Details

sample122.0ms

Algorithm

intervals

Results

31.0ms	262×	body	80	valid
31.0ms	44×	body	640	valid
12.0ms	18×	body	1280	valid
8.0ms	22×	body	320	valid
2.0ms	10×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4415
4	917
3	240
2	69
1	32
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
35.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite246.0ms

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` `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:

64.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
135.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series795.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
598.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.7s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
1	1387
0	458

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.8b

localize119.0ms

Local error

Found 4 expressions with local error:

2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
35.6b	(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))))

rewrite621.0ms

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` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

12.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
566.0ms	(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))))

series660.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2.0))
33.0ms	(cos (/ (+ phi1 phi2) 2.0))
38.0ms	(cos (/ (+ phi1 phi2) 2.0))
560.0ms	(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))))

simplify2.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
1	1283
0	424

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 23.8b

localize136.0ms

Local error

Found 4 expressions with local error:

2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
35.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite749.0ms

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` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

9.0ms	(cos (/ (+ phi1 phi2) 2.0))
15.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(cos (/ (+ phi1 phi2) 2.0))
697.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cos (/ (+ phi1 phi2) 2.0))
44.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
624.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.5s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
1	1293
0	427

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.8b

localize108.0ms

Local error

Found 4 expressions with local error:

2.2b	(cos (/ (+ phi1 phi2) 2.0))
2.2b	(cos (/ (+ phi1 phi2) 2.0))
35.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite328.0ms

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` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 172

Calls

4 calls:

16.0ms	(cos (/ (+ phi1 phi2) 2.0))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))
128.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
133.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

33.0ms	(cos (/ (+ phi1 phi2) 2.0))
34.0ms	(cos (/ (+ phi1 phi2) 2.0))
623.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
659.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

184 → 184

Iterations

Iter	Nodes
done	5001
1	1271
0	420

prune1.5s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 23.8b

regimes2.5s

Accuracy

68% (4.8b remaining)

Error of 29.7b against oracle of 24.8b and baseline of 39.9b

bsearch3.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.7s	8366×	body	80	valid
1.3s	1309×	body	640	valid
758.0ms	768×	body	320	valid
744.0ms	782×	body	1280	valid
108.0ms	398×	body	160	valid