Details

sample921.0ms

Algorithm

intervals

Results

390.0ms	76×	body	10240	exit
259.0ms	68×	body	1280	valid
97.0ms	47×	body	640	valid
59.0ms	100×	body	80	valid
21.0ms	32×	body	320	valid
4.0ms	9×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 30

Calls

3 calls:

1.0ms	(expm1 (sin (expm1 a)))
8.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series252.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(expm1 (sin (expm1 a)))
111.0ms	(sin (expm1 a))
17.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.4s

Counts

39 → 39

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	61	321
1	100	305
2	190	272
3	403	271
4	936	271
5	2429	271
done	5001	271

prune224.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 30.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
35.6b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `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 → 77

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
34.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series662.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (sin (expm1 a)))
227.0ms	(cbrt (sin (expm1 a)))
227.0ms	(* (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)

simplify2.9s

Counts

89 → 89

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	97	1079
1	181	979
2	450	738
3	1338	682
done	5001	676

prune591.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 29.6b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`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

3 → 30

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
3.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series200.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(expm1 (sin (expm1 a)))
64.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.3s

Counts

39 → 39

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	61	321
1	100	305
2	190	272
3	403	271
4	936	271
5	2429	271
done	5001	271

prune340.0ms

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 29.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `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:

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)

series111.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(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)

simplify6.1s

Counts

49 → 49

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	44	524
1	68	519
2	109	459
3	195	458
4	375	458
5	589	458
6	905	458
7	1725	458
8	4340	458
done	5001	458

prune326.0ms

Pruning

30 alts after pruning (28 fresh and 2 done)

Merged error: 29.4b

regimes890.0ms

Accuracy

0% (1.7b remaining)

Error of 33.4b against oracle of 31.7b and baseline of 33.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	21
1	12	21
done	12	21

end0.0ms

sample18.3s

Algorithm

intervals

Results

9.5s	2561×	body	10240	exit
5.6s	2240×	body	1280	valid
1.8s	1705×	body	640	valid
448.0ms	2811×	body	80	valid
405.0ms	833×	body	320	valid
134.0ms	402×	body	160	valid
22.0ms	3×	body	5120	valid
17.0ms	6×	body	2560	valid