Details

sample234.0ms

Algorithm

intervals

Results

93.0ms	271×	body	80	valid
48.0ms	32×	body	1280	valid
36.0ms	33×	body	640	valid
18.0ms	21×	body	320	valid
5.0ms	11×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	2141
4	757
3	225
2	66
1	32
0	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
2.7b	(cos (/ (+ phi1 phi2) 2))
2.7b	(cos (/ (+ phi1 phi2) 2))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite225.0ms

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:

77.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
7.0ms	(cos (/ (+ phi1 phi2) 2))
9.0ms	(cos (/ (+ phi1 phi2) 2))
128.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series895.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
39.0ms	(cos (/ (+ phi1 phi2) 2))
41.0ms	(cos (/ (+ phi1 phi2) 2))
650.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
1	1357
0	460

prune954.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 26.0b

localize72.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (+ phi1 phi2) 2))
2.7b	(cos (/ (+ phi1 phi2) 2))
2.7b	(cos (/ (+ phi1 phi2) 2))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

290×	`associate-*l/`
198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
74×	`associate-*r/`
72×	`cbrt-div` `cos-mult`
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 → 176

Calls

4 calls:

9.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
11.0ms	(cos (/ (+ phi1 phi2) 2))
125.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2))
39.0ms	(cos (/ (+ phi1 phi2) 2))
40.0ms	(cos (/ (+ phi1 phi2) 2))
629.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.4s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
1	2494
0	831

prune1.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 24.1b

localize69.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (+ phi1 phi2) 2))
2.7b	(cos (/ (+ phi1 phi2) 2))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
37.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite216.0ms

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:

9.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
96.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
96.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

36.0ms	(cos (/ (+ phi1 phi2) 2))
25.0ms	(cos (/ (+ phi1 phi2) 2))
602.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
640.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.1s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
1	1245
0	421

prune1.5s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 24.1b

localize102.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (* 1/2 (+ phi1 phi2)))
2.7b	(cos (* 1/2 (+ phi1 phi2)))
2.7b	(cos (* 1/2 (+ phi1 phi2)))
37.2b	(sqrt (+ (- (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) (+ (* lambda2 lambda2) (* lambda1 lambda1))) (* 2 (* (* lambda1 lambda2) (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*r/`
80×	`cos-mult`
66×	`sqrt-div`
64×	`frac-add`
56×	`flip3--` `flip--`
48×	`frac-times`
40×	`frac-sub`
32×	`associate-*l/`
17×	`flip3-+` `flip-+`
8×	`sub-div`
6×	`add-sqr-sqrt` `cos-sum`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 110

Calls

4 calls:

8.0ms	(cos (* 1/2 (+ phi1 phi2)))
9.0ms	(cos (* 1/2 (+ phi1 phi2)))
12.0ms	(cos (* 1/2 (+ phi1 phi2)))
336.0ms	(sqrt (+ (- (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) (+ (* lambda2 lambda2) (* lambda1 lambda1))) (* 2 (* (* lambda1 lambda2) (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2))))))) (* (- phi1 phi2) (- phi1 phi2))))

series953.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (* 1/2 (+ phi1 phi2)))
23.0ms	(cos (* 1/2 (+ phi1 phi2)))
26.0ms	(cos (* 1/2 (+ phi1 phi2)))
878.0ms	(sqrt (+ (- (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) (+ (* lambda2 lambda2) (* lambda1 lambda1))) (* 2 (* (* lambda1 lambda2) (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.5s

Counts

122 → 122

Iterations

Iter	Nodes
done	5004
1	1474
0	515

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 19.0b

regimes1.4s

Accuracy

42.5% (10.6b remaining)

Error of 29.6b against oracle of 19.0b and baseline of 37.4b

bsearch4.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.0s	8378×	body	80	valid
2.0s	1236×	body	640	valid
1.3s	844×	body	1280	valid
660.0ms	722×	body	320	valid
210.0ms	356×	body	160	valid