Details

sample258.0ms

Algorithm

intervals

Results

115.0ms	90×	body	1280	valid
57.0ms	78×	body	640	valid
43.0ms	258×	body	80	valid
12.0ms	23×	body	320	valid
6.0ms	15×	body	160	valid

simplify173.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.2b	(* (/ (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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 180

Calls

4 calls:

26.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
50.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
10.0ms	(/ (cos th) (sqrt 2))
10.0ms	(/ (cos th) (sqrt 2))

series519.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
148.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
76.0ms	(/ (cos th) (sqrt 2))
106.0ms	(/ (cos th) (sqrt 2))

simplify4.1s

Counts

192 → 192

Iterations

Iter	Nodes
3	7069
2	1733
1	518
0	189

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 481

Calls

4 calls:

47.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
11.0ms	(/ (cos th) (sqrt (sqrt 2)))
20.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
20.0ms	(/ (cos th) (sqrt 2))

series452.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
141.0ms	(/ (cos th) (sqrt (sqrt 2)))
76.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
90.0ms	(/ (cos th) (sqrt 2))

simplify1.2s

Counts

493 → 493

Iterations

Iter	Nodes
2	2888
1	1132
0	488

prune7.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (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))

rewrite95.0ms

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×	`expm1-log1p-u` `associate-r` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`

Counts

4 → 177

Calls

4 calls:

41.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
14.0ms	(* (/ (cos th) (sqrt 2)) a2)
18.0ms	(/ (cos th) (sqrt 2))
18.0ms	(/ (cos th) (sqrt 2))

series521.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
155.0ms	(* (/ (cos th) (sqrt 2)) a2)
107.0ms	(/ (cos th) (sqrt 2))
74.0ms	(/ (cos th) (sqrt 2))

simplify2.5s

Counts

189 → 189

Iterations

Iter	Nodes
3	4555
2	1380
1	474
0	183

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) a1)
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
349×	`add-sqr-sqrt`
341×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
24×	`associate-/r*`
22×	`associate-l`
18×	`add-cbrt-cube` `add-exp-log`
14×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `unswap-sqr`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 478

Calls

4 calls:

26.0ms	(* (/ (cos th) (sqrt 2)) a1)
21.0ms	(/ (cos th) (sqrt (sqrt 2)))
28.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
10.0ms	(/ (cos th) (sqrt 2))

series441.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (/ (cos th) (sqrt 2)) a1)
117.0ms	(/ (cos th) (sqrt (sqrt 2)))
89.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
93.0ms	(/ (cos th) (sqrt 2))

simplify1.1s

Counts

490 → 490

Iterations

Iter	Nodes
2	2504
1	1074
0	483

prune7.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes724.0ms

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	16
1	16
0	12

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.9s	2571×	body	1280	valid
1.7s	2063×	body	640	valid
1.5s	8110×	body	80	valid
1.3s	1009×	body	320	valid
185.0ms	512×	body	160	valid