Details

sample729.0ms

Algorithm

intervals

Results

307.0ms	81×	body	10240	exit
221.0ms	81×	body	1280	valid
53.0ms	46×	body	640	valid
50.0ms	12×	body	160	valid
16.0ms	93×	body	80	valid
13.0ms	24×	body	320	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize453.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

0.0ms	(expm1 (sin (expm1 a)))
2.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series121.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(expm1 (sin (expm1 a)))
108.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.5s

Counts

30 → 30

Iterations

Iter	Nodes
done	5004
9	3941
8	1231
7	506
6	246
5	116
4	66
3	44
2	35
1	31
0	28

prune268.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 32.1b

localize46.0ms

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))))
37.9b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
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 → 69

Calls

4 calls:

2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
27.0ms	(* (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)

series864.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt (sin (expm1 a)))
266.0ms	(cbrt (sin (expm1 a)))
302.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify4.5s

Counts

81 → 81

Iterations

Iter	Nodes
done	5006
4	4321
3	977
2	294
1	117
0	63

prune612.0ms

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 31.4b

localize105.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
37.9b	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series755.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (sin (expm1 a)))
245.0ms	(cbrt (sin (expm1 a)))
301.0ms	(cbrt (sin (expm1 a)))
5.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify4.3s

Counts

52 → 52

Iterations

Iter	Nodes
done	5009
5	4519
4	995
3	281
2	118
1	58
0	35

prune653.0ms

Pruning

34 alts after pruning (32 fresh and 2 done)

Merged error: 31.3b

localize137.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (expm1 a)))
0.5b	(cbrt (sin (expm1 a)))
0.6b	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
37.9b	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
18×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`pow1/3`
9×	`-un-lft-identity` `associate-r*` `add-exp-log` `pow-prod-up` `add-cube-cbrt`
6×	`pow-plus`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `unswap-sqr`
2×	`pow2`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
64.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
1.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

series737.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt (sin (expm1 a)))
210.0ms	(cbrt (sin (expm1 a)))
249.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
5.0ms	(fmod (atan2 (expm1 (* (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a)))))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))) (atan a)) a)

simplify2.3s

Counts

80 → 80

Iterations

Iter	Nodes
done	5004
3	1968
2	405
1	156
0	79

prune451.0ms

Pruning

36 alts after pruning (34 fresh and 2 done)

Merged error: 31.2b

regimes1.1s

Accuracy

0% (1.9b remaining)

Error of 33.8b against oracle of 31.9b and baseline of 33.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample22.3s

Algorithm

intervals

Results

11.7s	2585×	body	10240	exit
6.6s	2281×	body	1280	valid
2.0s	1720×	body	640	valid
876.0ms	821×	body	320	valid
629.0ms	2763×	body	80	valid
150.0ms	408×	body	160	valid
27.0ms	4×	body	5120	valid
9.0ms	3×	body	2560	valid