Details

sample767.0ms

Algorithm

intervals

Results

362.0ms	74×	body	10240	exit
162.0ms	65×	body	1280	valid
78.0ms	57×	body	640	valid
18.0ms	97×	body	80	valid
16.0ms	25×	body	320	valid
5.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize23.0ms

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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

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

series19.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
11.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.4s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
8	3071
7	934
6	395
5	166
4	66
3	44
2	35
1	31
0	28

prune338.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 30.9b

localize49.0ms

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)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `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))))
4.0ms	(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)

series511.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (expm1 (sin (expm1 a))))
196.0ms	(cbrt (expm1 (sin (expm1 a))))
168.0ms	(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)

simplify6.1s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
5	4467
4	772
3	234
2	93
1	43
0	31

prune397.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 30.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-cbrt-cube` `add-exp-log` `log-pow`
3×	`log-prod`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 40

Calls

4 calls:

0.0ms	(expm1 (sin (expm1 a)))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series48.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(expm1 (sin (expm1 a)))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify845.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
6	1459
5	526
4	249
3	148
2	99
1	67
0	51

prune407.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 30.5b

localize48.0ms

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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `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)

series166.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	1236
3	226
2	85
1	38
0	26

prune259.0ms

Pruning

23 alts after pruning (20 fresh and 3 done)

Merged error: 30.5b

regimes584.0ms

Accuracy

0% (1.7b remaining)

Error of 33.5b against oracle of 31.8b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample22.4s

Algorithm

intervals

Results

11.2s	2610×	body	10240	exit
6.6s	2248×	body	1280	valid
1.9s	1680×	body	640	valid
952.0ms	824×	body	320	valid
689.0ms	435×	body	160	valid
592.0ms	2806×	body	80	valid
27.0ms	4×	body	5120	valid
10.0ms	3×	body	2560	valid