Details

sample149.0ms

Algorithm

intervals

Results

54.0ms	88×	body	1280	valid
29.0ms	277×	body	80	valid
29.0ms	58×	body	640	valid
8.0ms	28×	body	320	valid
3.0ms	14×	body	160	valid

simplify153.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.5b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.8b	(/ (cos th) (sqrt 2.0))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite121.0ms

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:

55.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
38.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
8.0ms	(/ (cos th) (sqrt 2.0))
8.0ms	(/ (cos th) (sqrt 2.0))

series493.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
190.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
79.0ms	(/ (cos th) (sqrt 2.0))
83.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	1723
1	533
0	187

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ (cos th) (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)))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite104.0ms

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:

29.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
24.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms	(/ (cos th) (sqrt 2.0))

series482.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
134.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
76.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
79.0ms	(/ (cos th) (sqrt 2.0))

simplify2.1s

Counts

489 → 489

Iterations

Iter	Nodes
done	5000
2	2811
1	1134
0	485

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* a1 a1) (cos th)) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (* a1 a1) (cos th))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite92.0ms

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`
23×	`associate-l`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*l/`

Counts

4 → 140

Calls

4 calls:

33.0ms	(/ (* (* a1 a1) (cos th)) (sqrt 2.0))
29.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
16.0ms	(* (* a1 a1) (cos th))
9.0ms	(/ (cos th) (sqrt 2.0))

series418.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (* (* a1 a1) (cos th)) (sqrt 2.0))
130.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
54.0ms	(* (* a1 a1) (cos th))
89.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

152 → 152

Iterations

Iter	Nodes
done	5003
2	2005
1	563
0	200

prune913.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a1 (cos th))
0.2b	(/ (* a1 (* a1 (cos th))) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
44×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
29×	`add-cbrt-cube` `add-exp-log`
28×	`sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1`
10×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*l/`

Counts

4 → 139

Calls

4 calls:

9.0ms	(* a1 (cos th))
19.0ms	(/ (* a1 (* a1 (cos th))) (sqrt 2.0))
44.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms	(/ (cos th) (sqrt 2.0))

series419.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* a1 (cos th))
119.0ms	(/ (* a1 (* a1 (cos th))) (sqrt 2.0))
150.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
103.0ms	(/ (cos th) (sqrt 2.0))

simplify2.2s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	1904
1	543
0	207

prune951.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes512.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.3s	2546×	body	1280	valid
1.1s	2126×	body	640	valid
1.1s	7977×	body	80	valid
888.0ms	1079×	body	320	valid
170.0ms	545×	body	160	valid