Details

sample1.1s

Algorithm

intervals

Results

521.0ms	92×	body	10240	exit
272.0ms	72×	body	1280	valid
93.0ms	51×	body	640	valid
81.0ms	89×	body	80	valid
35.0ms	1×	body	2560	valid
19.0ms	30×	body	320	valid
7.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 a)
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

Calls

4 calls:

0.0ms	(expm1 a)
0.0ms	(expm1 (sin (expm1 a)))
3.0ms	(sin (expm1 a))
34.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series81.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(expm1 a)
2.0ms	(expm1 (sin (expm1 a)))
65.0ms	(sin (expm1 a))
12.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

40 → 40

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	35	274
1	39	274
2	44	238
3	55	238
4	84	238
5	217	238
6	519	238
7	1209	238
8	4017	238
done	5001	238

prune226.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

Calls

4 calls:

2.0ms	(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)

series89.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sin (expm1 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)

simplify1.5s

Counts

40 → 40

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	21	430
1	23	430
2	26	370
3	33	370
4	48	370
5	115	370
6	275	370
7	652	370
8	2140	370
done	5001	370

prune374.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.7b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.4b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite22.0ms

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×	`add-cbrt-cube` `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 → 61

Calls

4 calls:

19.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (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)

series297.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
4.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (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)

simplify7.0s

Counts

73 → 73

Iterations

Useful iterations: done (7.0s)

Iter	Nodes	Cost
0	68	1007
1	124	934
2	467	760
3	3499	691
done	5000	675

prune681.0ms

Pruning

28 alts after pruning (26 fresh and 2 done)

Merged error: 32.4b

localize107.0ms

Local error

Found 4 expressions with local error:

38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 28

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)

series12.0ms

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)

simplify1.7s

Counts

40 → 40

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	30	436
5	64	436
6	149	436
7	330	436
8	1065	436
done	5000	436

prune382.0ms

Pruning

28 alts after pruning (26 fresh and 2 done)

Merged error: 32.4b

regimes969.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	90
1	24	90
done	24	90

end0.0ms

sample22.2s

Algorithm

intervals

Results

11.5s	2608×	body	10240	exit
6.2s	2319×	body	1280	valid
2.4s	1671×	body	640	valid
876.0ms	2766×	body	80	valid
508.0ms	807×	body	320	valid
151.0ms	430×	body	160	valid
20.0ms	3×	body	5120	valid
13.0ms	4×	body	2560	valid