Details

sample384.0ms

Algorithm

intervals

Results

177.0ms	70×	body	10240	exit
131.0ms	79×	body	1280	valid
44.0ms	57×	body	640	valid
9.0ms	87×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	8×	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: 34.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
40.0b	(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	(expm1 (sin (expm1 a)))
1.0ms	(sin (expm1 a))
0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series150.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(expm1 (sin (expm1 a)))
61.0ms	(sin (expm1 a))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.3s

Counts

51 → 51

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	70	438
1	110	422
2	234	375
3	622	374
4	2475	374
done	5001	374

prune220.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

6.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (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)

series146.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (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)

simplify1.1s

Counts

81 → 81

Iterations

Useful iterations: 3 (192.0ms)

Iter	Nodes	Cost
0	57	1571
1	95	1418
2	301	1302
3	1091	1115
done	5000	1115

prune335.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 33.2b

localize23.0ms

Local error

Found 4 expressions with local error:

40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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)

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

prune299.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 33.2b

localize27.0ms

Local error

Found 4 expressions with local error:

40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(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)

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

prune238.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 33.2b

regimes232.0ms

Accuracy

0% (1.3b remaining)

Error of 33.7b against oracle of 32.4b and baseline of 33.7b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	12	33
done	12	33

end0.0ms

sample12.7s

Algorithm

intervals

Results

6.7s	2596×	body	10240	exit
4.0s	2359×	body	1280	valid
1.1s	1645×	body	640	valid
285.0ms	2776×	body	80	valid
280.0ms	814×	body	320	valid
86.0ms	402×	body	160	valid
9.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid