Details

sample188.0ms

Algorithm

intervals

Results

80.0ms	84×	body	1280	valid
34.0ms	67×	body	640	valid
27.0ms	255×	body	80	valid
10.0ms	30×	body	320	valid
4.0ms	20×	body	160	valid

simplify200.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	57	12
3	87	12
4	114	12
5	132	12
6	151	12
7	173	12
8	175	12
done	175	12

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

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))

rewrite154.0ms

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

Counts

4 → 176

Calls

4 calls:

50.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
52.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
23.0ms	(/ (cos th) (sqrt 2.0))
17.0ms	(/ (cos th) (sqrt 2.0))

series512.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
161.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
83.0ms	(/ (cos th) (sqrt 2.0))
91.0ms	(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts

188 → 188

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	187	2182
1	547	2076
2	2825	1894
done	5000	1890

prune948.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `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 → 477

Calls

4 calls:

30.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
16.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
32.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms	(/ (cos th) (sqrt 2.0))

series464.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
146.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
87.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
73.0ms	(/ (cos th) (sqrt 2.0))

simplify797.0ms

Counts

489 → 489

Iterations

Useful iterations: done (762.0ms)

Iter	Nodes	Cost
0	485	9926
1	1165	8596
done	5001	8073

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 742

Calls

4 calls:

160.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
35.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
18.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
47.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
161.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
182.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
90.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.1s

Counts

754 → 754

Iterations

Useful iterations: done (985.0ms)

Iter	Nodes	Cost
0	592	14782
1	1780	13091
done	5000	12185

prune3.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))) (* a2 a2))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

rewrite830.0ms

Algorithm

rewrite-expression-head

Rules

1506×	`sqrt-prod`
1153×	`times-frac`
1034×	`add-sqr-sqrt`
476×	`*-un-lft-identity`
408×	`add-cube-cbrt`
377×	`associate-r`
173×	`add-exp-log`
153×	`unswap-sqr`
101×	`add-cbrt-cube`
78×	`prod-exp`
58×	`div-exp`
42×	`cbrt-unprod`
41×	`associate-l`
31×	`cbrt-undiv`
18×	`pow1`
16×	`div-inv`
15×	`associate-/r*`
9×	`rec-exp` `1-exp` `pow-prod-down`
5×	`associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-times` `clear-num` `frac-2neg` `associate-r/` `-commutative`

Counts

4 → 744

Calls

4 calls:

279.0ms	(* (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))) (* a2 a2))
28.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
428.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))) (* a2 a2))
182.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
167.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
86.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

simplify2.8s

Counts

756 → 756

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	801	20205
1	2998	18174
done	5001	15725

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes631.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	45
1	28	45
done	28	45

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.3s	2548×	body	1280	valid
1.5s	8045×	body	80	valid
1.1s	2150×	body	640	valid
334.0ms	970×	body	320	valid
146.0ms	558×	body	160	valid