Details

sample520.0ms

Algorithm

intervals

Results

326.0ms	76×	body	10240	exit
122.0ms	76×	body	1280	valid
36.0ms	54×	body	640	valid
8.0ms	85×	body	80	valid
6.0ms	19×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	20×	body	160	valid
2.0ms	1×	body	2560	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.6b	(sin (expm1 a))
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

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

series163.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
92.0ms	(expm1 (sin (expm1 a)))
67.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.5s

Counts

51 → 51

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	70	438
1	110	422
2	214	375
3	501	374
4	1630	374
5	4913	374
done	5000	374

prune213.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 33.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(sin (expm1 a))
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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:

1.0ms	(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)

series71.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(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)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

49 → 49

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	44	524
1	68	519
2	120	459
3	283	458
4	960	458
5	2504	458
done	5000	458

prune278.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.8b

localize20.0ms

Local error

Found 4 expressions with local error:

38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

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

series9.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify982.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	40	516
6	61	516
7	124	516
8	337	516
9	1271	516
done	5000	516

prune274.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.8b

localize25.0ms

Local error

Found 4 expressions with local error:

38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

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

series9.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify980.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	40	516
6	61	516
7	124	516
8	337	516
9	1271	516
done	5000	516

prune205.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.8b

regimes217.0ms

Accuracy

0% (1.5b remaining)

Error of 33.2b against oracle of 31.7b and baseline of 33.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	102
1	16	102
done	16	102

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.6s	2627×	body	10240	exit
4.0s	2327×	body	1280	valid
1.1s	1618×	body	640	valid
278.0ms	2852×	body	80	valid
266.0ms	798×	body	320	valid
84.0ms	401×	body	160	valid
9.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid