Details

sample711.0ms

Algorithm

intervals

Results

278.0ms	74×	body	10240	exit
184.0ms	75×	body	1280	valid
72.0ms	99×	body	80	valid
51.0ms	47×	body	640	valid
14.0ms	25×	body	320	valid
4.0ms	10×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.2b	(sin (expm1 a))
35.7b	(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)

series221.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
109.0ms	(expm1 (sin (expm1 a)))
99.0ms	(sin (expm1 a))
10.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify3.6s

Counts

51 → 51

Iterations

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

prune423.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 30.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite13.0ms

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:

4.0ms	(sin (expm1 a))
4.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series147.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sin (expm1 a))
3.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
39.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify4.6s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
7	4799
6	2393
5	1111
4	526
3	284
2	167
1	116
0	77

prune550.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 29.9b

localize105.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

3.0ms	(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)

series74.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
6.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
6.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
5.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify3.8s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
8	3575
7	987
6	364
5	185
4	112
3	77
2	59
1	43
0	34

prune669.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.6b

localize156.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
35.7b	(fmod (log (log (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite5.0ms

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:

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(log (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))
4.0ms	(fmod (log (log (exp (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)

simplify3.7s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
8	2472
7	820
6	375
5	205
4	127
3	97
2	79
1	68
0	57

prune634.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 29.6b

regimes632.0ms

Accuracy

0% (1.7b remaining)

Error of 33.3b against oracle of 31.6b and baseline of 33.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	20

end0.0ms

sample21.4s

Algorithm

intervals

Results

11.7s	2689×	body	10240	exit
5.8s	2260×	body	1280	valid
2.0s	1659×	body	640	valid
993.0ms	2809×	body	80	valid
520.0ms	840×	body	320	valid
150.0ms	426×	body	160	valid
19.0ms	3×	body	5120	valid
7.0ms	3×	body	2560	valid