Details

sample145.0ms

Algorithm

intervals

Results

51.0ms	273×	body	80	valid
24.0ms	31×	body	1280	valid
20.0ms	40×	body	640	valid
11.0ms	30×	body	320	valid
3.0ms	12×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
5	2141
4	757
3	225
2	66
1	32
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
35.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

27.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
122.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series896.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
47.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
661.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.2s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
1	1296
0	444

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.8b

localize101.0ms

Local error

Found 4 expressions with local error:

2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
35.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite654.0ms

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:

10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))
608.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series804.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
50.0ms	(cos (/ (+ phi1 phi2) 2.0))
673.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.4s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
1	1264
0	424

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.8b

localize224.0ms

Local error

Found 4 expressions with local error:

22.7b	(sqrt (* (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

17602×	`associate-*l/`
13152×	`flip3--` `flip--`
13124×	`frac-times`
9042×	`cbrt-div`
8768×	`frac-add`
4488×	`sqrt-div`
4450×	`associate-*r/`
137×	`flip3-+` `flip-+`
12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 4738

Calls

4 calls:

633.0ms	(sqrt (* (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
62.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
95.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
59.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series3.0s

Counts

4 → 12

Calls

4 calls:

800.0ms	(sqrt (* (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
745.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
721.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
722.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify30.0s

Counts

4750 → 4750

Iterations

Iter	Nodes
done	12339
0	12339

prune2.1m

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.8b

localize145.0ms

Local error

Found 4 expressions with local error:

35.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.1b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 312

Calls

4 calls:

87.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
88.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
55.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
55.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.0s

Counts

4 → 12

Calls

4 calls:

462.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
463.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
526.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
532.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.5s

Counts

324 → 324

Iterations

Iter	Nodes
done	5002
1	1410
0	547

prune2.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.8b

regimes1.5s

Accuracy

70.3% (4.2b remaining)

Error of 29.2b against oracle of 24.9b and baseline of 39.2b

bsearch2.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	8291×	body	80	valid
876.0ms	1305×	body	640	valid
536.0ms	797×	body	1280	valid
227.0ms	771×	body	320	valid
92.0ms	357×	body	160	valid