Details

sample99.0ms

Algorithm

intervals

Results

30.0ms	73×	body	1280	valid
19.0ms	254×	body	80	valid
15.0ms	49×	body	640	valid
7.0ms	34×	body	320	valid
4.0ms	20×	body	160	valid

simplify190.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

34.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
47.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
14.0ms	(/ (cos th) (sqrt 2.0))
9.0ms	(/ (cos th) (sqrt 2.0))

series422.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
129.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
67.0ms	(/ (cos th) (sqrt 2.0))
87.0ms	(/ (cos th) (sqrt 2.0))

simplify1.4s

Counts

180 → 180

Iterations

Iter	Nodes
done	5001
2	1722
1	521
0	181

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 744

Calls

4 calls:

161.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
44.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
9.0ms	(/ (cos th) (sqrt 2.0))

series514.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
110.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
125.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
99.0ms	(/ (cos th) (sqrt 2.0))

simplify3.0s

Counts

756 → 756

Iterations

Iter	Nodes
done	5004
2	4946
1	1628
0	560

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

1507×	`sqrt-prod`
1492×	`times-frac`
814×	`add-sqr-sqrt`
769×	`*-un-lft-identity` `add-cube-cbrt`
386×	`cbrt-prod`
376×	`associate-l`
37×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
29×	`div-inv`
27×	`associate-/r*`
17×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 937

Calls

4 calls:

177.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
19.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
62.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
16.0ms	(/ (cos th) (sqrt 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

598.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
146.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
366.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
82.0ms	(/ (cos th) (sqrt 2.0))

simplify2.7s

Counts

949 → 949

Iterations

Iter	Nodes
done	5001
1	2019
0	718

prune6.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

1365×	`sqrt-prod`
1326×	`times-frac`
709×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
192×	`cbrt-prod`
68×	`associate-/l*`
39×	`associate-/r*`
27×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 866

Calls

4 calls:

28.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
18.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
41.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

series837.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
177.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
153.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
408.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

simplify2.8s

Counts

878 → 878

Iterations

Iter	Nodes
done	5009
2	3519
1	1662
0	749

prune4.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes613.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample6.0s

Algorithm

intervals

Results

1.9s	2566×	body	1280	valid
1.4s	2044×	body	640	valid
1.2s	8116×	body	80	valid
777.0ms	1079×	body	320	valid
195.0ms	510×	body	160	valid