Details

sample740.0ms

Algorithm

intervals

Results

334.0ms	81×	body	10240	exit
191.0ms	81×	body	1280	valid
52.0ms	12×	body	160	valid
45.0ms	46×	body	640	valid
14.0ms	93×	body	80	valid
12.0ms	24×	body	320	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize40.0ms

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)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

3 → 30

Calls

3 calls:

1.0ms	(expm1 (sin (expm1 a)))
6.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series251.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(expm1 (sin (expm1 a)))
114.0ms	(sin (expm1 a))
18.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.6s

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
5	2055
4	919
3	408
2	188
1	105
0	61

prune348.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 32.1b

localize48.0ms

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)

rewrite36.0ms

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×	`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:

2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
28.0ms	(* (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)

series618.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (sin (expm1 a)))
189.0ms	(cbrt (sin (expm1 a)))
215.0ms	(* (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)

simplify2.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5002
3	1413
2	495
1	201
0	97

prune765.0ms

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 31.4b

localize110.0ms

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)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

2.0ms	(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)

series612.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(cbrt (sin (expm1 a)))
188.0ms	(cbrt (sin (expm1 a)))
192.0ms	(cbrt (sin (expm1 a)))
9.0ms	(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)

simplify2.5s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
4	1474
3	529
2	222
1	104
0	55

prune773.0ms

Pruning

34 alts after pruning (32 fresh and 2 done)

Merged error: 31.3b

localize196.0ms

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)

rewrite79.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `unswap-sqr`
2×	`pow2`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 76

Calls

4 calls:

2.0ms	(cbrt (sin (expm1 a)))
2.0ms	(cbrt (sin (expm1 a)))
71.0ms	(* (* (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)

series652.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt (sin (expm1 a)))
253.0ms	(cbrt (sin (expm1 a)))
196.0ms	(* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a)))))
11.0ms	(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)

simplify2.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
4	2062
3	907
2	430
1	205
0	101

prune640.0ms

Pruning

35 alts after pruning (33 fresh and 2 done)

Merged error: 31.2b

regimes1.2s

Accuracy

0% (1.9b remaining)

Error of 33.8b against oracle of 32.0b and baseline of 33.8b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample22.1s

Algorithm

intervals

Results

11.1s	2585×	body	10240	exit
6.7s	2281×	body	1280	valid
2.3s	1720×	body	640	valid
855.0ms	2763×	body	80	valid
534.0ms	821×	body	320	valid
234.0ms	408×	body	160	valid
23.0ms	4×	body	5120	valid
11.0ms	3×	body	2560	valid