Details

sample486.0ms

Algorithm

intervals

Results

331.0ms	146×	body	1280	valid
104.0ms	66×	body	640	valid
9.0ms	9×	body	320	valid
8.0ms	29×	body	80	valid
4.0ms	6×	body	160	valid
1.0ms	1×	body	160	nan

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2160
6	829
5	453
4	319
3	192
2	102
1	58
0	26

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.9b

localize139.0ms

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))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

17.0ms	(cos (/ (- phi1 phi2) 2))
14.0ms	(cos (/ (- phi1 phi2) 2))
22.0ms	(sin (/ (- phi1 phi2) 2))
18.0ms	(sin (/ (- phi1 phi2) 2))

series123.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (/ (- phi1 phi2) 2))
24.0ms	(cos (/ (- phi1 phi2) 2))
31.0ms	(sin (/ (- phi1 phi2) 2))
45.0ms	(sin (/ (- phi1 phi2) 2))

simplify1.9s

Counts

48 → 48

Iterations

Iter	Nodes
done	5009
5	2847
4	760
3	344
2	171
1	94
0	54

prune697.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.6b

localize103.0ms

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))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `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 → 39

Calls

4 calls:

9.0ms	(sin (/ (- phi1 phi2) 2))
11.0ms	(sin (/ (- phi1 phi2) 2))
9.0ms	(sin (/ (- phi1 phi2) 2))
77.0ms	(cbrt (* (* (sin (/ (- phi1 phi2) 2)) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sin (/ (- phi1 phi2) 2))
51.0ms	(sin (/ (- phi1 phi2) 2))
37.0ms	(sin (/ (- phi1 phi2) 2))
32.0ms	(cbrt (* (* (sin (/ (- phi1 phi2) 2)) (sin (/ (- phi1 phi2) 2))) (sin (/ (- phi1 phi2) 2))))

simplify2.8s

Counts

51 → 51

Iterations

Iter	Nodes
done	5002
6	2555
5	958
4	486
3	263
2	133
1	80
0	51

prune900.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.5b

localize124.0ms

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)) (* (* (cbrt (sin (/ (- phi1 phi2) 2))) (cbrt (sin (/ (- phi1 phi2) 2)))) (cbrt (sin (/ (- phi1 phi2) 2))))) (sin (/ (- phi1 phi2) 2))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`div-sub` `sin-diff`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 37

Calls

4 calls:

19.0ms	(sin (/ (- phi1 phi2) 2))
18.0ms	(sin (/ (- phi1 phi2) 2))
18.0ms	(sin (/ (- phi1 phi2) 2))
954.0ms	(cbrt (* (* (sin (/ (- phi1 phi2) 2)) (* (* (cbrt (sin (/ (- phi1 phi2) 2))) (cbrt (sin (/ (- phi1 phi2) 2)))) (cbrt (sin (/ (- phi1 phi2) 2))))) (sin (/ (- phi1 phi2) 2))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sin (/ (- phi1 phi2) 2))
50.0ms	(sin (/ (- phi1 phi2) 2))
33.0ms	(sin (/ (- phi1 phi2) 2))
40.0ms	(cbrt (* (* (sin (/ (- phi1 phi2) 2)) (* (* (cbrt (sin (/ (- phi1 phi2) 2))) (cbrt (sin (/ (- phi1 phi2) 2)))) (cbrt (sin (/ (- phi1 phi2) 2))))) (sin (/ (- phi1 phi2) 2))))

simplify2.8s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
6	2282
5	772
4	410
3	228
2	125
1	75
0	46

prune940.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 22.5b

localize151.0ms

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))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

23.0ms	(cos (/ (- phi1 phi2) 2))
19.0ms	(cos (/ (- phi1 phi2) 2))
18.0ms	(sin (/ (- phi1 phi2) 2))
16.0ms	(sin (/ (- phi1 phi2) 2))

series164.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (- phi1 phi2) 2))
33.0ms	(cos (/ (- phi1 phi2) 2))
50.0ms	(sin (/ (- phi1 phi2) 2))
50.0ms	(sin (/ (- phi1 phi2) 2))

simplify2.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5009
5	2847
4	760
3	344
2	171
1	94
0	54

prune632.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 22.5b

regimes3.9s

Accuracy

0% (0.5b remaining)

Error of 24.6b against oracle of 24.1b and baseline of 24.6b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	41
1	41
0	33

end0.0ms

sample20.7s

Algorithm

intervals

Results

14.4s	4780×	body	1280	valid
4.4s	1934×	body	640	valid
1.1s	521×	body	320	valid
261.0ms	572×	body	80	valid
118.0ms	194×	body	160	valid
2.0ms	2×	body	640	nan
1.0ms	1×	body	160	nan