Details

sample288.0ms

Algorithm

intervals

Results

140.0ms	104×	body	1280	valid
54.0ms	65×	body	640	valid
46.0ms	290×	body	80	valid
21.0ms	36×	body	320	valid
6.0ms	18×	body	160	valid

simplify158.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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:

23.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
36.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series458.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
154.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
66.0ms	(/ (cos th) (sqrt 2))
70.0ms	(/ (cos th) (sqrt 2))

simplify4.5s

Counts

192 → 192

Iterations

Iter	Nodes
3	7069
2	1733
1	518
0	189

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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:

25.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
12.0ms	(* (/ (cos th) (sqrt 2)) a1)
11.0ms	(/ (cos th) (sqrt 2))
22.0ms	(/ (cos th) (sqrt 2))

series399.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
125.0ms	(* (/ (cos th) (sqrt 2)) a1)
77.0ms	(/ (cos th) (sqrt 2))
66.0ms	(/ (cos th) (sqrt 2))

simplify2.9s

Counts

189 → 189

Iterations

Iter	Nodes
3	5297
2	1454
1	490
0	184

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

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:

21.0ms	(* (/ (cos th) (sqrt 2)) a1)
32.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
20.0ms	(/ (cos th) (sqrt (sqrt 2)))
18.0ms	(/ (cos th) (sqrt 2))

series449.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (/ (cos th) (sqrt 2)) a1)
79.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
130.0ms	(/ (cos th) (sqrt (sqrt 2)))
99.0ms	(/ (cos th) (sqrt 2))

simplify1.1s

Counts

490 → 490

Iterations

Iter	Nodes
2	2529
1	1068
0	483

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt (sqrt 2)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

1188×	`sqrt-prod`
1152×	`times-frac`
620×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
68×	`associate-/l*`
36×	`associate-/r*`
24×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 782

Calls

4 calls:

31.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms	(/ (cos th) (sqrt (sqrt 2)))
16.0ms	(/ (cos th) (sqrt (sqrt 2)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
85.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
130.0ms	(/ (cos th) (sqrt (sqrt 2)))
128.0ms	(/ (cos th) (sqrt (sqrt 2)))

simplify6.5s

Counts

794 → 794

Iterations

Iter	Nodes
3	11893
2	1889
1	860
0	398

prune5.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes562.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.2s	2578×	body	1280	valid
1.7s	2062×	body	640	valid
1.5s	8121×	body	80	valid
1.0s	1010×	body	320	valid
244.0ms	523×	body	160	valid