Details

sample205.0ms

Algorithm

intervals

Results

68.0ms	263×	body	80	valid
66.0ms	77×	body	1280	valid
34.0ms	57×	body	640	valid
13.0ms	31×	body	320	valid
5.0ms	19×	body	160	valid

simplify119.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.5b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite79.0ms

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

Counts

4 → 168

Calls

4 calls:

18.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
34.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms	(/ (cos th) (sqrt 2))
8.0ms	(/ (cos th) (sqrt 2))

series414.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
150.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
59.0ms	(/ (cos th) (sqrt 2))
78.0ms	(/ (cos th) (sqrt 2))

simplify3.9s

Counts

180 → 180

Iterations

Iter	Nodes
3	6665
2	1718
1	518
0	180

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

26.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
10.0ms	(* (/ (cos th) (sqrt 2)) a2)
7.0ms	(/ (cos th) (sqrt 2))
18.0ms	(/ (cos th) (sqrt 2))

series441.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
139.0ms	(* (/ (cos th) (sqrt 2)) a2)
71.0ms	(/ (cos th) (sqrt 2))
76.0ms	(/ (cos th) (sqrt 2))

simplify4.0s

Counts

177 → 177

Iterations

Iter	Nodes
3	4945
2	1532
1	469
0	174

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* (cos th) a2) (sqrt 2)) a2)
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.4b	(/ (* (cos th) a2) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

30.0ms	(* (/ (* (cos th) a2) (sqrt 2)) a2)
29.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms	(/ (* (cos th) a2) (sqrt 2))
8.0ms	(/ (cos th) (sqrt 2))

series602.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (/ (* (cos th) a2) (sqrt 2)) a2)
190.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
142.0ms	(/ (* (cos th) a2) (sqrt 2))
98.0ms	(/ (cos th) (sqrt 2))

simplify6.3s

Counts

153 → 153

Iterations

Iter	Nodes
3	8636
2	1962
1	560
0	204

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) a2)
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
640×	`add-sqr-sqrt`
593×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
37×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
22×	`add-cbrt-cube` `add-exp-log`
13×	`unswap-sqr`
8×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 739

Calls

4 calls:

24.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) a2)
8.0ms	(/ (cos th) (sqrt (sqrt 2)))
12.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
7.0ms	(/ (cos th) (sqrt 2))

series420.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) a2)
137.0ms	(/ (cos th) (sqrt (sqrt 2)))
61.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
68.0ms	(/ (cos th) (sqrt 2))

simplify1.4s

Counts

751 → 751

Iterations

Iter	Nodes
2	3280
1	1332
0	552

prune12.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes677.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	17
1	17
0	13

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.2s	2487×	body	1280	valid
2.2s	2128×	body	640	valid
1.7s	7966×	body	80	valid
699.0ms	1040×	body	320	valid
203.0ms	495×	body	160	valid