Details

sample120.0ms

Algorithm

intervals

Results

28.0ms	25×	body	1280	valid
25.0ms	258×	body	80	valid
23.0ms	49×	body	640	valid
10.0ms	31×	body	320	valid
2.0ms	10×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
38.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite133.0ms

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:

17.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
90.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series843.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
56.0ms	(cos (/ (+ phi1 phi2) 2.0))
611.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
1	1322
0	444

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.7b

localize87.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
38.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

32.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
123.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
47.0ms	(cos (/ (+ phi1 phi2) 2.0))
51.0ms	(cos (/ (+ phi1 phi2) 2.0))
635.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
1	1306
0	444

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 27.6b

localize208.0ms

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))))))
39.9b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
39.9b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
39.9b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.8s

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:

596.0ms	(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))))))
58.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
69.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
88.0ms	(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:

742.0ms	(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))))))
707.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
788.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
755.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify30.2s

Counts

4750 → 4750

Iterations

Iter	Nodes
done	12339
0	12339

prune1.8m

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 27.6b

localize70.0ms

Local error

Found 4 expressions with local error:

3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
39.9b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
41.5b	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (/ (+ 1/3 1/3) 2))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`cbrt-div`
64×	`frac-times` `frac-add`
40×	`pow-unpow` `*-un-lft-identity`
36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`associate-*r/`
9×	`distribute-rgt-out` `distribute-lft-out`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `distribute-lft1-in` `count-2` `distribute-rgt1-in`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `pow-exp` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 145

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2.0))
8.0ms	(cos (/ (+ phi1 phi2) 2.0))
43.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
78.0ms	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (/ (+ 1/3 1/3) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

31.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
504.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
510.0ms	(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (/ (+ 1/3 1/3) 2))

simplify1.2s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
1	1597
0	522

prune866.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 27.6b

regimes896.0ms

Accuracy

66.6% (4.9b remaining)

Error of 29.6b against oracle of 24.7b and baseline of 39.5b

bsearch3.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	8314×	body	80	valid
651.0ms	1272×	body	640	valid
444.0ms	770×	body	1280	valid
189.0ms	740×	body	320	valid
58.0ms	346×	body	160	valid