Details

sample135.0ms

Algorithm

intervals

Results

45.0ms	41×	body	640	valid
43.0ms	285×	body	80	valid
16.0ms	19×	body	1280	valid
10.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	2001
4	757
3	225
2	66
1	32
0	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite147.0ms

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` `insert-posit16` `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 → 139

Calls

4 calls:

56.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
8.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
72.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
31.0ms	(cos (/ (+ phi1 phi2) 2))
30.0ms	(cos (/ (+ phi1 phi2) 2))
483.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.2s

Counts

151 → 151

Iterations

Iter	Nodes
done	2004
2	2004
1	1357
0	460

prune728.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.9b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

146×	`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×	`insert-posit16` `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 → 119

Calls

4 calls:

29.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
12.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
215.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
22.0ms	(cos (/ (+ phi1 phi2) 2))
30.0ms	(cos (/ (+ phi1 phi2) 2))
521.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	2001
2	2001
1	1300
0	456

prune788.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.8b

localize53.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 176

Calls

4 calls:

15.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
94.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
107.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (/ (+ phi1 phi2) 2))
24.0ms	(cos (/ (+ phi1 phi2) 2))
986.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
560.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.4s

Counts

188 → 188

Iterations

Iter	Nodes
done	2002
2	2002
1	1245
0	421

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.8b

localize116.0ms

Local error

Found 4 expressions with local error:

19.3b	(sqrt (* (cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))))
37.0b	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))
37.0b	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))
37.0b	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

19794×	`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` `insert-posit16` `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 → 4742

Calls

4 calls:

396.0ms	(sqrt (* (cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))))
141.0ms	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))
161.0ms	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))
109.0ms	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

series2.7s

Counts

4 → 12

Calls

4 calls:

702.0ms	(sqrt (* (cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))))
662.0ms	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))
664.0ms	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))
636.0ms	(cbrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify32.2s

Counts

4754 → 4754

Iterations

Iter	Nodes
done	12349
0	12349

prune1.8m

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 22.8b

regimes945.0ms

Accuracy

58.2% (5.7b remaining)

Error of 29.4b against oracle of 23.7b and baseline of 37.4b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	8360×	body	80	valid
1.2s	1312×	body	640	valid
676.0ms	748×	body	1280	valid
406.0ms	720×	body	320	valid
97.0ms	365×	body	160	valid