Details

sample244.0ms

Algorithm

intervals

Results

70.0ms	265×	body	80	valid
61.0ms	28×	body	320	valid
45.0ms	26×	body	1280	valid
29.0ms	25×	body	640	valid
8.0ms	14×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
1.8b	(cos (/ (+ phi1 phi2) 2))
1.8b	(cos (/ (+ phi1 phi2) 2))
32.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite205.0ms

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:

63.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
9.0ms	(cos (/ (+ phi1 phi2) 2))
18.0ms	(cos (/ (+ phi1 phi2) 2))
112.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series798.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
24.0ms	(cos (/ (+ phi1 phi2) 2))
39.0ms	(cos (/ (+ phi1 phi2) 2))
571.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
1	1357
0	460

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.0b

localize77.0ms

Local error

Found 4 expressions with local error:

22.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
22.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
22.1b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
32.5b	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

29930×	`associate-*l/`
20428×	`frac-times`
16050×	`flip3--` `flip--`
15576×	`cbrt-div`
5990×	`associate-*r/`
5826×	`sqrt-div`
5824×	`frac-add`
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×	`cbrt-prod` `pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 5894

Calls

4 calls:

48.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
49.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
87.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
450.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

287.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
412.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
354.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
571.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify55.4s

Counts

5906 → 5906

Iterations

Iter	Nodes
done	22401
0	22401

prune1.8m

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.2b

localize58.0ms

Local error

Found 4 expressions with local error:

1.8b	(cos (/ (+ phi1 phi2) 2))
32.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
32.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
32.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

384×	`associate-*l/`
288×	`flip3--` `flip--`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
96×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 248

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2))
64.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
65.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
66.0ms	(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:

21.0ms	(cos (/ (+ phi1 phi2) 2))
388.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
388.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
392.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.4s

Counts

260 → 260

Iterations

Iter	Nodes
done	5000
1	1245
0	421

prune1.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 20.2b

localize53.0ms

Local error

Found 4 expressions with local error:

1.8b	(cos (/ (+ phi1 phi2) 2))
1.8b	(cos (/ (+ phi1 phi2) 2))
26.5b	(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
32.5b	(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite81.0ms

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-+` `remove-posit16`

Counts

4 → 105

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
0.0ms	(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
64.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cos (/ (+ phi1 phi2) 2))
23.0ms	(cos (/ (+ phi1 phi2) 2))
21.0ms	(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
393.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5003
1	1269
0	433

prune731.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 20.2b

regimes1.1s

Accuracy

58.4% (5.4b remaining)

Error of 29.0b against oracle of 23.6b and baseline of 36.5b

bsearch3.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	8526×	body	80	valid
1.1s	794×	body	1280	valid
947.0ms	1269×	body	640	valid
350.0ms	738×	body	320	valid
100.0ms	330×	body	160	valid