Details

sample117.0ms

Algorithm

intervals

Results

35.0ms	295×	body	80	valid
20.0ms	29×	body	1280	valid
17.0ms	36×	body	640	valid
9.0ms	28×	body	320	valid
4.0ms	18×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	177	32
4	414	32
5	1014	32
6	3312	32
done	5001	32

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.0b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
35.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite62.0ms

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:

14.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
156.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify583.0ms

Counts

147 → 147

Iterations

Useful iterations: done (574.0ms)

Iter	Nodes	Cost
0	454	7854
1	1182	7191
done	5001	7065

prune280.0ms

Filtered

76 candidates to 147 candidates (-93.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	7	148

Merged error: 25.3b

Counts

148 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

3.6b	(cos (/ (+ phi1 phi2) 2.0))
35.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

384×	`associate-*l/`
288×	`flip3--` `flip--`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
96×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 244

Calls

4 calls:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
22.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2.0))
150.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
152.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
150.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.3s

Counts

256 → 256

Iterations

Useful iterations: 2 (434.0ms)

Iter	Nodes	Cost
0	417	19757
1	1080	18383
2	4990	17930
done	5000	17930

prune996.0ms

Filtered

129 candidates to 256 candidates (-98.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	256	7	263

Merged error: 25.3b

Counts

263 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
6.0b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
35.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `exp-diff`
64×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`log-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

4 → 179

Calls

4 calls:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
153.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
155.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify436.0ms

Counts

191 → 191

Iterations

Useful iterations: done (422.0ms)

Iter	Nodes	Cost
0	656	13899
1	1326	12673
done	5000	12589

prune397.0ms

Filtered

97 candidates to 191 candidates (-96.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	188	10	198

Merged error: 25.3b

Counts

198 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

3.6b	(cos (/ (+ phi1 phi2) 2.0))
5.4b	(pow (exp (sqrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))) (sqrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))))))
35.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
18×	`sqrt-prod`
13×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow-pow`
9×	`pow-unpow` `exp-prod`
6×	`log-pow`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
2×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 197

Calls

4 calls:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.0ms	(pow (exp (sqrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))) (sqrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))))))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
20.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series746.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
437.0ms	(pow (exp (sqrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))) (sqrt (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))))))
153.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
152.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify429.0ms

Counts

209 → 209

Iterations

Useful iterations: 1 (128.0ms)

Iter	Nodes	Cost
0	473	15710
1	1192	14442
done	5000	14442

prune747.0ms

Filtered

112 candidates to 209 candidates (-86.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	207	12	219

Merged error: 21.0b

Counts

219 → 12

regimes1.7s

Accuracy

16.2% (15.5b remaining)

Error of 36.5b against oracle of 21.0b and baseline of 39.5b

bsearch1.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	60	204
1	75	204
done	75	204

end0.0ms

sample3.2s

Algorithm

intervals

Results

881.0ms	8404×	body	80	valid
610.0ms	1298×	body	640	valid
596.0ms	883×	body	1280	valid
278.0ms	798×	body	320	valid
99.0ms	382×	body	160	valid

Details

sample117.0ms

simplify2.4s

prune5.0ms

localize17.0ms

rewrite62.0ms

series201.0ms

simplify583.0ms

prune280.0ms

localize23.0ms

rewrite106.0ms

series460.0ms

simplify1.3s

prune996.0ms

localize21.0ms

rewrite84.0ms

series319.0ms

simplify436.0ms

prune397.0ms

localize30.0ms

rewrite79.0ms

series746.0ms

simplify429.0ms

prune747.0ms

regimes1.7s

bsearch1.0ms

simplify8.0ms

end0.0ms

sample3.2s

Profiling