Details

sample238.0ms

Algorithm

intervals

Results

72.0ms	293×	body	80	valid
62.0ms	21×	body	1280	valid
45.0ms	43×	body	640	valid
21.0ms	27×	body	320	valid
5.0ms	9×	body	160	valid

simplify726.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
1.5b	(cos (/ (+ phi1 phi2) 2))
1.5b	(cos (/ (+ phi1 phi2) 2))
37.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite247.0ms

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:

66.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
9.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
151.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series833.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
25.0ms	(cos (/ (+ phi1 phi2) 2))
33.0ms	(cos (/ (+ phi1 phi2) 2))
606.0ms	(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	6665
1	1344
0	460

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.3b

localize60.0ms

Local error

Found 4 expressions with local error:

1.5b	(cos (/ (+ phi1 phi2) 2))
1.5b	(cos (/ (+ phi1 phi2) 2))
1.5b	(cos (/ (+ phi1 phi2) 2))
37.8b	(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))))

rewrite465.0ms

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:

7.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
440.0ms	(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))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cos (/ (+ phi1 phi2) 2))
24.0ms	(cos (/ (+ phi1 phi2) 2))
22.0ms	(cos (/ (+ phi1 phi2) 2))
522.0ms	(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))))

simplify2.7s

Counts

116 → 116

Iterations

Iter	Nodes
2	6987
1	1262
0	425

prune3.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.8b

localize101.0ms

Local error

Found 4 expressions with local error:

1.5b	(cos (/ (+ phi1 phi2) 2))
1.5b	(cos (/ (+ phi1 phi2) 2))
1.5b	(cos (/ (+ phi1 phi2) 2))
37.8b	(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)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite535.0ms

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))
7.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
503.0ms	(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)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2))
22.0ms	(cos (/ (+ phi1 phi2) 2))
26.0ms	(cos (/ (+ phi1 phi2) 2))
519.0ms	(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)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts

188 → 188

Iterations

Iter	Nodes
1	2345
0	790

prune5.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.7b

localize76.0ms

Local error

Found 4 expressions with local error:

1.5b	(cos (/ (+ phi1 phi2) 2))
1.5b	(cos (/ (+ phi1 phi2) 2))
37.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
37.8b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite242.0ms

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:

16.0ms	(cos (/ (+ phi1 phi2) 2))
15.0ms	(cos (/ (+ phi1 phi2) 2))
88.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
109.0ms	(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:

38.0ms	(cos (/ (+ phi1 phi2) 2))
40.0ms	(cos (/ (+ phi1 phi2) 2))
606.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
556.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.3s

Counts

188 → 188

Iterations

Iter	Nodes
2	6309
1	1243
0	421

prune5.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.7b

regimes1.2s

Accuracy

56.2% (6.1b remaining)

Error of 29.2b against oracle of 23.1b and baseline of 37.0b

bsearch5.0ms

simplify20.0ms

Iterations

Iter	Nodes
2	43
1	43
0	32

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.7s	8314×	body	80	valid
1.6s	1334×	body	640	valid
1.1s	790×	body	1280	valid
978.0ms	715×	body	320	valid
310.0ms	384×	body	160	valid