Details

sample222.0ms

Algorithm

intervals

Results

98.0ms	84×	body	1280	valid
43.0ms	258×	body	80	valid
40.0ms	65×	body	640	valid
16.0ms	35×	body	320	valid
6.0ms	21×	body	160	valid

simplify500.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

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))

rewrite133.0ms

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:

43.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
43.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
23.0ms	(/ (cos th) (sqrt 2))

series549.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
161.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
104.0ms	(/ (cos th) (sqrt 2))
76.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

192 → 192

Iterations

Iter	Nodes
done	2003
3	2003
2	1524
1	528
0	189

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite87.0ms

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:

16.0ms	(* (cos th) (* a1 a1))
22.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
38.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series382.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos th) (* a1 a1))
134.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
122.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
78.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

156 → 156

Iterations

Iter	Nodes
done	2076
3	2076
2	1548
1	528
0	202

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

256×	`sqrt-prod`
254×	`times-frac`
125×	`add-sqr-sqrt`
120×	`*-un-lft-identity` `add-cube-cbrt`
41×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
17×	`associate-/l*`
14×	`div-inv`
13×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
9×	`pow1`
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 → 289

Calls

4 calls:

25.0ms	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2)))
39.0ms	(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
51.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))

series601.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2)))
147.0ms	(/ (/ (* (cos th) (* a1 a1)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
126.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
75.0ms	(/ (cos th) (sqrt 2))

simplify1.2s

Counts

301 → 301

Iterations

Iter	Nodes
done	2000
2	2000
1	929
0	361

prune3.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

718×	`sqrt-prod`
555×	`times-frac`
487×	`add-sqr-sqrt`
164×	`*-un-lft-identity` `add-cube-cbrt`
161×	`associate-r`
88×	`unswap-sqr`
62×	`associate-l`
55×	`add-cbrt-cube` `add-exp-log`
19×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod` `div-inv`
15×	`associate-/r*`
11×	`pow1`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 442

Calls

4 calls:

21.0ms	(/ (* a1 a1) (sqrt (sqrt 2)))
89.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
44.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
19.0ms	(/ (cos th) (sqrt 2))

series554.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (* a1 a1) (sqrt (sqrt 2)))
152.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ (* a1 a1) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
172.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
66.0ms	(/ (cos th) (sqrt 2))

simplify1.4s

Counts

454 → 454

Iterations

Iter	Nodes
done	2001
2	2001
1	1732
0	506

prune7.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes533.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.8s	2475×	body	1280	valid
1.7s	2117×	body	640	valid
1.6s	8010×	body	80	valid
679.0ms	1052×	body	320	valid
182.0ms	540×	body	160	valid