Details

sample150.0ms

Algorithm

intervals

Results

75.0ms	82×	body	1280	valid
25.0ms	66×	body	640	valid
22.0ms	245×	body	80	valid
9.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

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))

rewrite99.0ms

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:

33.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
34.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
16.0ms	(/ (cos th) (sqrt 2))
11.0ms	(/ (cos th) (sqrt 2))

series462.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
163.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
93.0ms	(/ (cos th) (sqrt 2))
59.0ms	(/ (cos th) (sqrt 2))

simplify1.5s

Counts

184 → 184

Iterations

Iter	Nodes
done	5001
2	1563
1	533
0	183

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 748

Calls

4 calls:

193.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
24.0ms	(/ (cos th) (sqrt (sqrt 2)))
53.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
11.0ms	(/ (cos th) (sqrt 2))

series500.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
137.0ms	(/ (cos th) (sqrt (sqrt 2)))
85.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
89.0ms	(/ (cos th) (sqrt 2))

simplify3.0s

Counts

760 → 760

Iterations

Iter	Nodes
done	5002
2	4646
1	1634
0	563

prune3.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2)))
0.2b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))

rewrite513.0ms

Algorithm

rewrite-expression-head

Rules

1519×	`sqrt-prod`
1036×	`times-frac`
635×	`add-sqr-sqrt`
519×	`*-un-lft-identity`
506×	`associate-l`
503×	`add-cube-cbrt`
117×	`add-exp-log`
81×	`add-cbrt-cube`
45×	`div-exp`
44×	`prod-exp`
41×	`unswap-sqr`
30×	`cbrt-unprod`
27×	`cbrt-undiv`
18×	`div-inv`
15×	`associate-/r*`
14×	`associate-r`
11×	`pow1`
4×	`rec-exp` `1-exp` `pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 702

Calls

4 calls:

36.0ms	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2)))
346.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))))
37.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
29.0ms	(/ (cos th) (sqrt 2))

series685.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2)))
156.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2)))) (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))))
201.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
71.0ms	(/ (cos th) (sqrt 2))

simplify1.7s

Counts

714 → 714

Iterations

Iter	Nodes
done	5001
1	1748
0	561

prune4.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.4b	(* a1 (/ (cos th) (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

36.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
22.0ms	(* a1 (/ (cos th) (sqrt 2)))
10.0ms	(/ (cos th) (sqrt 2))
16.0ms	(/ (cos th) (sqrt 2))

series506.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
174.0ms	(* a1 (/ (cos th) (sqrt 2)))
75.0ms	(/ (cos th) (sqrt 2))
90.0ms	(/ (cos th) (sqrt 2))

simplify2.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	1424
1	483
0	179

prune883.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes474.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	16
1	16
0	12

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	2565×	body	1280	valid
1.4s	8111×	body	80	valid
1.0s	2148×	body	640	valid
526.0ms	1069×	body	320	valid
124.0ms	530×	body	160	valid