Details

sample704.0ms

Algorithm

intervals

Results

342.0ms	90×	body	10240	exit
206.0ms	66×	body	1280	valid
69.0ms	70×	body	640	valid
14.0ms	86×	body	80	valid
11.0ms	18×	body	320	valid
6.0ms	16×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize477.0ms

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))
39.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite11.0ms

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))
1.0ms	(expm1 (sin (expm1 a)))
6.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series318.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
162.0ms	(expm1 (sin (expm1 a)))
134.0ms	(sin (expm1 a))
18.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.3s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
6	4242
5	1814
4	879
3	411
2	200
1	114
0	70

prune529.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 32.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite8.0ms

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:

2.0ms	(sin (expm1 a))
2.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series179.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sin (expm1 a))
61.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify4.0s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
7	4886
6	2399
5	1147
4	532
3	284
2	167
1	115
0	77

prune575.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.4b

localize150.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series13.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify3.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
8	2275
7	662
6	287
5	148
4	92
3	70
2	60
1	53
0	45

prune882.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.2b

localize190.0ms

Local error

Found 4 expressions with local error:

39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
39.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite3.0ms

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

series20.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify4.3s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
9	948
8	286
7	141
6	69
5	47
4	35
3	27
2	22
1	20
0	19

prune449.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.2b

regimes665.0ms

Accuracy

0% (1.7b remaining)

Error of 33.4b against oracle of 31.7b and baseline of 33.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample22.0s

Algorithm

intervals

Results

11.8s	2608×	body	10240	exit
6.6s	2279×	body	1280	valid
1.9s	1648×	body	640	valid
608.0ms	830×	body	320	valid
589.0ms	2819×	body	80	valid
150.0ms	416×	body	160	valid
16.0ms	3×	body	5120	valid
14.0ms	5×	body	2560	valid