Details

sample409.0ms

Algorithm

intervals

Results

222.0ms	86×	body	10240	exit
108.0ms	62×	body	1280	valid
41.0ms	62×	body	640	valid
9.0ms	93×	body	80	valid
8.0ms	24×	body	320	valid
5.0ms	1×	body	5120	valid
3.0ms	14×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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

series151.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
85.0ms	(expm1 (sin (expm1 a)))
62.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.3s

Counts

51 → 51

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	70	438
1	110	422
2	206	375
3	429	374
4	1100	374
5	3065	374
done	5001	374

prune200.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 31.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(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`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

Calls

4 calls:

1.0ms	(sin (expm1 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)

series65.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.3s

Counts

49 → 49

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	44	524
1	68	519
2	108	459
3	201	458
4	576	458
5	1614	458
done	5000	458

prune274.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.1b

localize21.0ms

Local error

Found 4 expressions with local error:

37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(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)

series9.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.5s

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	40	516
6	61	516
7	124	516
8	337	516
9	1272	516
done	5000	516

prune266.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.1b

localize22.0ms

Local error

Found 4 expressions with local error:

37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.1b	(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)

series8.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.5s

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	16	588
1	17	588
2	19	516
3	24	516
4	30	516
5	40	516
6	61	516
7	124	516
8	337	516
9	1272	516
done	5000	516

prune215.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 31.1b

regimes213.0ms

Accuracy

0% (1.5b remaining)

Error of 33.0b against oracle of 31.6b and baseline of 33.0b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	79
1	17	79
done	17	79

end0.0ms

sample12.4s

Algorithm

intervals

Results

6.7s	2645×	body	10240	exit
3.7s	2236×	body	1280	valid
1.1s	1665×	body	640	valid
288.0ms	2870×	body	80	valid
273.0ms	815×	body	320	valid
85.0ms	410×	body	160	valid
9.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid