Details

sample394.0ms

Algorithm

intervals

Results

192.0ms	76×	body	10240	exit
127.0ms	76×	body	1280	valid
37.0ms	54×	body	640	valid
8.0ms	85×	body	80	valid
6.0ms	19×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	20×	body	160	valid
2.0ms	1×	body	2560	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

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)))
0.6b	(sin (expm1 a))
38.7b	(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)

series158.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
88.0ms	(expm1 (sin (expm1 a)))
65.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.5s

Counts

51 → 51

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	70	438
1	110	422
2	236	375
3	624	374
4	2488	374
done	5001	374

prune212.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 33.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(sin (expm1 a))
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(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)

series67.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sin (expm1 a))
4.0ms	(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)

simplify1.2s

Counts

49 → 49

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	44	524
1	68	519
2	125	459
3	316	458
4	1175	458
done	5000	458

prune279.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.8b

localize21.0ms

Local error

Found 4 expressions with local error:

38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(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)

simplify1.7s

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	53	516
6	111	516
7	426	516
8	1290	516
done	5001	516

prune271.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.8b

localize22.0ms

Local error

Found 4 expressions with local error:

38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.7b	(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)

simplify1.7s

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	53	516
6	111	516
7	426	516
8	1290	516
done	5001	516

prune209.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 32.8b

regimes238.0ms

Accuracy

0% (1.5b remaining)

Error of 33.2b against oracle of 31.7b and baseline of 33.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	102
1	20	102
done	20	102

end0.0ms

sample12.8s

Algorithm

intervals

Results

6.7s	2627×	body	10240	exit
4.0s	2327×	body	1280	valid
1.1s	1618×	body	640	valid
303.0ms	2852×	body	80	valid
284.0ms	798×	body	320	valid
97.0ms	401×	body	160	valid
9.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid