Details

sample698.0ms

Algorithm

intervals

Results

303.0ms	74×	body	10240	exit
209.0ms	65×	body	1280	valid
65.0ms	57×	body	640	valid
17.0ms	97×	body	80	valid
15.0ms	25×	body	320	valid
4.0ms	12×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 29

Calls

3 calls:

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

series211.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
170.0ms	(expm1 (sin (expm1 a)))
36.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.1s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
4	2832
3	619
2	191
1	77
0	49

prune363.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 30.9b

localize45.0ms

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))))
37.0b	(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` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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)

series770.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt (expm1 (sin (expm1 a))))
240.0ms	(cbrt (expm1 (sin (expm1 a))))
248.0ms	(cbrt (expm1 (sin (expm1 a))))
7.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify1.1s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
4	1690
3	576
2	203
1	92
0	52

prune563.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 30.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

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)

series242.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.4s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
4	1143
3	237
2	91
1	42
0	30

prune609.0ms

Pruning

24 alts after pruning (21 fresh and 3 done)

Merged error: 30.6b

localize168.0ms

Local error

Found 4 expressions with local error:

37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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)

series22.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
9	4827
8	944
7	327
6	146
5	66
4	32
3	24
2	19
1	17
0	16

prune396.0ms

Pruning

24 alts after pruning (21 fresh and 3 done)

Merged error: 30.6b

regimes1.4s

Accuracy

0% (1.6b remaining)

Error of 33.5b against oracle of 31.9b and baseline of 33.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample21.8s

Algorithm

intervals

Results

11.3s	2610×	body	10240	exit
6.5s	2248×	body	1280	valid
2.0s	1680×	body	640	valid
861.0ms	2806×	body	80	valid
452.0ms	824×	body	320	valid
200.0ms	435×	body	160	valid
30.0ms	4×	body	5120	valid
8.0ms	3×	body	2560	valid