Details

sample709.0ms

Algorithm

intervals

Results

350.0ms	97×	body	10240	exit
144.0ms	64×	body	1280	valid
67.0ms	64×	body	640	valid
47.0ms	1×	body	5120	valid
19.0ms	32×	body	320	valid
14.0ms	84×	body	80	valid
3.0ms	11×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms	(expm1 (sin (expm1 a)))
8.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series220.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
130.0ms	(expm1 (sin (expm1 a)))
76.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.8s

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
3	1239
2	311
1	114
0	70

prune462.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 33.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(sin (expm1 a))
40.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `sin-diff` `expm1-udef` `rem-exp-log`

Counts

4 → 49

Calls

4 calls:

5.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(sin (expm1 a))
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series169.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
56.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
100.0ms	(sin (expm1 a))
6.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify860.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	773
2	238
1	116
0	77

prune406.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 33.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
1×	`sin-diff` `expm1-udef`

Counts

4 → 37

Calls

4 calls:

2.0ms	(sin (expm1 a))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series91.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sin (expm1 a))
3.0ms	(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)

simplify5.6s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4871
3	673
2	166
1	71
0	44

prune600.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 33.3b

localize86.0ms

Local error

Found 4 expressions with local error:

40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

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

series11.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify4.3s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
9	4827
8	944
7	327
6	146
5	66
4	32
3	24
2	19
1	17
0	16

prune326.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 33.3b

regimes679.0ms

Accuracy

0% (1.6b remaining)

Error of 33.6b against oracle of 31.9b and baseline of 33.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample19.3s

Algorithm

intervals

Results

9.7s	2578×	body	10240	exit
6.1s	2340×	body	1280	valid
2.1s	1624×	body	640	valid
497.0ms	2786×	body	80	valid
391.0ms	824×	body	320	valid
136.0ms	420×	body	160	valid
21.0ms	3×	body	5120	valid
8.0ms	3×	body	2560	valid