Details

sample123.0ms

Algorithm

intervals

Results

38.0ms	85×	body	1280	valid
25.0ms	78×	body	640	valid
19.0ms	239×	body	80	valid
9.0ms	38×	body	320	valid
3.0ms	11×	body	160	valid

simplify60.0ms

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

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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:

10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
11.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series50.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
17.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms	(/ (cos th) (sqrt 2.0))
7.0ms	(/ (cos th) (sqrt 2.0))

simplify589.0ms

Counts

180 → 180

Iterations

Useful iterations: done (584.0ms)

Iter	Nodes	Cost
0	181	2118
1	500	2042
2	1874	1850
done	5000	1812

prune374.0ms

Filtered

120 candidates to 180 candidates (-50.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	170	10	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	10	181

Merged error: 0.0b

Counts

181 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
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))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
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×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 744

Calls

4 calls:

54.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
18.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series39.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify457.0ms

Counts

756 → 756

Iterations

Useful iterations: done (422.0ms)

Iter	Nodes	Cost
0	560	14715
1	1551	13426
done	5001	13127

prune1.8s

Filtered

390 candidates to 756 candidates (-93.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	755	1	756
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	756	10	766

Merged error: 0.0b

Counts

766 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos th) (sqrt 2.0))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
12×	`sqrt-prod`
9×	`cbrt-prod`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 72

Calls

4 calls:

5.0ms	(/ (cos th) (sqrt 2.0))
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)

series6.0ms

Counts

4 → 6

Calls

4 calls:

6.0ms	(/ (cos th) (sqrt 2.0))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify920.0ms

Counts

78 → 78

Iterations

Useful iterations: 5 (515.0ms)

Iter	Nodes	Cost
0	91	644
1	157	613
2	358	579
3	808	567
4	1883	567
5	3940	564
done	5001	564

prune281.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	78	10	88

Merged error: 0.0b

Counts

88 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
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))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 469

Calls

4 calls:

10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
18.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series38.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify736.0ms

Counts

481 → 481

Iterations

Useful iterations: done (713.0ms)

Iter	Nodes	Cost
0	477	9858
1	1119	8887
2	3580	8079
done	5000	7985

prune716.0ms

Filtered

205 candidates to 481 candidates (-134.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	481	10	491

Merged error: 0.0b

Counts

491 → 10

regimes508.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	30	35
done	30	35

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	2688×	body	1280	valid
672.0ms	2072×	body	640	valid
635.0ms	7888×	body	80	valid
243.0ms	1030×	body	320	valid
95.0ms	543×	body	160	valid

Details

sample123.0ms

simplify60.0ms

prune11.0ms

localize12.0ms

rewrite38.0ms

series50.0ms

simplify589.0ms

prune374.0ms

localize18.0ms

rewrite151.0ms

series39.0ms

simplify457.0ms

prune1.8s

localize25.0ms

rewrite12.0ms

series6.0ms

simplify920.0ms

prune281.0ms

localize15.0ms

rewrite76.0ms

series38.0ms

simplify736.0ms

prune716.0ms

regimes508.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.5s

Profiling