Details

sample864.0ms

Algorithm

intervals

Results

368.0ms	75×	body	10240	exit
261.0ms	64×	body	1280	valid
86.0ms	54×	body	640	valid
25.0ms	35×	body	320	valid
19.0ms	90×	body	80	valid
8.0ms	13×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize41.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 14

Calls

2 calls:

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

series25.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(expm1 (sin (expm1 a)))
22.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

20 → 20

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	21	189
1	23	189
2	26	163
3	33	163
4	48	163
5	115	163
6	275	163
7	652	163
8	2140	163
done	5001	163

prune239.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (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)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

5.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series250.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(cbrt (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)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.9s

Counts

44 → 44

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	26	591
1	38	587
2	85	473
3	228	470
4	1222	470
done	5000	470

prune523.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 32.3b

localize78.0ms

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)

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:

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

series24.0ms

Counts

4 → 12

Calls

4 calls:

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)
7.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts

40 → 40

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	30	436
5	64	436
6	149	436
7	330	436
8	1065	436
done	5000	436

prune584.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.3b

localize99.0ms

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)

rewrite3.0ms

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

simplify2.3s

Counts

40 → 40

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	30	436
5	64	436
6	149	436
7	330	436
8	1065	436
done	5000	436

prune412.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 32.3b

regimes523.0ms

Accuracy

0% (0.8b remaining)

Error of 33.5b against oracle of 32.7b and baseline of 33.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	33
1	12	33
done	12	33

end0.0ms

sample28.4s

Algorithm

intervals

Results

14.4s	2708×	body	10240	exit
8.5s	2271×	body	1280	valid
2.7s	1662×	body	640	valid
1.1s	860×	body	320	valid
743.0ms	2791×	body	80	valid
239.0ms	412×	body	160	valid
11.0ms	3×	body	2560	valid
8.0ms	1×	body	5120	valid