a))

rewrite3.0ms

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:

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

series7.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify3.4s

Counts

39 → 39

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	51	463
1	73	410
2	95	359
3	139	359
4	231	359
5	483	359
6	1346	359
7	4991	359
done	5000	359

prune141.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.7b

localize16.0ms

Local error

Found 4 expressions with local error:

2.8b	(log (sqrt (exp (fmod (cosh a) (* a a)))))
2.8b	(log (sqrt (exp (fmod (cosh a) (* a a)))))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod` `log-pow`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `sqrt-pow1`
6×	`add-exp-log` `exp-prod` `sqrt-prod`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow1/2` `rem-log-exp`

Counts

4 → 54

Calls

4 calls:

2.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
2.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series223.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
109.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify3.0s

Counts

66 → 66

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	49	782
1	66	736
2	83	660
3	109	660
4	164	660
5	307	660
6	827	660
7	2894	660
done	5001	660

prune295.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 59.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.6b	(asin (pow (fmod (cosh a) (* a a)) (log1p a)))
0.7b	(- (/ PI 2) (asin (pow (fmod (cosh a) (* a a)) (log1p a))))
59.9b	(fmod (cosh a) (* a a))

rewrite13.0ms

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:

0.0ms	(asin (pow (fmod (cosh a) (* a a)) (log1p a)))
11.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (* a a)) (log1p a))))
0.0ms	(fmod (cosh a) (* a a))

series35.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(asin (pow (fmod (cosh a) (* a a)) (log1p a)))
30.0ms	(- (/ PI 2) (asin (pow (fmod (cosh a) (* a a)) (log1p a))))
2.0ms	(fmod (cosh a) (* a a))

simplify1.3s

Counts

40 → 40

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	62	663
1	123	625
2	216	585
3	365	581
4	737	581
5	1783	581
done	5001	581

prune124.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.2b

regimes77.0ms

Accuracy

0% (0.1b remaining)

Error of 59.5b against oracle of 59.4b and baseline of 59.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
done	13	27

end0.0ms

sample22.8s

Algorithm

intervals

Results

13.9s	8006×	body	10240	exit
5.1s	3190×	body	2560	valid
1.8s	2499×	body	1280	valid
682.0ms	16177×	body	80	nan
490.0ms	1264×	body	640	valid
167.0ms	615×	body	320	valid
65.0ms	325×	body	160	valid
21.0ms	10×	body	5120	nan
13.0ms	107×	body	80	valid
7.0ms	8×	body	2560	nan
4.0ms	12×	body	640	nan
3.0ms	12×	body	320	nan
2.0ms	4×	body	1280	nan
1.0ms	10×	body	160	nan