Details

sample811.0ms

Algorithm

intervals

Results

328.0ms	81×	body	10240	exit
210.0ms	72×	body	1280	valid
57.0ms	48×	body	640	valid
26.0ms	38×	body	320	valid
18.0ms	85×	body	80	valid
6.0ms	13×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize40.0ms

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)

rewrite9.0ms

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

series116.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(expm1 (sin (expm1 a)))
100.0ms	(sin (expm1 a))
14.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.4s

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

prune255.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 33.2b

localize49.0ms

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)

rewrite6.0ms

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:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
2.0ms	(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)

series503.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (expm1 (sin (expm1 a))))
186.0ms	(cbrt (expm1 (sin (expm1 a))))
164.0ms	(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)

simplify3.7s

Counts

56 → 56

Iterations

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

prune395.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 32.8b

localize56.0ms

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)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
20×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
6×	`pow1` `add-exp-log` `unswap-sqr`
4×	`add-cbrt-cube` `pow1/3` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-prod-down`
1×	`pow3` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
26.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
2.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
1.0ms	(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)

series498.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (expm1 (sin (expm1 a))))
154.0ms	(* (cbrt (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))
155.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
5.0ms	(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)

simplify2.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5002
4	1772
3	622
2	297
1	131
0	77

prune784.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 32.3b

localize131.0ms

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)

rewrite4.0ms

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:

2.0ms	(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)
1.0ms	(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)

series164.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
5.0ms	(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)
5.0ms	(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)
5.0ms	(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)

simplify4.7s

Counts

51 → 51

Iterations

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

prune500.0ms

Pruning

40 alts after pruning (39 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	24
1	24
0	20

end0.0ms

sample25.8s

Algorithm

intervals

Results

12.5s	2582×	body	10240	exit
8.3s	2296×	body	1280	valid
2.5s	1647×	body	640	valid
1.1s	2678×	body	80	valid
796.0ms	895×	body	320	valid
317.0ms	477×	body	160	valid
37.0ms	5×	body	5120	valid
7.0ms	2×	body	2560	valid