Details

sample231.0ms

Algorithm

intervals

Results

104.0ms	276×	body	80	valid
39.0ms	39×	body	640	valid
39.0ms	26×	body	1280	valid
13.0ms	17×	body	320	valid
7.0ms	15×	body	160	valid

simplify766.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
35.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite510.0ms

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:

55.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
351.0ms	(cos (/ (+ phi1 phi2) 2))
11.0ms	(cos (/ (+ phi1 phi2) 2))
85.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
24.0ms	(cos (/ (+ phi1 phi2) 2))
35.0ms	(cos (/ (+ phi1 phi2) 2))
526.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.5s

Counts

151 → 151

Iterations

Iter	Nodes
2	6655
1	1344
0	460

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.6b

localize72.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
35.2b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite576.0ms

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` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 104

Calls

4 calls:

14.0ms	(cos (/ (+ phi1 phi2) 2))
15.0ms	(cos (/ (+ phi1 phi2) 2))
15.0ms	(cos (/ (+ phi1 phi2) 2))
525.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2))
22.0ms	(cos (/ (+ phi1 phi2) 2))
32.0ms	(cos (/ (+ phi1 phi2) 2))
592.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.1s

Counts

116 → 116

Iterations

Iter	Nodes
2	6989
1	1264
0	425

prune2.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.6b

localize78.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
35.2b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite781.0ms

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` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 104

Calls

4 calls:

16.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
730.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cos (/ (+ phi1 phi2) 2))
39.0ms	(cos (/ (+ phi1 phi2) 2))
22.0ms	(cos (/ (+ phi1 phi2) 2))
611.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.9s

Counts

116 → 116

Iterations

Iter	Nodes
2	6489
1	1247
0	422

prune2.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize83.0ms

Local error

Found 4 expressions with local error:

21.0b	(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))))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
36.3b	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.0s

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` `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:

235.0ms	(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))))))
56.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
88.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
77.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.4s

Counts

4 → 12

Calls

4 calls:

580.0ms	(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))))))
582.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
642.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
639.0ms	(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify21.0s

Counts

4754 → 4754

Iterations

Iter	Nodes
1	14076
0	12340

prune3.2m

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.5b

regimes742.0ms

Accuracy

60.5% (5.5b remaining)

Error of 28.9b against oracle of 23.4b and baseline of 37.2b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	37
1	37
0	28

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.7s	8311×	body	80	valid
1.3s	1306×	body	640	valid
774.0ms	786×	body	1280	valid
416.0ms	705×	body	320	valid
162.0ms	377×	body	160	valid