Details

sample409.0ms

Algorithm

intervals

Results

214.0ms	86×	body	10240	exit
117.0ms	65×	body	1280	valid
44.0ms	62×	body	640	valid
9.0ms	87×	body	80	valid
8.0ms	27×	body	320	valid
3.0ms	15×	body	160	valid

simplify1.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
39.1b	(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	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series68.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
61.0ms	(sin (expm1 a))
2.0ms	(expm1 (sin (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify976.0ms

Counts

40 → 40

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	70	293
5	101	293
6	176	293
7	436	293
8	1564	293
done	5001	293

prune156.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.7b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.1b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
2.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
0.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series39.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(expm1 (sin (expm1 a)))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
32.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: 3 (377.0ms)

Iter	Nodes	Cost
0	67	979
1	114	804
2	286	704
3	1997	696
done	5001	696

prune193.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 32.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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:

1.0ms	(cbrt (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)

series128.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.6s

Counts

44 → 44

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	26	591
1	35	587
2	63	473
3	117	470
4	434	470
5	2941	470
done	5001	470

prune213.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 32.5b

localize21.0ms

Local error

Found 4 expressions with local error:

39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.1b	(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)

series11.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.4s

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	59	436
7	125	436
8	406	436
9	1820	436
done	5000	436

prune156.0ms

Pruning

21 alts after pruning (18 fresh and 3 done)

Merged error: 32.5b

regimes290.0ms

Accuracy

0% (1.6b remaining)

Error of 33.6b against oracle of 32.0b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
done	11	13

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.5s	2614×	body	10240	exit
3.8s	2273×	body	1280	valid
1.1s	1654×	body	640	valid
274.0ms	846×	body	320	valid
264.0ms	2798×	body	80	valid
84.0ms	420×	body	160	valid
32.0ms	7×	body	5120	valid
4.0ms	2×	body	2560	valid