Details

sample80.0ms

Algorithm

intervals

Results

23.0ms	74×	body	1280	valid
15.0ms	69×	body	640	valid
12.0ms	260×	body	80	valid
6.0ms	17×	body	160	valid
5.0ms	36×	body	320	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7
done	141	7

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (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))

rewrite88.0ms

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:

29.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
32.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
10.0ms	(/ (cos th) (sqrt 2.0))
10.0ms	(/ (cos th) (sqrt 2.0))

series357.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
114.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
64.0ms	(/ (cos th) (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify49.0ms

Counts

180 → 180

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	504	1284
1	2009	1156
2	5002	1136
done	5002	1136

prune463.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

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:

31.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
26.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
16.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
10.0ms	(/ (cos th) (sqrt 2.0))

series552.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
311.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms	(/ (cos th) (sqrt 2.0))

simplify104.0ms

Counts

481 → 481

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	1115	6666
1	4569	5845
2	5002	5839
done	5002	5839

prune821.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize13.0ms

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

1188×	`sqrt-prod`
1152×	`times-frac`
620×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
68×	`associate-/l*`
36×	`associate-/r*`
24×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 770

Calls

4 calls:

26.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
29.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
11.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
11.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
58.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
100.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
103.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify126.0ms

Counts

782 → 782

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	869	12144
1	3419	10626
2	5001	10588
done	5001	10588

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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:

20.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
26.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
10.0ms	(/ (cos th) (sqrt 2.0))

series329.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
59.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
99.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
64.0ms	(/ (cos th) (sqrt 2.0))

simplify113.0ms

Counts

478 → 478

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	1055	6589
1	4296	5793
2	5002	5784
done	5002	5784

prune821.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes376.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	15
1	19	15
done	19	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

772.0ms	2504×	body	1280	valid
441.0ms	2115×	body	640	valid
388.0ms	8016×	body	80	valid
156.0ms	1035×	body	320	valid
49.0ms	495×	body	160	valid