Details

sample112.0ms

Algorithm

intervals

Results

29.0ms	272×	body	80	valid
22.0ms	42×	body	640	valid
17.0ms	25×	body	1280	valid
9.0ms	25×	body	320	valid
3.0ms	14×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	240	32
4	960	32
done	5000	32

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite309.0ms

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-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `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 → 135

Calls

4 calls:

96.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
18.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
162.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
471.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify756.0ms

Counts

147 → 147

Iterations

Useful iterations: done (743.0ms)

Iter	Nodes	Cost
0	455	7854
1	1367	7209
done	5000	6873

prune642.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod` `sqrt-prod`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `unpow3` `rem-cbrt-cube` `flip-+` `sqr-pow`

Counts

4 → 114

Calls

4 calls:

3.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
13.0ms	(cos (/ (+ phi1 phi2) 2.0))
14.0ms	(cos (/ (+ phi1 phi2) 2.0))
143.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series748.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
33.0ms	(cos (/ (+ phi1 phi2) 2.0))
46.0ms	(cos (/ (+ phi1 phi2) 2.0))
640.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify666.0ms

Counts

126 → 126

Iterations

Useful iterations: done (656.0ms)

Iter	Nodes	Cost
0	445	7377
1	1356	6534
done	5000	6377

prune838.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite325.0ms

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-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `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 → 135

Calls

4 calls:

105.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))
12.0ms	(cos (/ (+ phi1 phi2) 2.0))
172.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
49.0ms	(cos (/ (+ phi1 phi2) 2.0))
49.0ms	(cos (/ (+ phi1 phi2) 2.0))
714.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify737.0ms

Counts

147 → 147

Iterations

Useful iterations: done (723.0ms)

Iter	Nodes	Cost
0	455	7854
1	1367	7209
done	5000	6873

prune801.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.6b

localize48.0ms

Local error

Found 4 expressions with local error:

2.3b	(cos (/ (+ phi1 phi2) 2.0))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
2.3b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) (* 2 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite439.0ms

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` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

11.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
21.0ms	(cos (/ (+ phi1 phi2) 2.0))
378.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) (* 2 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

series778.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cos (/ (+ phi1 phi2) 2.0))
36.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
671.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) (* 2 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify644.0ms

Counts

112 → 112

Iterations

Useful iterations: done (634.0ms)

Iter	Nodes	Cost
0	424	8057
1	1275	7401
done	5002	7261

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 26.6b

regimes871.0ms

Accuracy

74.2% (3.5b remaining)

Error of 28.9b against oracle of 25.4b and baseline of 39.1b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	71
1	32	69
2	33	69
done	33	69

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.0s	8396×	body	80	valid
1.5s	1291×	body	640	valid
796.0ms	754×	body	1280	valid
435.0ms	710×	body	320	valid
102.0ms	381×	body	160	valid