Details

sample233.0ms

Algorithm

intervals

Results

75.0ms	74×	body	1280	valid
74.0ms	69×	body	640	valid
42.0ms	246×	body	80	valid
16.0ms	30×	body	320	valid
7.0ms	19×	body	160	valid

simplify166.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite113.0ms

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×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

37.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
48.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series490.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
175.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
74.0ms	(/ (cos th) (sqrt 2))
90.0ms	(/ (cos th) (sqrt 2))

simplify4.3s

Counts

184 → 184

Iterations

Iter	Nodes
3	7109
2	1765
1	523
0	183

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
51×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`unswap-sqr`
4×	`pow-prod-down` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 147

Calls

4 calls:

16.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
25.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms	(/ (* a1 a1) (sqrt 2))
8.0ms	(/ (cos th) (sqrt 2))

series485.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
152.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
94.0ms	(/ (* a1 a1) (sqrt 2))
96.0ms	(/ (cos th) (sqrt 2))

simplify5.7s

Counts

159 → 159

Iterations

Iter	Nodes
3	6468
2	1814
1	525
0	205

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a2 (/ a2 (sqrt 2))))
0.2b	(* a2 (/ a2 (sqrt 2)))
0.3b	(/ (* a1 a1) (sqrt 2))
0.4b	(/ a2 (sqrt 2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
28×	`sqrt-prod`
25×	`add-cbrt-cube` `add-exp-log`
23×	`associate-r`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`associate-*r/` `div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`

Counts

4 → 133

Calls

4 calls:

21.0ms	(* (cos th) (* a2 (/ a2 (sqrt 2))))
16.0ms	(* a2 (/ a2 (sqrt 2)))
18.0ms	(/ (* a1 a1) (sqrt 2))
9.0ms	(/ a2 (sqrt 2))

series464.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (cos th) (* a2 (/ a2 (sqrt 2))))
100.0ms	(* a2 (/ a2 (sqrt 2)))
107.0ms	(/ (* a1 a1) (sqrt 2))
90.0ms	(/ a2 (sqrt 2))

simplify1.9s

Counts

145 → 145

Iterations

Iter	Nodes
3	4343
2	1135
1	406
0	178

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a1 (sqrt (sqrt 2)))
0.2b	(/ a1 (sqrt (sqrt 2)))
0.3b	(* (/ a1 (sqrt (sqrt 2))) (/ a1 (sqrt (sqrt 2))))
0.4b	(/ a2 (sqrt 2))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

252×	`sqrt-prod`
243×	`add-sqr-sqrt`
240×	`times-frac`
151×	`*-un-lft-identity` `add-cube-cbrt`
49×	`swap-sqr`
31×	`associate-r` `associate-l`
24×	`associate-/r*`
22×	`add-cbrt-cube` `add-exp-log`
16×	`unswap-sqr`
11×	`pow1`
9×	`associate-/l*`
7×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 296

Calls

4 calls:

13.0ms	(/ a1 (sqrt (sqrt 2)))
5.0ms	(/ a1 (sqrt (sqrt 2)))
28.0ms	(* (/ a1 (sqrt (sqrt 2))) (/ a1 (sqrt (sqrt 2))))
9.0ms	(/ a2 (sqrt 2))

series557.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ a1 (sqrt (sqrt 2)))
183.0ms	(/ a1 (sqrt (sqrt 2)))
126.0ms	(* (/ a1 (sqrt (sqrt 2))) (/ a1 (sqrt (sqrt 2))))
74.0ms	(/ a2 (sqrt 2))

simplify2.5s

Counts

308 → 308

Iterations

Iter	Nodes
3	5644
2	1769
1	710
0	244

prune4.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes596.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	24
1	24
0	18

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.0s	2473×	body	1280	valid
2.3s	8136×	body	80	valid
1.9s	2142×	body	640	valid
656.0ms	1055×	body	320	valid
281.0ms	527×	body	160	valid