Details

sample885.0ms

Algorithm

intervals

Results

406.0ms	83×	body	10240	exit
279.0ms	73×	body	1280	valid
69.0ms	48×	body	640	valid
24.0ms	97×	body	80	valid
15.0ms	20×	body	320	valid
10.0ms	18×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
36.5b	(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` `insert-posit16` `add-log-exp`

Counts

3 → 24

Calls

3 calls:

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

series21.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
3.0ms	(expm1 (sin (expm1 a)))
15.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.2s

Counts

33 → 33

Iterations

Iter	Nodes
done	2114
9	2114
8	1246
7	493
6	231
5	124
4	69
3	47
2	38
1	34
0	31

prune505.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0b	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.5b	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 74

Calls

4 calls:

12.0ms	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
20.0ms	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
31.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series71.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
46.0ms	(* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
5.0ms	(fmod (cbrt (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	2001
4	2001
3	952
2	449
1	164
0	70

prune1.4s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 30.0b

localize102.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))))
0.7b	(cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
1.0b	(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.5b	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
15×	`add-exp-log`
13×	`add-sqr-sqrt`
9×	`cbrt-prod` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
8×	`pow-prod-down`
7×	`pow1/3` `associate-r` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`swap-sqr` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 75

Calls

4 calls:

25.0ms	(* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))))
96.0ms	(cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
126.0ms	(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series214.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))))
3.0ms	(cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
37.0ms	(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.9s

Counts

87 → 87

Iterations

Iter	Nodes
done	2002
4	2002
3	1636
2	603
1	223
0	97

prune1.5s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 29.9b

localize106.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.5b	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.5b	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.5b	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r`
1×	`associate-l` `*-commutative`

Counts

4 → 46

Calls

4 calls:

109.0ms	(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series55.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
7.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
7.0ms	(fmod (cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify1.6s

Counts

58 → 58

Iterations

Iter	Nodes
done	2015
4	2015
3	1498
2	501
1	143
0	60

prune1.1s

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 29.7b

regimes589.0ms

Accuracy

0% (2.1b remaining)

Error of 33.2b against oracle of 31.1b and baseline of 33.2b

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample25.4s

Algorithm

intervals

Results

13.1s	2593×	body	10240	exit
6.9s	2191×	body	1280	valid
3.3s	1679×	body	640	valid
832.0ms	815×	body	320	valid
704.0ms	2851×	body	80	valid
270.0ms	456×	body	160	valid
23.0ms	3×	body	5120	valid
19.0ms	5×	body	2560	valid