Details

sample1.3s

Algorithm

intervals

Results

650.0ms	81×	body	10240	exit
341.0ms	72×	body	1280	valid
74.0ms	48×	body	640	valid
34.0ms	38×	body	320	valid
33.0ms	85×	body	80	valid
8.0ms	13×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
39.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

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	(expm1 (sin (expm1 a)))
5.0ms	(sin (expm1 a))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series148.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(expm1 (sin (expm1 a)))
130.0ms	(sin (expm1 a))
15.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.2s

Counts

33 → 33

Iterations

Iter	Nodes
done	5018
9	3945
8	1246
7	493
6	231
5	124
4	69
3	47
2	38
1	34
0	31

prune285.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 33.2b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite9.0ms

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` `insert-posit16` `add-log-exp`
3×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt (expm1 (sin (expm1 a))))
2.0ms	(cbrt (expm1 (sin (expm1 a))))
4.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series495.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (expm1 (sin (expm1 a))))
181.0ms	(cbrt (expm1 (sin (expm1 a))))
175.0ms	(cbrt (expm1 (sin (expm1 a))))
5.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify3.3s

Counts

56 → 56

Iterations

Iter	Nodes
done	5004
6	3938
5	1073
4	433
3	136
2	76
1	45
0	33

prune421.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 32.8b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 (sin (expm1 a))))
0.6b	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

141×	`cbrt-prod`
100×	`add-sqr-sqrt`
46×	`unswap-sqr`
36×	`associate-l`
20×	`*-un-lft-identity` `add-cube-cbrt`
15×	`associate-r`
12×	`swap-sqr`
8×	`add-cbrt-cube`
6×	`pow1` `add-exp-log` `*-commutative`
4×	`pow1/3` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow3` `pow-prod-down`
1×	`prod-exp`

Counts

4 → 122

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
59.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
1.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

series475.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (expm1 (sin (expm1 a))))
166.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
162.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify3.9s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
4	3117
3	1031
2	478
1	220
0	125

prune1.2s

Pruning

37 alts after pruning (36 fresh and 1 done)

Merged error: 32.3b

localize128.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
39.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
1×	`pow1/3`

Counts

4 → 39

Calls

4 calls:

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

series147.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
6.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
6.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)
6.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify5.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
7	4818
6	1584
5	563
4	258
3	144
2	82
1	58
0	43

prune511.0ms

Pruning

42 alts after pruning (41 fresh and 1 done)

Merged error: 32.1b

regimes1.4s

Accuracy

0% (2.1b remaining)

Error of 34.2b against oracle of 32.1b and baseline of 34.2b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	23
1	23
0	20

end0.0ms

sample25.8s

Algorithm

intervals

Results

12.3s	2582×	body	10240	exit
7.9s	2296×	body	1280	valid
3.0s	1647×	body	640	valid
1.1s	2678×	body	80	valid
834.0ms	895×	body	320	valid
256.0ms	477×	body	160	valid
37.0ms	5×	body	5120	valid
7.0ms	2×	body	2560	valid