Details

sample67.0ms

Algorithm

intervals

Results

18.0ms	265×	body	80	valid
14.0ms	32×	body	1280	valid
11.0ms	36×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	11×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	177	32
4	414	32
5	1014	32
6	3276	32
done	5000	32

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite102.0ms

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:

27.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
50.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
391.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify358.0ms

Counts

147 → 147

Iterations

Useful iterations: done (351.0ms)

Iter	Nodes	Cost
0	455	7854
1	1182	7209
done	5000	7047

prune443.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.1b

localize22.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite106.0ms

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` `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 → 172

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
64.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
402.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify638.0ms

Counts

184 → 184

Iterations

Useful iterations: 1 (206.0ms)

Iter	Nodes	Cost
0	785	16760
1	2171	14784
done	5000	14784

prune746.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.7b

localize23.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite267.0ms

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:

6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
240.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
411.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify390.0ms

Counts

112 → 112

Iterations

Useful iterations: done (383.0ms)

Iter	Nodes	Cost
0	421	8318
1	1173	7826
done	5000	7808

prune458.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.7b

localize32.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2.0))
3.7b	(cos (/ (+ phi1 phi2) 2.0))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite511.0ms

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

Counts

4 → 172

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
239.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
240.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series901.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
427.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
419.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify422.0ms

Counts

184 → 184

Iterations

Useful iterations: done (402.0ms)

Iter	Nodes	Cost
0	421	16256
1	1173	15272
done	5000	15236

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 25.7b

regimes437.0ms

Accuracy

33.8% (10.0b remaining)

Error of 34.2b against oracle of 24.2b and baseline of 39.3b

bsearch90.0ms

Steps

Iters	Range		Point
10	-18.915819521398753	-2.574374193275519e-17	-13.518212446430018

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	58
1	34	58
done	34	58

end0.0ms

sample2.0s

Algorithm

intervals

Results

569.0ms	8349×	body	80	valid
408.0ms	1321×	body	640	valid
366.0ms	842×	body	1280	valid
162.0ms	750×	body	320	valid
54.0ms	381×	body	160	valid