Details

sample713.0ms

Algorithm

intervals

Results

423.0ms	139×	body	1280	valid
183.0ms	73×	body	640	valid
67.0ms	23×	body	320	valid
6.0ms	14×	body	80	valid
5.0ms	7×	body	160	valid
1.0ms	1×	body	640	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2020
7	2020
6	985
5	580
4	386
3	195
2	107
1	58
0	26

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.1b

localize74.0ms

Local error

Found 4 expressions with local error:

4.2b	(sin (/ (- phi1 phi2) 2))
4.2b	(sin (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `div-sub` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cos-diff` `sin-diff`

Counts

4 → 44

Calls

4 calls:

7.0ms	(sin (/ (- phi1 phi2) 2))
7.0ms	(sin (/ (- phi1 phi2) 2))
7.0ms	(cos (/ (- phi1 phi2) 2))
7.0ms	(cos (/ (- phi1 phi2) 2))

series142.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sin (/ (- phi1 phi2) 2))
40.0ms	(sin (/ (- phi1 phi2) 2))
29.0ms	(cos (/ (- phi1 phi2) 2))
28.0ms	(cos (/ (- phi1 phi2) 2))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
5	2001
4	859
3	384
2	188
1	101
0	58

prune788.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.8b

localize102.0ms

Local error

Found 4 expressions with local error:

4.2b	(sin (/ (- phi1 phi2) 2))
4.2b	(sin (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `div-sub` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cos-diff` `sin-diff`

Counts

4 → 44

Calls

4 calls:

7.0ms	(sin (/ (- phi1 phi2) 2))
7.0ms	(sin (/ (- phi1 phi2) 2))
13.0ms	(cos (/ (- phi1 phi2) 2))
7.0ms	(cos (/ (- phi1 phi2) 2))

series433.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sin (/ (- phi1 phi2) 2))
317.0ms	(sin (/ (- phi1 phi2) 2))
35.0ms	(cos (/ (- phi1 phi2) 2))
35.0ms	(cos (/ (- phi1 phi2) 2))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
5	2001
4	859
3	384
2	188
1	101
0	58

prune823.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 25.8b

localize167.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

4×	`cos-diff` `add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `div-sub` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

7.0ms	(cos (/ (- phi1 phi2) 2))
7.0ms	(cos (/ (- phi1 phi2) 2))
10.0ms	(cos (/ (- phi1 phi2) 2))
23.0ms	(cos (/ (- phi1 phi2) 2))

series125.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cos (/ (- phi1 phi2) 2))
38.0ms	(cos (/ (- phi1 phi2) 2))
27.0ms	(cos (/ (- phi1 phi2) 2))
32.0ms	(cos (/ (- phi1 phi2) 2))

simplify968.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
6	2000
5	1083
4	396
3	202
2	107
1	60
0	36

prune932.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.8b

localize199.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))
4.2b	(cos (/ (- phi1 phi2) 2))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

4×	`cos-diff` `add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `div-sub` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

14.0ms	(cos (/ (- phi1 phi2) 2))
15.0ms	(cos (/ (- phi1 phi2) 2))
12.0ms	(cos (/ (- phi1 phi2) 2))
22.0ms	(cos (/ (- phi1 phi2) 2))

series120.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (/ (- phi1 phi2) 2))
32.0ms	(cos (/ (- phi1 phi2) 2))
25.0ms	(cos (/ (- phi1 phi2) 2))
38.0ms	(cos (/ (- phi1 phi2) 2))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
6	2000
5	1083
4	396
3	202
2	107
1	60
0	36

prune899.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.8b

regimes3.5s

Accuracy

0% (0.5b remaining)

Error of 24.2b against oracle of 23.7b and baseline of 24.2b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample26.7s

Algorithm

intervals

Results

19.0s	4744×	body	1280	valid
5.5s	1927×	body	640	valid
941.0ms	518×	body	320	valid
587.0ms	212×	body	160	valid
277.0ms	600×	body	80	valid
2.0ms	1×	body	640	nan
2.0ms	1×	body	320	nan
0.0ms	1×	body	80	nan