Details

sample120.0ms

Algorithm

intervals

Results

28.0ms	72×	body	1280	valid
20.0ms	75×	body	640	valid
16.0ms	251×	body	80	valid
7.0ms	35×	body	320	valid
2.0ms	16×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

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))

rewrite112.0ms

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:

39.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
43.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
12.0ms	(/ (cos th) (sqrt 2.0))
11.0ms	(/ (cos th) (sqrt 2.0))

series436.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
150.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
76.0ms	(/ (cos th) (sqrt 2.0))
79.0ms	(/ (cos th) (sqrt 2.0))

simplify49.0ms

Counts: 180 → 180

prune813.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.2b	(/ (pow a1 2) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
121×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
77×	`sqrt-prod`
53×	`associate-r`
41×	`unpow-prod-down`
33×	`add-exp-log`
25×	`associate-l` `add-cbrt-cube`
15×	`unpow2` `sqr-pow`
12×	`associate-/r*` `unswap-sqr`
11×	`pow1` `associate-/l*`
10×	`prod-exp`
9×	`div-exp`
8×	`cbrt-unprod`
5×	`cbrt-undiv`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative`
1×	`associate-r/` `associate-l/`

Counts

4 → 240

Calls

4 calls:

45.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
21.0ms	(/ (pow a1 2) (sqrt 2.0))
39.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
12.0ms	(/ (cos th) (sqrt 2.0))

series561.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
88.0ms	(/ (pow a1 2) (sqrt 2.0))
164.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
115.0ms	(/ (cos th) (sqrt 2.0))

simplify80.0ms

Counts: 252 → 252

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow a1 2) (sqrt 2.0))
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)))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

1167×	`times-frac`
1164×	`sqrt-prod`
643×	`add-sqr-sqrt`
609×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
42×	`associate-/l*`
37×	`add-exp-log`
34×	`add-cbrt-cube`
24×	`associate-/r*`
23×	`div-inv`
21×	`unpow-prod-down`
13×	`div-exp` `unswap-sqr`
11×	`cbrt-undiv`
9×	`pow1` `prod-exp` `cbrt-unprod`
7×	`unpow2` `sqr-pow`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`pow-to-exp` `associate-r` `associate-l/` `pow-exp` `-commutative` `associate-/l/`

Counts

4 → 781

Calls

4 calls:

21.0ms	(/ (pow a1 2) (sqrt 2.0))
217.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
46.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
13.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (pow a1 2) (sqrt 2.0))
221.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
127.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
129.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify127.0ms

Counts: 793 → 793

prune3.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
0.2b	(/ (pow a1 2) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite602.0ms

Algorithm

rewrite-expression-head

Rules

1461×	`sqrt-prod`
1017×	`times-frac`
545×	`add-sqr-sqrt`
538×	`add-cube-cbrt` `*-un-lft-identity`
515×	`associate-l`
138×	`add-exp-log`
89×	`add-cbrt-cube`
61×	`prod-exp`
46×	`div-exp`
39×	`cbrt-unprod`
25×	`cbrt-undiv`
21×	`unpow-prod-down`
18×	`pow1`
16×	`div-inv`
15×	`associate-/r*`
11×	`associate-/l*`
9×	`pow-prod-down`
7×	`unpow2` `sqr-pow`
5×	`rec-exp` `1-exp`
4×	`associate-*l/` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`frac-times` `pow-to-exp` `associate-*r/` `pow-exp`

Counts

4 → 721

Calls

4 calls:

379.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
12.0ms	(/ (pow a1 2) (sqrt 2.0))
49.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
25.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
131.0ms	(/ (pow a1 2) (sqrt 2.0))
276.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
124.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify141.0ms

Counts: 733 → 733

prune4.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes730.0ms

Accuracy

-18.6% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify58.0ms

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	2486×	body	1280	valid
1.3s	2091×	body	640	valid
1.1s	8121×	body	80	valid
780.0ms	1064×	body	320	valid
662.0ms	528×	body	160	valid