Details

sample136.0ms

Algorithm

intervals

Results

42.0ms	82×	body	1280	valid
24.0ms	66×	body	640	valid
20.0ms	245×	body	80	valid
7.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify362.0ms

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite194.0ms

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×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

62.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
79.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(/ (cos th) (sqrt 2.0))
19.0ms	(/ (cos th) (sqrt 2.0))

series666.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
226.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
124.0ms	(/ (cos th) (sqrt 2.0))
110.0ms	(/ (cos th) (sqrt 2.0))

simplify3.1s

Counts

184 → 184

Iterations

Iter	Nodes
done	5000
2	1756
1	536
0	184

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite611.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 748

Calls

4 calls:

303.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
29.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
59.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
29.0ms	(/ (cos th) (sqrt 2.0))

series572.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
183.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
114.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
75.0ms	(/ (cos th) (sqrt 2.0))

simplify7.3s

Counts

760 → 760

Iterations

Iter	Nodes
done	5001
2	4968
1	1634
0	564

prune7.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize149.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

793×	`sqrt-prod`
788×	`times-frac`
434×	`add-sqr-sqrt`
429×	`*-un-lft-identity` `add-cube-cbrt`
192×	`cbrt-prod`
37×	`associate-/l*`
27×	`associate-/r*`
25×	`add-cbrt-cube` `add-exp-log`
22×	`associate-l`
17×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 569

Calls

4 calls:

45.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
17.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
47.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
24.0ms	(/ (cos th) (sqrt 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

240.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
147.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
566.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
117.0ms	(/ (cos th) (sqrt 2.0))

simplify5.3s

Counts

581 → 581

Iterations

Iter	Nodes
done	5000
2	3516
1	1415
0	619

prune5.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) a1)
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite157.0ms

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` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`

Counts

4 → 169

Calls

4 calls:

54.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
50.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
14.0ms	(/ (cos th) (sqrt 2.0))
24.0ms	(/ (cos th) (sqrt 2.0))

series659.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
212.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
121.0ms	(/ (cos th) (sqrt 2.0))
101.0ms	(/ (cos th) (sqrt 2.0))

simplify3.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	1508
1	483
0	179

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes1.7s

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	16
1	16
0	12

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.0s	2148×	body	640	valid
1.8s	2565×	body	1280	valid
1.1s	8111×	body	80	valid
400.0ms	1069×	body	320	valid
101.0ms	530×	body	160	valid