Details

sample441.0ms

Algorithm

intervals

Results

239.0ms	95×	body	10240	exit
132.0ms	79×	body	1280	valid
40.0ms	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))
1.0ms	(expm1 (sin (expm1 a)))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series161.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
62.0ms	(sin (expm1 a))
93.0ms	(expm1 (sin (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify126.0ms

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

prune205.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.0b

localize16.0ms

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)

series354.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
121.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
115.0ms	(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)

simplify93.0ms

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

prune268.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.7b

localize24.0ms

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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series130.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(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)
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)
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)

simplify90.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	42	990
1	72	848
2	149	846
3	483	801
4	2459	801
5	5002	801
done	5002	801

prune320.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 32.4b

localize35.0ms

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)))) (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)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite3.0ms

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)))) (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)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series132.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
8.0ms	(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)
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)
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)

simplify51.0ms

Counts

52 → 52

Iterations

Useful iterations: 4 (44.0ms)

Iter	Nodes	Cost
0	72	1023
1	124	881
2	314	879
3	1187	834
4	5001	833
done	5001	833

prune286.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 32.4b

regimes311.0ms

Accuracy

0% (1.8b remaining)

Error of 33.7b against oracle of 31.9b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	71
1	22	71
done	22	71

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.6s	2668×	body	10240	exit
3.8s	2276×	body	1280	valid
1.1s	1668×	body	640	valid
282.0ms	882×	body	320	valid
265.0ms	2764×	body	80	valid
86.0ms	401×	body	160	valid
23.0ms	5×	body	5120	valid
8.0ms	4×	body	2560	valid