Details

sample174.0ms

Algorithm

intervals

Results

71.0ms	292×	body	80	valid
33.0ms	24×	body	1280	valid
29.0ms	34×	body	640	valid
13.0ms	17×	body	320	valid
3.0ms	9×	body	160	valid

simplify639.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
2.2b	(cos (/ (+ phi1 phi2) 2))
2.2b	(cos (/ (+ phi1 phi2) 2))
32.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite183.0ms

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:

62.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
17.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
85.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series796.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
37.0ms	(cos (/ (+ phi1 phi2) 2))
24.0ms	(cos (/ (+ phi1 phi2) 2))
573.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify876.0ms

Counts

151 → 151

Iterations

Iter	Nodes
done	2004
1	1357
0	460

prune732.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.4b

localize93.0ms

Local error

Found 4 expressions with local error:

2.2b	(cos (/ (+ phi1 phi2) 2))
2.2b	(cos (/ (+ phi1 phi2) 2))
32.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
32.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite263.0ms

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))
17.0ms	(cos (/ (+ phi1 phi2) 2))
116.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
105.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

22.0ms	(cos (/ (+ phi1 phi2) 2))
22.0ms	(cos (/ (+ phi1 phi2) 2))
591.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
573.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts

188 → 188

Iterations

Iter	Nodes
done	2002
1	1245
0	421

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))
2.2b	(cos (/ (+ phi1 phi2) 2))
2.2b	(cos (/ (+ phi1 phi2) 2))
32.6b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

160×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
34×	`associate-*r/`
14×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip-+`

Counts

4 → 126

Calls

4 calls:

140.0ms	(* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))
9.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
200.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

series774.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))
37.0ms	(cos (/ (+ phi1 phi2) 2))
23.0ms	(cos (/ (+ phi1 phi2) 2))
577.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts

138 → 138

Iterations

Iter	Nodes
done	2001
1	1364
0	474

prune896.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.4b

localize152.0ms

Local error

Found 4 expressions with local error:

32.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
33.7b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
33.7b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
33.7b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

512×	`associate-*l/`
384×	`flip3--` `flip--`
256×	`frac-times` `frac-add`
198×	`cbrt-div`
128×	`associate-*r/`
66×	`sqrt-div`
9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 314

Calls

4 calls:

98.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
81.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
62.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
66.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.5s

Counts

4 → 12

Calls

4 calls:

610.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
633.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
658.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
620.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.4s

Counts

326 → 326

Iterations

Iter	Nodes
done	2014
1	1410
0	548

prune2.9s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.4b

regimes1.0s

Accuracy

61.1% (5.2b remaining)

Error of 29.0b against oracle of 23.8b and baseline of 37.2b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.6s	8394×	body	80	valid
2.0s	1304×	body	640	valid
1.2s	787×	body	1280	valid
605.0ms	725×	body	320	valid
162.0ms	374×	body	160	valid