Details

sample371.0ms

Algorithm

intervals

Results

178.0ms	70×	body	10240	exit
128.0ms	79×	body	1280	valid
35.0ms	57×	body	640	valid
8.0ms	87×	body	80	valid
8.0ms	25×	body	320	valid
1.0ms	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

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 (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)

series66.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
60.0ms	(sin (expm1 a))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.6s

Counts

40 → 40

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	35	339
1	39	339
2	44	293
3	55	293
4	70	293
5	111	293
6	222	293
7	612	293
8	2064	293
done	5001	293

prune162.0ms

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×	`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:

5.0ms	(* (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)

series151.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (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)

simplify1.3s

Counts

73 → 73

Iterations

Useful iterations: 3 (166.0ms)

Iter	Nodes	Cost
0	53	1467
1	89	1310
2	243	1198
3	976	1027
done	5000	1027

prune285.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 33.2b

localize20.0ms

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` `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)

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)

simplify1.5s

Counts

40 → 40

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	48	436
6	105	436
7	330	436
8	1161	436
done	5000	436

prune245.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 33.2b

localize24.0ms

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)

rewrite1.0ms

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)

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)

simplify1.5s

Counts

40 → 40

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	48	436
6	105	436
7	330	436
8	1161	436
done	5000	436

prune180.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 33.2b

regimes233.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.5s	2596×	body	10240	exit
3.9s	2359×	body	1280	valid
1.1s	1645×	body	640	valid
261.0ms	814×	body	320	valid
259.0ms	2776×	body	80	valid
86.0ms	402×	body	160	valid
9.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid