Details

sample421.0ms

Algorithm

intervals

Results

231.0ms	94×	body	10240	exit
118.0ms	77×	body	1280	valid
38.0ms	51×	body	640	valid
9.0ms	30×	body	320	valid
8.0ms	85×	body	80	valid
3.0ms	13×	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: 34.2b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 29

Calls

3 calls:

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

series98.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
92.0ms	(expm1 (sin (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify51.0ms

Counts

38 → 38

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	73	248
1	147	216
2	421	216
3	1258	216
4	5001	216
done	5001	216

prune157.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
39.5b	(fmod (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 (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)

series128.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify253.0ms

Counts

52 → 52

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	38	471
1	67	393
2	144	391
3	589	391
4	4672	391
5	5001	391
done	5001	391

prune241.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 33.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

series11.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify95.0ms

Counts

48 → 48

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	408
1	19	356
2	23	356
3	28	356
4	47	356
5	101	356
6	507	356
7	1681	356
8	5001	356
done	5001	356

prune264.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 33.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

series11.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify95.0ms

Counts

48 → 48

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	408
1	19	356
2	23	356
3	28	356
4	47	356
5	101	356
6	507	356
7	1681	356
8	5001	356
done	5001	356

prune222.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 33.0b

regimes206.0ms

Accuracy

0% (1.2b remaining)

Error of 33.8b against oracle of 32.6b and baseline of 33.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	12	24
done	12	24

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.4s	2556×	body	10240	exit
3.8s	2297×	body	1280	valid
1.1s	1704×	body	640	valid
266.0ms	816×	body	320	valid
261.0ms	2744×	body	80	valid
87.0ms	434×	body	160	valid
18.0ms	4×	body	5120	valid
2.0ms	1×	body	2560	valid