Details

sample442.0ms

Algorithm

intervals

Results

234.0ms	95×	body	10240	exit
133.0ms	79×	body	1280	valid
44.0ms	57×	body	640	valid
8.0ms	86×	body	80	valid
6.0ms	20×	body	320	valid
3.0ms	14×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7
done	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series155.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
60.0ms	(sin (expm1 a))
90.0ms	(expm1 (sin (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify124.0ms

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2934	264
4	5001	264
done	5001	264

prune193.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.5b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (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 (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series335.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
110.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
113.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify92.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	42	714
1	72	632
2	149	626
3	483	611
4	2459	611
5	5002	611
done	5002	611

prune258.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.5b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (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 (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series336.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
107.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
114.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify49.0ms

Counts

60 → 60

Iterations

Useful iterations: 4 (43.0ms)

Iter	Nodes	Cost
0	60	771
1	112	685
2	302	679
3	1175	679
4	5001	676
done	5001	676

prune296.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 32.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
39.5b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
39.5b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
39.5b	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
0.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series128.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
7.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
7.0ms	(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify55.0ms

Counts

52 → 52

Iterations

Useful iterations: 4 (44.0ms)

Iter	Nodes	Cost
0	60	1161
1	112	1007
2	302	1005
3	1175	1005
4	5001	1004
done	5001	1004

prune269.0ms

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 32.6b

regimes309.0ms

Accuracy

0% (1.7b remaining)

Error of 33.8b against oracle of 32.1b and baseline of 33.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	126
1	21	126
done	21	126

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.7s	2668×	body	10240	exit
3.8s	2276×	body	1280	valid
1.1s	1668×	body	640	valid
282.0ms	882×	body	320	valid
273.0ms	2764×	body	80	valid
82.0ms	401×	body	160	valid
23.0ms	5×	body	5120	valid
8.0ms	4×	body	2560	valid