Details

sample1.3s

Algorithm

intervals

Results

532.0ms	77×	body	10240	exit
388.0ms	73×	body	1280	valid
143.0ms	55×	body	640	valid
31.0ms	89×	body	80	valid
23.0ms	24×	body	320	valid
12.0ms	15×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
1	8
0	8

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

0.0ms	(expm1 a)
0.0ms	(expm1 (sin (expm1 a)))
5.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series133.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(expm1 a)
2.0ms	(expm1 (sin (expm1 a)))
114.0ms	(sin (expm1 a))
15.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.5s

Counts

44 → 44

Iterations

Iter	Nodes
9	6178
8	1865
7	702
6	318
5	165
4	88
3	59
2	48
1	43
0	39

prune679.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 32.5b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 a))
0.5b	(cbrt (expm1 a))
0.5b	(cbrt (expm1 a))
38.3b	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt (expm1 a))
1.0ms	(cbrt (expm1 a))
2.0ms	(cbrt (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

series465.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (expm1 a))
153.0ms	(cbrt (expm1 a))
163.0ms	(cbrt (expm1 a))
5.0ms	(fmod (atan2 (expm1 (sin (* (* (cbrt (expm1 a)) (cbrt (expm1 a))) (cbrt (expm1 a))))) (atan a)) a)

simplify6.4s

Counts

56 → 56

Iterations

Iter	Nodes
6	7715
5	1353
4	364
3	133
2	76
1	45
0	35

prune956.0ms

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 32.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

2.0ms	(sin (expm1 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)

series79.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.6s

Counts

44 → 44

Iterations

Iter	Nodes
9	2953
8	939
7	361
6	166
5	89
4	50
3	35
2	28
1	25
0	23

prune919.0ms

Pruning

28 alts after pruning (26 fresh and 2 done)

Merged error: 31.8b

localize81.0ms

Local error

Found 4 expressions with local error:

38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.3b	(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` `insert-posit16` `add-log-exp`

Counts

4 → 32

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)

series10.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify8.1s

Counts

44 → 44

Iterations

Iter	Nodes
10	7483
9	1571
8	497
7	195
6	90
5	51
4	31
3	23
2	18
1	16
0	15

prune675.0ms

Pruning

29 alts after pruning (27 fresh and 2 done)

Merged error: 31.8b

regimes684.0ms

Accuracy

0% (1.7b remaining)

Error of 33.5b against oracle of 31.8b and baseline of 33.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample25.6s

Algorithm

intervals

Results

13.0s	2630×	body	10240	exit
7.8s	2298×	body	1280	valid
2.5s	1623×	body	640	valid
821.0ms	860×	body	320	valid
814.0ms	2803×	body	80	valid
235.0ms	409×	body	160	valid
37.0ms	5×	body	5120	valid
7.0ms	2×	body	2560	valid