Details

sample378.0ms

Algorithm

intervals

Results

190.0ms	76×	body	10240	exit
121.0ms	68×	body	1280	valid
33.0ms	47×	body	640	valid
10.0ms	100×	body	80	valid
10.0ms	32×	body	320	valid
2.0ms	9×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7
done	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize18.0ms

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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 21

Calls

3 calls:

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

series64.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(expm1 (sin (expm1 a)))
59.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify110.0ms

Counts

30 → 30

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	173
1	35	148
2	43	148
3	54	148
4	91	148
5	185	148
6	781	148
7	2680	148
8	5001	148
done	5001	148

prune121.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 30.3b

localize17.0ms

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)

rewrite21.0ms

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×	`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:

1.0ms	(cbrt (sin (expm1 a)))
1.0ms	(cbrt (sin (expm1 a)))
16.0ms	(* (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)

series535.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (sin (expm1 a)))
174.0ms	(cbrt (sin (expm1 a)))
193.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify78.0ms

Counts

81 → 81

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	99	673
1	366	578
2	2587	543
3	5002	526
done	5002	526

prune347.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 29.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
35.5b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite21.0ms

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`
3×	`cbrt-prod` `pow1/3`

Counts

4 → 34

Calls

4 calls:

7.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
7.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
7.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series577.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
192.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
189.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify91.0ms

Counts

46 → 46

Iterations

Useful iterations: 5 (86.0ms)

Iter	Nodes	Cost
0	45	698
1	70	578
2	141	572
3	323	572
4	1214	572
5	5001	544
done	5001	544

prune301.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 29.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a)))))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.8b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
35.5b	(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-prod`
23×	`add-sqr-sqrt`
16×	`pow1`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
11×	`add-exp-log`
10×	`pow1/3`
7×	`associate-l` `pow-prod-down`
6×	`swap-sqr`
5×	`add-cbrt-cube`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 81

Calls

4 calls:

49.0ms	(* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a)))))
13.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
7.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series574.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a)))))
189.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
187.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify39.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	208	1246
1	964	1074
2	5001	991
done	5001	991

prune331.0ms

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 29.2b

regimes632.0ms

Accuracy

0% (2.0b remaining)

Error of 33.5b against oracle of 31.5b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	38
1	23	38
done	23	38

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.4s	2561×	body	10240	exit
3.8s	2240×	body	1280	valid
1.2s	1705×	body	640	valid
292.0ms	2811×	body	80	valid
269.0ms	833×	body	320	valid
86.0ms	402×	body	160	valid
14.0ms	3×	body	5120	valid
12.0ms	6×	body	2560	valid