Details

sample509.0ms

Algorithm

intervals

Results

248.0ms	67×	body	10240	exit
126.0ms	69×	body	1280	valid
44.0ms	52×	body	640	valid
12.0ms	27×	body	320	valid
11.0ms	88×	body	80	valid
5.0ms	20×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize20.0ms

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)

rewrite3.0ms

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)

series13.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(expm1 (sin (expm1 a)))
11.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.1s

Counts

20 → 20

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	21	189
1	23	189
2	26	163
3	33	163
4	42	163
5	59	163
6	98	163
7	246	163
8	833	163
9	3625	163
done	5001	163

prune156.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.7b

localize25.0ms

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))))
38.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite6.0ms

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

series513.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (expm1 (sin (expm1 a))))
175.0ms	(cbrt (expm1 (sin (expm1 a))))
154.0ms	(cbrt (expm1 (sin (expm1 a))))
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.4s

Counts

52 → 52

Iterations

Useful iterations: 3 (53.0ms)

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

prune350.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 32.3b

localize45.0ms

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)))))
38.3b	(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)

rewrite6.0ms

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:

1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
1.0ms	(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)

series538.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
181.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
163.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
12.0ms	(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 (759.0ms)

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

prune372.0ms

Pruning

23 alts after pruning (20 fresh and 3 done)

Merged error: 31.9b

localize67.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0b	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
38.3b	(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 (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))))) (atan a)) a)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
13×	`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 → 58

Calls

4 calls:

13.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
4.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
5.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(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 (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))))) (atan a)) a)

series527.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
178.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
188.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
6.0ms	(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 (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))))) (atan a)) a)

simplify3.7s

Counts

70 → 70

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	51	1312
1	70	1294
2	128	1032
3	286	999
4	679	891
5	1680	867
done	5001	757

prune382.0ms

Pruning

30 alts after pruning (27 fresh and 3 done)

Merged error: 31.8b

regimes1.3s

Accuracy

0% (1.8b remaining)

Error of 33.6b against oracle of 31.9b and baseline of 33.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample22.4s

Algorithm

intervals

Results

12.0s	2604×	body	10240	exit
6.3s	2252×	body	1280	valid
2.5s	1648×	body	640	valid
524.0ms	837×	body	320	valid
505.0ms	2790×	body	80	valid
168.0ms	470×	body	160	valid
9.0ms	1×	body	5120	valid
7.0ms	2×	body	2560	valid