Details

sample224.0ms

Algorithm

intervals

Results

63.0ms	271×	body	80	valid
44.0ms	32×	body	1280	valid
32.0ms	33×	body	640	valid
15.0ms	21×	body	320	valid
13.0ms	11×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5014
5	2701
4	858
3	238
2	69
1	32
0	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize34.0ms

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))))

rewrite233.0ms

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:

90.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
7.0ms	(cos (/ (+ phi1 phi2) 2))
13.0ms	(cos (/ (+ phi1 phi2) 2))
115.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series709.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
33.0ms	(cos (/ (+ phi1 phi2) 2))
26.0ms	(cos (/ (+ phi1 phi2) 2))
546.0ms	(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	5001
1	1357
0	460

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 26.5b

localize53.0ms

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

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

266×	`associate-*l/`
198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
98×	`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:

7.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
167.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cos (/ (+ phi1 phi2) 2))
31.0ms	(cos (/ (+ phi1 phi2) 2))
38.0ms	(cos (/ (+ phi1 phi2) 2))
534.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.5s

Counts

188 → 188

Iterations

Iter	Nodes
done	5002
1	2341
0	789

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 25.8b

localize62.0ms

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))))

rewrite190.0ms

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:

7.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
76.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
92.0ms	(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))
37.0ms	(cos (/ (+ phi1 phi2) 2))
616.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
522.0ms	(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

12 alts after pruning (10 fresh and 2 done)

Merged error: 25.8b

localize79.0ms

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) (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

80×	`associate-l/` `associate-r/` `cos-mult`
66×	`sqrt-div`
64×	`frac-add`
56×	`flip3--` `flip--`
48×	`frac-times`
40×	`frac-sub`
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:

17.0ms	(cos (* 1/2 (+ phi1 phi2)))
11.0ms	(cos (* 1/2 (+ phi1 phi2)))
9.0ms	(cos (* 1/2 (+ phi1 phi2)))
343.0ms	(sqrt (+ (- (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) (+ (* lambda2 lambda2) (* lambda1 lambda1))) (* (* 2 lambda1) (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

41.0ms	(cos (* 1/2 (+ phi1 phi2)))
40.0ms	(cos (* 1/2 (+ phi1 phi2)))
41.0ms	(cos (* 1/2 (+ phi1 phi2)))
976.0ms	(sqrt (+ (- (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) (+ (* lambda2 lambda2) (* lambda1 lambda1))) (* (* 2 lambda1) (* (* (cos (* 1/2 (+ phi1 phi2))) (cos (* 1/2 (+ phi1 phi2)))) lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.6s

Counts

122 → 122

Iterations

Iter	Nodes
done	5013
1	1475
0	515

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 20.4b

regimes1.5s

Accuracy

43.7% (10.1b remaining)

Error of 29.6b against oracle of 19.5b and baseline of 37.4b

bsearch3.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.8s	8378×	body	80	valid
1.8s	844×	body	1280	valid
1.5s	1236×	body	640	valid
573.0ms	722×	body	320	valid
189.0ms	356×	body	160	valid