Details

sample78.0ms

Algorithm

intervals

Results

24.0ms	77×	body	1280	valid
14.0ms	67×	body	640	valid
13.0ms	264×	body	80	valid
7.0ms	44×	body	320	valid
1.0ms	13×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	45	13
3	65	13
4	84	13
5	102	13
6	115	13
done	115	13

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.5b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series347.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
113.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
62.0ms	(/ (cos th) (sqrt 2.0))
64.0ms	(/ (cos th) (sqrt 2.0))

simplify824.0ms

Counts

180 → 180

Iterations

Useful iterations: done (820.0ms)

Iter	Nodes	Cost
0	181	2118
1	493	2012
2	1600	1832
done	5000	1812

prune472.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b	(* (/ (cos th) (sqrt 2.0)) a2)
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 165

Calls

4 calls:

18.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
11.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series334.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
103.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
63.0ms	(/ (cos th) (sqrt 2.0))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify1.2s

Counts

177 → 177

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	175	1959
1	437	1860
2	1410	1720
done	5000	1704

prune467.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2.0)) a2)
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
349×	`add-sqr-sqrt`
341×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-/l*`
24×	`associate-/r*`
22×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
14×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `unswap-sqr`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 466

Calls

4 calls:

12.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
18.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series327.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
98.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
59.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify1.0s

Counts

478 → 478

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	471	9699
1	1054	8386
2	2380	7821
done	5001	7819

prune877.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.4b	(/ (* (cos th) a2) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

1143×	`sqrt-prod`
1125×	`times-frac`
615×	`add-sqr-sqrt`
581×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`add-exp-log` `add-cbrt-cube`
35×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
12×	`cbrt-undiv` `div-exp`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 732

Calls

4 calls:

94.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
4.0ms	(/ (* (cos th) a2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
18.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
109.0ms	(/ (* (cos th) a2) (sqrt 2.0))
98.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
60.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.5s

Counts

744 → 744

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	571	14580
1	1590	12916
2	4010	11905
done	5000	11899

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes314.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	32
1	27	32
done	27	32

end0.0ms

sample2.2s

Algorithm

intervals

Results

811.0ms	2511×	body	1280	valid
437.0ms	2041×	body	640	valid
418.0ms	8164×	body	80	valid
167.0ms	1027×	body	320	valid
56.0ms	537×	body	160	valid