Details

sample580.0ms

Algorithm

intervals

Results

409.0ms	146×	body	1280	valid
101.0ms	66×	body	640	valid
11.0ms	9×	body	320	valid
8.0ms	29×	body	80	valid
5.0ms	6×	body	160	valid
1.0ms	1×	body	160	nan

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	2642
6	985
5	580
4	386
3	195
2	107
1	58
0	26

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.9b

localize105.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (- phi1 phi2) 2))
2.7b	(cos (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))

rewrite91.0ms

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:

22.0ms	(cos (/ (- phi1 phi2) 2))
27.0ms	(cos (/ (- phi1 phi2) 2))
19.0ms	(sin (/ (- phi1 phi2) 2))
22.0ms	(sin (/ (- phi1 phi2) 2))

series564.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cos (/ (- phi1 phi2) 2))
446.0ms	(cos (/ (- phi1 phi2) 2))
36.0ms	(sin (/ (- phi1 phi2) 2))
45.0ms	(sin (/ (- phi1 phi2) 2))

simplify2.6s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
5	2553
4	858
3	381
2	188
1	101
0	58

prune806.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.6b

localize134.0ms

Local error

Found 4 expressions with local error:

2.8b	(sin (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))
6.7b	(cbrt (* (* (sin (/ (- phi1 phi2) 2)) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

rewrite167.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `sin-diff`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `rem-cbrt-cube` `sin-mult`

Counts

4 → 47

Calls

4 calls:

21.0ms	(sin (/ (- phi1 phi2) 2))
21.0ms	(sin (/ (- phi1 phi2) 2))
20.0ms	(sin (/ (- phi1 phi2) 2))
104.0ms	(cbrt (* (* (sin (/ (- phi1 phi2) 2)) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sin (/ (- phi1 phi2) 2))
33.0ms	(sin (/ (- phi1 phi2) 2))
45.0ms	(sin (/ (- phi1 phi2) 2))
55.0ms	(cbrt (* (* (sin (/ (- phi1 phi2) 2)) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

simplify2.8s

Counts

59 → 59

Iterations

Iter	Nodes
done	5005
6	2125
5	936
4	548
3	271
2	145
1	86
0	55

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.6b

localize133.0ms

Local error

Found 4 expressions with local error:

2.8b	(sin (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))
6.7b	(cbrt (* (* (* (* (cbrt (sin (/ (- phi1 phi2) 2))) (cbrt (sin (/ (- phi1 phi2) 2)))) (cbrt (sin (/ (- phi1 phi2) 2)))) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

rewrite1.4s

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `sin-diff`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 45

Calls

4 calls:

11.0ms	(sin (/ (- phi1 phi2) 2))
11.0ms	(sin (/ (- phi1 phi2) 2))
11.0ms	(sin (/ (- phi1 phi2) 2))
1.4s	(cbrt (* (* (* (* (cbrt (sin (/ (- phi1 phi2) 2))) (cbrt (sin (/ (- phi1 phi2) 2)))) (cbrt (sin (/ (- phi1 phi2) 2)))) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sin (/ (- phi1 phi2) 2))
53.0ms	(sin (/ (- phi1 phi2) 2))
52.0ms	(sin (/ (- phi1 phi2) 2))
38.0ms	(cbrt (* (* (* (* (cbrt (sin (/ (- phi1 phi2) 2))) (cbrt (sin (/ (- phi1 phi2) 2)))) (cbrt (sin (/ (- phi1 phi2) 2)))) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

simplify2.6s

Counts

57 → 57

Iterations

Iter	Nodes
done	5001
6	2486
5	952
4	485
3	262
2	141
1	81
0	50

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.5b

localize173.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (- phi1 phi2) 2))
2.7b	(cos (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))
2.8b	(sin (/ (- phi1 phi2) 2))

rewrite60.0ms

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:

20.0ms	(cos (/ (- phi1 phi2) 2))
11.0ms	(cos (/ (- phi1 phi2) 2))
11.0ms	(sin (/ (- phi1 phi2) 2))
18.0ms	(sin (/ (- phi1 phi2) 2))

series168.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(cos (/ (- phi1 phi2) 2))
43.0ms	(cos (/ (- phi1 phi2) 2))
35.0ms	(sin (/ (- phi1 phi2) 2))
48.0ms	(sin (/ (- phi1 phi2) 2))

simplify3.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
5	2553
4	858
3	381
2	188
1	101
0	58

prune778.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 22.5b

regimes4.2s

Accuracy

0% (0.7b remaining)

Error of 24.8b against oracle of 24.1b and baseline of 24.8b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	41
1	41
0	33

end0.0ms

sample21.1s

Algorithm

intervals

Results

15.5s	4780×	body	1280	valid
3.7s	1934×	body	640	valid
706.0ms	572×	body	80	valid
647.0ms	521×	body	320	valid
122.0ms	194×	body	160	valid
3.0ms	2×	body	640	nan
0.0ms	1×	body	160	nan