Details

sample396.0ms

Algorithm

intervals

Results

192.0ms	76×	body	10240	exit
130.0ms	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

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize14.0ms

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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

Calls

4 calls:

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
63.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.2s

Counts

40 → 40

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	70	293
5	101	293
6	180	293
7	413	293
8	1250	293
9	4942	293
done	5000	293

prune162.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.1b

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` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

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)

series63.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(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)

simplify1.7s

Counts

40 → 40

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	21	430
1	23	430
2	26	370
3	33	370
4	42	370
5	59	370
6	100	370
7	218	370
8	638	370
9	2502	370
done	5001	370

prune219.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.9b

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` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `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)

series8.0ms

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)

simplify935.0ms

Counts

40 → 40

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	38	436
6	60	436
7	119	436
8	330	436
9	1257	436
done	5000	436

prune230.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.9b

localize27.0ms

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` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `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)

series8.0ms

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)

simplify935.0ms

Counts

40 → 40

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	38	436
6	60	436
7	119	436
8	330	436
9	1257	436
done	5000	436

prune163.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 32.9b

regimes219.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	15	79
1	18	79
done	18	79

end0.0ms

sample12.1s

Algorithm

intervals

Results

6.4s	2627×	body	10240	exit
3.8s	2327×	body	1280	valid
1.0s	1618×	body	640	valid
263.0ms	2852×	body	80	valid
249.0ms	798×	body	320	valid
79.0ms	401×	body	160	valid
9.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid