Details

sample263.0ms

Algorithm

intervals

Results

92.0ms	84×	body	1280	valid
68.0ms	258×	body	80	valid
50.0ms	65×	body	640	valid
20.0ms	35×	body	320	valid
8.0ms	21×	body	160	valid

simplify188.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

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:

40.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
30.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
15.0ms	(/ (cos th) (sqrt 2))

series500.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
134.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
92.0ms	(/ (cos th) (sqrt 2))
91.0ms	(/ (cos th) (sqrt 2))

simplify4.2s

Counts

192 → 192

Iterations

Iter	Nodes
3	7072
2	1733
1	518
0	189

prune876.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
127×	`add-sqr-sqrt`
122×	`*-un-lft-identity` `add-cube-cbrt`
70×	`sqrt-prod`
31×	`associate-/r*`
25×	`add-cbrt-cube` `add-exp-log`
22×	`associate-l`
12×	`associate-/l*`
9×	`pow1`
8×	`div-inv`
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/` `associate-/r/` `-commutative`

Counts

4 → 241

Calls

4 calls:

13.0ms	(/ a1 (/ (sqrt 2) a1))
42.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
5.0ms	(/ (sqrt 2) a1)
9.0ms	(/ (cos th) (sqrt 2))

series407.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ a1 (/ (sqrt 2) a1))
158.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
75.0ms	(/ (sqrt 2) a1)
79.0ms	(/ (cos th) (sqrt 2))

simplify845.0ms

Counts

253 → 253

Iterations

Iter	Nodes
2	2397
1	790
0	322

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

44×	`times-frac`
43×	`add-sqr-sqrt`
37×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log`
28×	`sqrt-prod`
25×	`associate-l`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`associate-*l/`

Counts

4 → 144

Calls

4 calls:

29.0ms	(* (cos th) (* a1 a1))
27.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
36.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series405.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cos th) (* a1 a1))
125.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
138.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
73.0ms	(/ (cos th) (sqrt 2))

simplify3.9s

Counts

156 → 156

Iterations

Iter	Nodes
3	7699
2	1735
1	522
0	202

prune875.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`times-frac`
49×	`*-un-lft-identity` `add-cube-cbrt`
34×	`sqrt-prod`
23×	`associate-l`
22×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
9×	`associate-/r` `associate-/l`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-r`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/` `div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`

Counts

4 → 153

Calls

4 calls:

48.0ms	(* (* (/ (cos th) (sqrt 2)) a2) a2)
24.0ms	(* (/ (cos th) (sqrt 2)) a2)
10.0ms	(/ (sqrt 2) a1)
18.0ms	(/ (cos th) (sqrt 2))

series467.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (* (/ (cos th) (sqrt 2)) a2) a2)
161.0ms	(* (/ (cos th) (sqrt 2)) a2)
74.0ms	(/ (sqrt 2) a1)
82.0ms	(/ (cos th) (sqrt 2))

simplify4.8s

Counts

165 → 165

Iterations

Iter	Nodes
3	4566
2	1361
1	454
0	210

prune826.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes604.0ms

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	17
1	17
0	13

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.5s	2475×	body	1280	valid
1.8s	2117×	body	640	valid
1.7s	8010×	body	80	valid
1.1s	1052×	body	320	valid
227.0ms	540×	body	160	valid