Details

sample2.1s

Algorithm

intervals

Results

1.4s	259×	body	10240	exit
334.0ms	104×	body	2560	valid
152.0ms	82×	body	1280	valid
81.0ms	540×	body	80	nan
39.0ms	47×	body	640	valid
34.0ms	1×	body	5120	nan
9.0ms	14×	body	320	valid
2.0ms	1×	body	2560	nan
2.0ms	4×	body	160	valid
1.0ms	5×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5009
7	3480
6	774
5	199
4	87
3	44
2	24
1	16
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize19.0ms

Local error

Found 2 expressions with local error:

0.8b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
59.9b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin`

Counts

2 → 21

Calls

2 calls:

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

series16.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
12.0ms	(fmod (cosh a) (* a a))

simplify3.1s

Counts

27 → 27

Iterations

Iter	Nodes
done	5023
7	3173
6	895
5	371
4	199
3	121
2	81
1	58
0	35

prune237.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 59.4b

localize49.0ms

Local error

Found 3 expressions with local error:

0.8b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
6.6b	(log (exp (fmod (cosh a) (* a a))))
59.9b	(fmod (cosh a) (* a a))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `log-pow`
3×	`expm1-log1p-u` `log-prod` `exp-prod` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `rem-log-exp`

Counts

3 → 39

Calls

3 calls:

2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
5.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(fmod (cosh a) (* a a))

series10.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(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))

simplify4.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5002
7	4732
6	1430
5	558
4	291
3	180
2	125
1	92
0	60

prune252.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.4b

localize59.0ms

Local error

Found 4 expressions with local error:

6.6b	(log (exp (fmod (cosh a) (* a a))))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`rem-log-exp`

Counts

4 → 48

Calls

4 calls:

2.0ms	(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))

series8.0ms

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

simplify2.5s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
7	2052
6	695
5	337
4	190
3	124
2	88
1	65
0	42

prune571.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.3b

localize44.0ms

Local error

Found 4 expressions with local error:

6.6b	(log (exp (fmod (cosh a) (* a a))))
6.6b	(log (exp (fmod (cosh a) (* a a))))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `log-pow` `add-cube-cbrt`
6×	`pow1` `log-prod` `exp-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`

Counts

4 → 56

Calls

4 calls:

2.0ms	(log (exp (fmod (cosh a) (* a a))))
5.0ms	(log (exp (fmod (cosh a) (* a a))))
0.0ms	(fmod (cosh a) (* a a))
1.0ms	(fmod (cosh a) (* a a))

series8.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
7	2052
6	695
5	337
4	190
3	124
2	88
1	65
0	42

prune468.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.3b

regimes367.0ms

Accuracy

0% (0.4b remaining)

Error of 59.6b against oracle of 59.2b and baseline of 59.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample45.2s

Algorithm

intervals

Results

26.1s	7988×	body	10240	exit
8.8s	3166×	body	2560	valid
4.3s	2525×	body	1280	valid
3.0s	15903×	body	80	nan
1.6s	1252×	body	640	valid
418.0ms	631×	body	320	valid
145.0ms	319×	body	160	valid
43.0ms	107×	body	80	valid
39.0ms	9×	body	5120	nan
11.0ms	7×	body	2560	nan
8.0ms	7×	body	1280	nan
3.0ms	10×	body	160	nan
3.0ms	5×	body	320	nan
3.0ms	4×	body	640	nan