Details

sample125.0ms

Algorithm

intervals

Results

39.0ms	85×	body	1280	valid
26.0ms	78×	body	640	valid
24.0ms	239×	body	80	valid
9.0ms	38×	body	320	valid
2.0ms	11×	body	160	valid

simplify62.0ms

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

prune12.0ms

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))

rewrite39.0ms

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))

series51.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
18.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms	(/ (cos th) (sqrt 2.0))
7.0ms	(/ (cos th) (sqrt 2.0))

simplify533.0ms

Counts

180 → 180

Iterations

Useful iterations: done (528.0ms)

Iter	Nodes	Cost
0	181	2118
1	500	2028
2	1629	1832
done	5000	1812

prune377.0ms

Filtered

116 candidates to 180 candidates (-55.2%)

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

localize15.0ms

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))

rewrite155.0ms

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))

series45.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
12.0ms	(/ (/ (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))

simplify811.0ms

Counts

756 → 756

Iterations

Useful iterations: 2 (456.0ms)

Iter	Nodes	Cost
0	560	14715
1	1551	13364
2	4477	12042
done	5000	12042

prune1.5s

Filtered

353 candidates to 756 candidates (-114.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	754	2	756
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	756	10	766

Merged error: 0.0b

Counts

766 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

1426×	`sqrt-prod`
977×	`times-frac`
520×	`add-sqr-sqrt`
515×	`add-cube-cbrt` `*-un-lft-identity`
506×	`associate-l`
135×	`add-exp-log`
89×	`add-cbrt-cube`
61×	`prod-exp`
44×	`div-exp`
39×	`cbrt-unprod`
25×	`cbrt-undiv`
18×	`pow1`
16×	`div-inv`
15×	`associate-/r*`
9×	`pow-prod-down`
6×	`associate-/l*`
5×	`rec-exp` `1-exp`
4×	`associate-*l/` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 674

Calls

4 calls:

10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
94.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series56.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
24.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify767.0ms

Counts

686 → 686

Iterations

Useful iterations: done (742.0ms)

Iter	Nodes	Cost
0	566	15411
1	1741	14089
done	5000	13822

prune2.9s

Filtered

381 candidates to 686 candidates (-80.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	684	2	686
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	687	9	696

Merged error: 0b

Counts

696 → 9

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))

rewrite77.0ms

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))
17.0ms	(/ (/ (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 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))

simplify649.0ms

Counts

481 → 481

Iterations

Useful iterations: 2 (329.0ms)

Iter	Nodes	Cost
0	477	9858
1	1119	8861
2	3282	7927
done	5000	7927

prune686.0ms

Filtered

189 candidates to 481 candidates (-154.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	481	9	490

Merged error: 0b

Counts

490 → 9

regimes474.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	18	24
done	18	24

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	2688×	body	1280	valid
703.0ms	2072×	body	640	valid
641.0ms	7888×	body	80	valid
252.0ms	1030×	body	320	valid
92.0ms	543×	body	160	valid

Details

sample125.0ms

simplify62.0ms

prune12.0ms

localize12.0ms

rewrite39.0ms

series51.0ms

simplify533.0ms

prune377.0ms

localize15.0ms

rewrite155.0ms

series45.0ms

simplify811.0ms

prune1.5s

localize22.0ms

rewrite191.0ms

series56.0ms

simplify767.0ms

prune2.9s

localize15.0ms

rewrite77.0ms

series39.0ms

simplify649.0ms

prune686.0ms

regimes474.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling