Details

sample189.0ms

Algorithm

intervals

Results

58.0ms	78×	body	1280	valid
44.0ms	68×	body	640	valid
28.0ms	242×	body	80	valid
14.0ms	39×	body	320	valid
3.0ms	12×	body	160	valid

simplify168.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

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

rewrite89.0ms

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

Counts

4 → 168

Calls

4 calls:

33.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
23.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
11.0ms	(/ (cos th) (sqrt 2.0))
16.0ms	(/ (cos th) (sqrt 2.0))

series540.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
172.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
107.0ms	(/ (cos th) (sqrt 2.0))
83.0ms	(/ (cos th) (sqrt 2.0))

simplify1.3s

Counts

180 → 180

Iterations

Iter	Nodes
done	5001
2	1722
1	521
0	181

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
51×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`unswap-sqr`
4×	`pow-prod-down` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 143

Calls

4 calls:

36.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2.0)))
34.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
14.0ms	(/ (* a2 a2) (sqrt 2.0))
16.0ms	(/ (cos th) (sqrt 2.0))

series521.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2.0)))
188.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
83.0ms	(/ (* a2 a2) (sqrt 2.0))
105.0ms	(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
2	1927
1	563
0	202

prune885.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite346.0ms

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`
37×	`add-cbrt-cube` `add-exp-log`
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×	`add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 732

Calls

4 calls:

197.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
17.0ms	(/ (* a2 a2) (sqrt 2.0))
11.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
27.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
91.0ms	(/ (* a2 a2) (sqrt 2.0))
152.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
87.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.7s

Counts

744 → 744

Iterations

Iter	Nodes
done	5000
1	1690
0	570

prune4.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a1 (/ a1 (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.4b	(/ a1 (sqrt 2.0))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
44×	`sqrt-prod`
25×	`add-cbrt-cube` `associate-l` `add-exp-log`
23×	`associate-r`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 165

Calls

4 calls:

22.0ms	(* a1 (/ a1 (sqrt 2.0)))
41.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
9.0ms	(/ a1 (sqrt 2.0))
16.0ms	(/ (cos th) (sqrt 2.0))

series452.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* a1 (/ a1 (sqrt 2.0)))
153.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
77.0ms	(/ a1 (sqrt 2.0))
114.0ms	(/ (cos th) (sqrt 2.0))

simplify1.5s

Counts

177 → 177

Iterations

Iter	Nodes
done	5014
2	1705
1	536
0	211

prune988.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes463.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample5.8s

Algorithm

intervals

Results

1.7s	2508×	body	1280	valid
1.6s	2077×	body	640	valid
1.0s	7978×	body	80	valid
436.0ms	518×	body	160	valid
301.0ms	1041×	body	320	valid