Details

sample132.0ms

Algorithm

intervals

Results

46.0ms	42×	body	640	valid
26.0ms	255×	body	80	valid
16.0ms	30×	body	1280	valid
5.0ms	17×	body	320	valid
3.0ms	13×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.0b	(cos (/ (+ phi1 phi2) 2.0))
2.0b	(cos (/ (+ phi1 phi2) 2.0))
34.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite243.0ms

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:

93.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
112.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series837.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
41.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
625.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify574.0ms

Counts

147 → 147

Iterations

Useful iterations: done (563.0ms)

Iter	Nodes	Cost
0	458	7854
1	1387	7191
done	5000	6855

prune878.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.0b	(cos (/ (+ phi1 phi2) 2.0))
2.0b	(cos (/ (+ phi1 phi2) 2.0))
34.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1`
5×	`add-cbrt-cube` `add-exp-log`
4×	`add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

6.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
16.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
164.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series796.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
38.0ms	(cos (/ (+ phi1 phi2) 2.0))
37.0ms	(cos (/ (+ phi1 phi2) 2.0))
645.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify665.0ms

Counts

128 → 128

Iterations

Useful iterations: done (652.0ms)

Iter	Nodes	Cost
0	452	7330
1	1442	6543
done	5000	6371

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.5b

localize48.0ms

Local error

Found 4 expressions with local error:

2.0b	(cos (/ (+ phi1 phi2) 2.0))
2.0b	(cos (/ (+ phi1 phi2) 2.0))
2.0b	(cos (/ (+ phi1 phi2) 2.0))
34.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite235.0ms

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:

16.0ms	(cos (/ (+ phi1 phi2) 2.0))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
180.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cos (/ (+ phi1 phi2) 2.0))
47.0ms	(cos (/ (+ phi1 phi2) 2.0))
47.0ms	(cos (/ (+ phi1 phi2) 2.0))
588.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify593.0ms

Counts

112 → 112

Iterations

Useful iterations: done (580.0ms)

Iter	Nodes	Cost
0	427	7796
1	1284	7316
done	5000	6497

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.5b

localize55.0ms

Local error

Found 4 expressions with local error:

2.0b	(cos (/ (+ phi1 phi2) 2.0))
2.0b	(cos (/ (+ phi1 phi2) 2.0))
2.0b	(cos (/ (+ phi1 phi2) 2.0))
34.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite212.0ms

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:

15.0ms	(cos (/ (+ phi1 phi2) 2.0))
14.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
166.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series789.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cos (/ (+ phi1 phi2) 2.0))
52.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
662.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify575.0ms

Counts

112 → 112

Iterations

Useful iterations: done (567.0ms)

Iter	Nodes	Cost
0	430	8057
1	1305	7280
done	5001	6149

prune816.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.5b

regimes1.4s

Accuracy

70.8% (4.2b remaining)

Error of 29.3b against oracle of 25.1b and baseline of 39.4b

bsearch5.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	69
1	27	69
done	27	69

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.5s	8252×	body	80	valid
1.5s	1308×	body	640	valid
1.2s	827×	body	1280	valid
384.0ms	715×	body	320	valid
112.0ms	391×	body	160	valid