Details

sample160.0ms

Algorithm

intervals

Results

58.0ms	77×	body	1280	valid
29.0ms	56×	body	640	valid
27.0ms	227×	body	80	valid
9.0ms	25×	body	320	valid
3.0ms	14×	body	160	valid

simplify222.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	49	13
3	76	13
4	95	13
5	111	13
6	125	13
7	139	13
done	139	13

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

58.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
32.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
11.0ms	(/ (cos th) (sqrt 2.0))
15.0ms	(/ (cos th) (sqrt 2.0))

series498.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
157.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
87.0ms	(/ (cos th) (sqrt 2.0))
97.0ms	(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts

180 → 180

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	181	2118
1	466	2012
2	1390	1832
done	5000	1812

prune653.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 469

Calls

4 calls:

41.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
25.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
59.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
10.0ms	(/ (cos th) (sqrt 2.0))

series497.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
157.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
95.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
81.0ms	(/ (cos th) (sqrt 2.0))

simplify2.0s

Counts

481 → 481

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	477	9858
1	1085	8538
2	2251	7927
done	5001	7755

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 770

Calls

4 calls:

28.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
24.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
57.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
42.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series781.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
513.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
83.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
63.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify2.6s

Counts

782 → 782

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	393	17598
1	860	15064
2	1555	14042
3	3573	13698
done	5001	13572

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

1389×	`sqrt-prod`
1272×	`times-frac`
667×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
102×	`cbrt-prod`
62×	`associate-/l*`
25×	`div-inv`
21×	`associate-/r*`
14×	`add-exp-log` `add-cbrt-cube`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `add-log-exp`
2×	`frac-2neg` `pow1/3` `clear-num` `associate-/l/`

Counts

4 → 786

Calls

4 calls:

60.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
63.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
2.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)

series620.0ms

Counts

4 → 8

Calls

4 calls:

106.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
514.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify3.0s

Counts

794 → 794

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	730	19723
1	1641	17092
2	3352	16543
done	5001	16356

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes451.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	37
1	29	37
done	29	37

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.8s	2525×	body	1280	valid
1.0s	7986×	body	80	valid
997.0ms	2049×	body	640	valid
580.0ms	1057×	body	320	valid
157.0ms	503×	body	160	valid