Details

sample183.0ms

Algorithm

intervals

Results

73.0ms	255×	body	80	valid
28.0ms	37×	body	640	valid
22.0ms	25×	body	1280	valid
15.0ms	28×	body	320	valid
4.0ms	14×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4415
4	917
3	240
2	69
1	32
0	17

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `add-exp-log`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

104.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
155.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series884.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
53.0ms	(cos (/ (+ phi1 phi2) 2.0))
46.0ms	(cos (/ (+ phi1 phi2) 2.0))
651.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify876.0ms

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
1	1387
0	458

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.5b

localize75.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.2b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite798.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

9.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
760.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cos (/ (+ phi1 phi2) 2.0))
40.0ms	(cos (/ (+ phi1 phi2) 2.0))
53.0ms	(cos (/ (+ phi1 phi2) 2.0))
641.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify600.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
1	1283
0	424

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.5b

localize85.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
36.2b	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))
36.2b	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-l/` `associate-r/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 172

Calls

4 calls:

9.0ms	(cos (/ (+ phi1 phi2) 2.0))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))
53.0ms	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))
91.0ms	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

51.0ms	(cos (/ (+ phi1 phi2) 2.0))
51.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.1s	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))
1.1s	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))

simplify558.0ms

Counts

184 → 184

Iterations

Iter	Nodes
done	5000
1	1241
0	419

prune2.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.5b

localize78.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2.0))
2.9b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(cbrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))
37.2b	(cbrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-l/` `associate-r/`
132×	`cbrt-div`
128×	`frac-times` `frac-add`
6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 168

Calls

4 calls:

9.0ms	(cos (/ (+ phi1 phi2) 2.0))
9.0ms	(cos (/ (+ phi1 phi2) 2.0))
44.0ms	(cbrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))
63.0ms	(cbrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

45.0ms	(cos (/ (+ phi1 phi2) 2.0))
48.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.2s	(cbrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))
1.2s	(cbrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))

simplify625.0ms

Counts

180 → 180

Iterations

Iter	Nodes
done	5001
1	1254
0	425

prune2.6s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 23.4b

regimes2.4s

Accuracy

68.1% (4.7b remaining)

Error of 29.2b against oracle of 24.4b and baseline of 39.3b

bsearch3.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.9s	8331×	body	80	valid
871.0ms	1253×	body	640	valid
777.0ms	758×	body	1280	valid
568.0ms	397×	body	160	valid
352.0ms	722×	body	320	valid