Details

sample635.0ms

Algorithm

intervals

Results

237.0ms	67×	body	10240	exit
220.0ms	69×	body	1280	valid
55.0ms	52×	body	640	valid
16.0ms	27×	body	320	valid
14.0ms	88×	body	80	valid
7.0ms	20×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize29.0ms

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)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`log1p-expm1-u`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
1×	`expm1-log1p` `expm1-udef`

Counts

2 → 20

Calls

2 calls:

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

series191.0ms

Counts

2 → 6

Calls

2 calls:

147.0ms	(expm1 (sin (expm1 a)))
44.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.2s

Counts

26 → 26

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	40	238
1	64	227
2	125	200
3	261	200
4	515	200
5	1138	200
6	3434	200
done	5000	200

prune241.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.7b

localize41.0ms

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)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

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

series877.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt (expm1 (sin (expm1 a))))
280.0ms	(cbrt (expm1 (sin (expm1 a))))
310.0ms	(cbrt (expm1 (sin (expm1 a))))
4.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify2.2s

Counts

60 → 60

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	52	747
1	89	699
2	160	510
3	293	471
4	682	471
5	2249	471
done	5001	471

prune418.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 32.3b

localize44.0ms

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)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(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 (expm1 (sin (expm1 a))))))) (atan a)) a)

series830.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
259.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
251.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
5.0ms	(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)

simplify4.2s

Counts

69 → 69

Iterations

Useful iterations: 6 (2.3s)

Iter	Nodes	Cost
0	61	1110
1	100	1074
2	167	841
3	292	802
4	544	693
5	1385	663
6	4602	645
done	5001	645

prune591.0ms

Pruning

23 alts after pruning (20 fresh and 3 done)

Merged error: 31.9b

localize56.0ms

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)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 66

Calls

4 calls:

2.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
2.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
2.0ms	(cbrt (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 (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))))) (atan a)) a)

series797.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
239.0ms	(cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))
277.0ms	(cbrt (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 (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (cbrt (cbrt (expm1 (sin (expm1 a))))))))) (atan a)) a)

simplify3.6s

Counts

78 → 78

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	72	1533
1	118	1485
2	219	1195
3	458	1156
4	1010	1024
5	2606	994
done	5000	864

prune508.0ms

Pruning

30 alts after pruning (27 fresh and 3 done)

Merged error: 31.8b

regimes823.0ms

Accuracy

0% (1.8b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample22.1s

Algorithm

intervals

Results

12.2s	2604×	body	10240	exit
5.9s	2252×	body	1280	valid
2.0s	1648×	body	640	valid
668.0ms	2790×	body	80	valid
648.0ms	837×	body	320	valid
228.0ms	470×	body	160	valid
8.0ms	1×	body	5120	valid
6.0ms	2×	body	2560	valid