Details

sample1.5s

Algorithm

intervals

Results

988.0ms	96×	body	10240	exit
230.0ms	69×	body	1280	valid
73.0ms	55×	body	640	valid
24.0ms	30×	body	320	valid
22.0ms	89×	body	80	valid
9.0ms	1×	body	5120	valid
5.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

3 → 21

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
32.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series139.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(expm1 (sin (expm1 a)))
113.0ms	(sin (expm1 a))
24.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
8	3071
7	934
6	395
5	166
4	66
3	44
2	35
1	31
0	28

prune278.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.7b

localize86.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

4.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series113.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
8	2114
7	643
6	275
5	115
4	48
3	33
2	26
1	23
0	21

prune449.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 32.5b

localize93.0ms

Local error

Found 4 expressions with local error:

38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series12.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
8	1013
7	319
6	142
5	64
4	30
3	22
2	17
1	15
0	14

prune515.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 32.5b

localize108.0ms

Local error

Found 4 expressions with local error:

38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series11.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.2s

Counts

40 → 40

Iterations

Iter	Nodes
done	5001
8	1013
7	319
6	142
5	64
4	30
3	22
2	17
1	15
0	14

prune332.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 32.5b

regimes656.0ms

Accuracy

0% (1.1b remaining)

Error of 33.8b against oracle of 32.7b and baseline of 33.8b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
0	8

end0.0ms

sample22.2s

Algorithm

intervals

Results

12.0s	2646×	body	10240	exit
6.3s	2367×	body	1280	valid
2.1s	1564×	body	640	valid
663.0ms	870×	body	320	valid
542.0ms	2758×	body	80	valid
214.0ms	433×	body	160	valid
35.0ms	5×	body	5120	valid
8.0ms	3×	body	2560	valid