Details

sample712.0ms

Algorithm

intervals

Results

365.0ms	83×	body	10240	exit
166.0ms	75×	body	1280	valid
59.0ms	50×	body	640	valid
16.0ms	99×	body	80	valid
14.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize80.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
36.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
5.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series124.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(expm1 (sin (expm1 a)))
104.0ms	(sin (expm1 a))
16.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.3s

Counts

30 → 30

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	28	238
1	31	238
2	35	206
3	44	206
4	56	206
5	80	206
6	137	206
7	342	206
8	1219	206
done	5000	206

prune229.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 31.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
36.9b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
3.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series521.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt (expm1 (sin (expm1 a))))
166.0ms	(cbrt (expm1 (sin (expm1 a))))
168.0ms	(cbrt (expm1 (sin (expm1 a))))
6.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.5s

Counts

52 → 52

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	31	602
1	40	590
2	69	421
3	130	388
4	345	388
5	1411	388
done	5000	388

prune322.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 30.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
36.9b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

3.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
2.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series521.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
160.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
168.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
9.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify2.8s

Counts

61 → 61

Iterations

Useful iterations: 6 (720.0ms)

Iter	Nodes	Cost
0	40	929
1	54	920
2	78	714
3	120	681
4	195	592
5	482	568
6	1495	550
done	5000	550

prune359.0ms

Pruning

29 alts after pruning (26 fresh and 3 done)

Merged error: 30.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.8b	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
36.9b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (* (cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2)) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

50×	`cbrt-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`unpow2` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
8.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
4.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (* (cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2)) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series515.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
196.0ms	(cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2))
137.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (* (cbrt (pow (cbrt (cbrt (expm1 (sin (expm1 a))))) 2)) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	96	1340
1	160	1204
2	268	1077
3	702	1068
done	5000	1001

prune457.0ms

Pruning

35 alts after pruning (32 fresh and 3 done)

Merged error: 29.8b

regimes1.0s

Accuracy

0% (2.0b remaining)

Error of 33.6b against oracle of 31.5b and baseline of 33.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	38
1	16	38
done	16	38

end0.0ms

sample23.3s

Algorithm

intervals

Results

11.9s	2622×	body	10240	exit
6.8s	2374×	body	1280	valid
2.2s	1607×	body	640	valid
1.2s	2797×	body	80	valid
524.0ms	819×	body	320	valid
144.0ms	398×	body	160	valid
23.0ms	3×	body	5120	valid
6.0ms	2×	body	2560	valid