Details

sample870.0ms

Algorithm

intervals

Results

403.0ms	83×	body	10240	exit
238.0ms	64×	body	1280	valid
68.0ms	64×	body	640	valid
17.0ms	93×	body	80	valid
12.0ms	21×	body	320	valid
5.0ms	14×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite37.0ms

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:

3.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series100.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(sin (expm1 a))
2.0ms	(expm1 (sin (expm1 a)))
14.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

Counts

30 → 30

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	28	238
1	31	238
2	35	206
3	44	206
4	56	206
5	80	206
6	137	206
7	342	206
8	1219	206
done	5000	206

prune193.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 32.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

3.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series226.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
6.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.0s

Counts

44 → 44

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	26	591
1	35	587
2	63	473
3	117	470
4	434	470
5	2941	470
done	5001	470

prune305.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 32.0b

localize35.0ms

Local error

Found 4 expressions with local error:

37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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`

Counts

4 → 28

Calls

4 calls:

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

series21.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.0s

Counts

40 → 40

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	38	436
6	59	436
7	125	436
8	406	436
9	1820	436
done	5000	436

prune300.0ms

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 32.0b

localize57.0ms

Local error

Found 4 expressions with local error:

37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.8b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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`

Counts

4 → 28

Calls

4 calls:

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

series17.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.7s

Counts

40 → 40

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	508
1	15	508
2	17	436
3	22	436
4	28	436
5	38	436
6	59	436
7	125	436
8	406	436
9	1820	436
done	5000	436

prune188.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 32.0b

regimes254.0ms

Accuracy

0% (0.8b remaining)

Error of 33.5b against oracle of 32.8b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
done	8	10

end0.0ms

sample14.8s

Algorithm

intervals

Results

7.9s	2556×	body	10240	exit
4.5s	2302×	body	1280	valid
1.3s	1690×	body	640	valid
346.0ms	2786×	body	80	valid
308.0ms	764×	body	320	valid
140.0ms	450×	body	160	valid
15.0ms	3×	body	5120	valid
10.0ms	5×	body	2560	valid