Details

sample124.0ms

Algorithm

intervals

Results

45.0ms	88×	body	1280	valid
24.0ms	277×	body	80	valid
21.0ms	58×	body	640	valid
7.0ms	28×	body	320	valid
2.0ms	14×	body	160	valid

simplify169.0ms

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize45.0ms

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))

rewrite116.0ms

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:

30.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
43.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
16.0ms	(/ (cos th) (sqrt 2.0))
16.0ms	(/ (cos th) (sqrt 2.0))

series483.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
172.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
81.0ms	(/ (cos th) (sqrt 2.0))
66.0ms	(/ (cos th) (sqrt 2.0))

simplify1.8s

Counts

180 → 180

Iterations

Iter	Nodes
done	5001
2	1722
1	521
0	181

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

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×	`associate-r` `pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*l/`

Counts

4 → 131

Calls

4 calls:

7.0ms	(* (cos th) a1)
24.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
36.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms	(/ (cos th) (sqrt 2.0))

series435.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos th) a1)
165.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
149.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
69.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

143 → 143

Iterations

Iter	Nodes
done	5004
2	1940
1	539
0	204

prune890.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite268.0ms

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

Counts

4 → 734

Calls

4 calls:

20.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
136.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
24.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
23.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
156.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
147.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
116.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.9s

Counts

746 → 746

Iterations

Iter	Nodes
done	5000
1	1745
0	588

prune4.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
0.2b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* a2 (* a2 (/ (cos th) (sqrt (sqrt 2.0))))))
0.3b	(* a2 (/ (cos th) (sqrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite520.0ms

Algorithm

rewrite-expression-head

Rules

1440×	`sqrt-prod`
975×	`times-frac`
522×	`add-sqr-sqrt`
511×	`*-un-lft-identity` `add-cube-cbrt`
487×	`associate-l`
110×	`add-exp-log`
74×	`add-cbrt-cube`
50×	`prod-exp`
34×	`div-exp`
32×	`associate-r` `cbrt-unprod`
20×	`cbrt-undiv`
16×	`div-inv`
15×	`pow1` `associate-/r*`
7×	`pow-prod-down`
6×	`associate-*r/`
4×	`rec-exp` `1-exp` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `associate-*l/`

Counts

4 → 663

Calls

4 calls:

35.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
327.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* a2 (* a2 (/ (cos th) (sqrt (sqrt 2.0))))))
32.0ms	(* a2 (/ (cos th) (sqrt (sqrt 2.0))))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
155.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* a2 (* a2 (/ (cos th) (sqrt (sqrt 2.0))))))
173.0ms	(* a2 (/ (cos th) (sqrt (sqrt 2.0))))
121.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify2.0s

Counts

675 → 675

Iterations

Iter	Nodes
done	5000
1	1702
0	567

prune5.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes534.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	27
1	27
0	19

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.0s	2546×	body	1280	valid
1.5s	7977×	body	80	valid
1.1s	2126×	body	640	valid
468.0ms	1079×	body	320	valid
162.0ms	545×	body	160	valid