Details

sample79.0ms

Algorithm

intervals

Results

25.0ms	77×	body	1280	valid
15.0ms	67×	body	640	valid
13.0ms	264×	body	80	valid
7.0ms	44×	body	320	valid
1.0ms	13×	body	160	valid

simplify129.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	52	12
3	75	12
4	102	12
5	122	12
6	139	12
7	143	12
8	145	12
done	145	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.5b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite48.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 176

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series326.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
106.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
59.0ms	(/ (cos th) (sqrt 2.0))
56.0ms	(/ (cos th) (sqrt 2.0))

simplify871.0ms

Counts

188 → 188

Iterations

Useful iterations: done (863.0ms)

Iter	Nodes	Cost
0	187	2182
1	498	2076
2	1609	1894
done	5000	1874

prune480.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b	(* (/ (cos th) (sqrt 2.0)) a2)
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
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` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 173

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series323.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
102.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
55.0ms	(/ (cos th) (sqrt 2.0))
59.0ms	(/ (cos th) (sqrt 2.0))

simplify1.0s

Counts

185 → 185

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	181	2019
1	444	1920
2	1423	1778
done	5000	1762

prune485.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2.0)) a2)
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))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
349×	`add-sqr-sqrt`
341×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-/l*`
24×	`associate-/r*`
22×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
14×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `unswap-sqr`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 474

Calls

4 calls:

12.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
18.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series328.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
98.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
56.0ms	(/ (cos th) (sqrt 2.0))

simplify1.1s

Counts

486 → 486

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	479	9763
1	1062	8440
2	2398	7873
done	5001	7871

prune890.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.4b	(/ (* (cos th) a2) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

1143×	`sqrt-prod`
1125×	`times-frac`
615×	`add-sqr-sqrt`
581×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`add-exp-log` `add-cbrt-cube`
35×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
12×	`cbrt-undiv` `div-exp`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 740

Calls

4 calls:

95.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
4.0ms	(/ (* (cos th) a2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
21.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
102.0ms	(/ (* (cos th) a2) (sqrt 2.0))
97.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
69.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.6s

Counts

752 → 752

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	579	14662
1	1598	12978
2	4035	11966
done	5000	11964

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes314.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: done (2.0ms)

Iter	Nodes	Cost
0	21	34
1	28	32
done	28	30

end0.0ms

sample2.3s

Algorithm

intervals

Results

814.0ms	2511×	body	1280	valid
452.0ms	2041×	body	640	valid
412.0ms	8164×	body	80	valid
163.0ms	1027×	body	320	valid
57.0ms	537×	body	160	valid