Details

sample155.0ms

Algorithm

intervals

Results

35.0ms	244×	body	80	valid
26.0ms	11×	body	160	valid
26.0ms	44×	body	640	valid
21.0ms	23×	body	1280	valid
12.0ms	28×	body	320	valid

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	238	32
4	742	32
5	1972	32
6	4486	32
done	5001	32

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
39.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite294.0ms

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-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
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:

85.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))
168.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series877.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
51.0ms	(cos (/ (+ phi1 phi2) 2.0))
49.0ms	(cos (/ (+ phi1 phi2) 2.0))
638.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify763.0ms

Counts

147 → 147

Iterations

Useful iterations: done (749.0ms)

Iter	Nodes	Cost
0	455	7854
1	1320	7209
done	5000	6835

prune750.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 28.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
39.2b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
130×	`associate-*l/`
74×	`associate-*r/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `rem-sqrt-square` `sqr-cos` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

14.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
21.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))
228.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
44.0ms	(cos (/ (+ phi1 phi2) 2.0))
689.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts

204 → 204

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	809	14625
1	2355	12593
done	5001	12377

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.5b

localize51.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ phi1 phi2) 2.0))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
39.2b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
39.2b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite796.0ms

Algorithm

rewrite-expression-head

Rules

396×	`flip3--` `flip--`
392×	`frac-times`
276×	`sqrt-div`
272×	`frac-add`
260×	`associate-*l/`
148×	`associate-*r/`
144×	`cos-mult`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 316

Calls

4 calls:

11.0ms	(cos (/ (+ phi1 phi2) 2.0))
14.0ms	(cos (/ (+ phi1 phi2) 2.0))
196.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
512.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

41.0ms	(cos (/ (+ phi1 phi2) 2.0))
38.0ms	(cos (/ (+ phi1 phi2) 2.0))
631.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
623.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.2s

Counts

328 → 328

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	781	28082
1	2296	24190
done	5002	23982

prune2.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 27.5b

localize52.0ms

Local error

Found 4 expressions with local error:

4.6b	(cos (/ (+ phi1 phi2) 2.0))
4.6b	(cos (/ (+ phi1 phi2) 2.0))
40.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
40.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

23.0ms	(cos (/ (+ phi1 phi2) 2.0))
22.0ms	(cos (/ (+ phi1 phi2) 2.0))
129.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
118.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

41.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
768.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
805.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify771.0ms

Counts

180 → 180

Iterations

Useful iterations: done (747.0ms)

Iter	Nodes	Cost
0	434	13262
1	1255	12470
done	5000	12200

prune1.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 27.5b

regimes1.1s

Accuracy

73.4% (3.8b remaining)

Error of 28.7b against oracle of 24.9b and baseline of 39.3b

bsearch5.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	69
1	33	69
done	33	69

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.7s	776×	body	1280	valid
1.5s	8470×	body	80	valid
896.0ms	1295×	body	640	valid
364.0ms	693×	body	320	valid
156.0ms	336×	body	160	valid