Details

sample1.2s

Algorithm

intervals

Results

575.0ms	99×	body	10240	exit
208.0ms	66×	body	1280	valid
195.0ms	99×	body	80	valid
95.0ms	62×	body	640	valid
12.0ms	17×	body	320	valid
5.0ms	12×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize105.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
0.5b	(sin (expm1 a))
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`expm1-udef`
2×	`expm1-log1p`
1×	`sin-diff`

Counts

4 → 41

Calls

4 calls:

1.0ms	(expm1 a)
1.0ms	(expm1 (sin (expm1 a)))
8.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series374.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(expm1 a)
182.0ms	(expm1 (sin (expm1 a)))
147.0ms	(sin (expm1 a))
16.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.7s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
5	3918
4	1687
3	638
2	252
1	131
0	73

prune599.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.7b

localize132.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (expm1 a))
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

Calls

4 calls:

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

series148.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(sin (expm1 a))
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify6.4s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
7	3240
6	1914
5	957
4	458
3	216
2	106
1	71
0	44

prune771.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 30.5b

localize170.0ms

Local error

Found 4 expressions with local error:

35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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

series21.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify5.7s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
9	1146
8	356
7	152
6	81
5	51
4	32
3	24
2	19
1	17
0	16

prune701.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 30.5b

localize228.0ms

Local error

Found 4 expressions with local error:

35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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

series23.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify6.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
9	1146
8	356
7	152
6	81
5	51
4	32
3	24
2	19
1	17
0	16

prune550.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 30.5b

regimes617.0ms

Accuracy

0% (1.1b remaining)

Error of 33.6b against oracle of 32.5b and baseline of 33.6b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample28.7s

Algorithm

intervals

Results

14.9s	2650×	body	10240	exit
8.9s	2305×	body	1280	valid
2.6s	1602×	body	640	valid
787.0ms	850×	body	320	valid
622.0ms	2781×	body	80	valid
210.0ms	458×	body	160	valid
18.0ms	2×	body	5120	valid
7.0ms	2×	body	2560	valid