Details

sample173.0ms

Algorithm

intervals

Results

75.0ms	76×	body	1280	valid
36.0ms	61×	body	640	valid
31.0ms	257×	body	80	valid
12.0ms	30×	body	320	valid
3.0ms	12×	body	160	valid

simplify106.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite88.0ms

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` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 180

Calls

4 calls:

25.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
35.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
16.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series426.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
136.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
80.0ms	(/ (cos th) (sqrt 2))
81.0ms	(/ (cos th) (sqrt 2))

simplify1.4s

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
2	1524
1	528
0	189

prune938.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 2) (cos th))
0.3b	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
78×	`add-sqr-sqrt`
73×	`*-un-lft-identity` `add-cube-cbrt`
52×	`sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
31×	`associate-/r*`
22×	`associate-l`
10×	`cbrt-undiv` `div-exp` `associate-/l*`
9×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 199

Calls

4 calls:

6.0ms	(/ (sqrt 2) (cos th))
13.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
22.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms	(/ (cos th) (sqrt 2))

series402.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (sqrt 2) (cos th))
136.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
138.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
63.0ms	(/ (cos th) (sqrt 2))

simplify1.9s

Counts

211 → 211

Iterations

Iter	Nodes
done	5000
2	2292
1	741
0	271

prune1.0s

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	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
0.7b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

1177×	`times-frac`
1155×	`sqrt-prod`
637×	`add-sqr-sqrt`
603×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
44×	`add-cbrt-cube` `add-exp-log`
40×	`associate-/r*`
35×	`associate-/l*`
25×	`div-inv`
16×	`cbrt-undiv` `div-exp`
13×	`unswap-sqr`
11×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `associate-/r/` `-commutative` `associate-/l/`

Counts

4 → 781

Calls

4 calls:

26.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
75.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
27.0ms	(/ (cos th) (sqrt (sqrt 2)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
137.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
131.0ms	(/ (cos th) (sqrt (sqrt 2)))
111.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify2.0s

Counts

793 → 793

Iterations

Iter	Nodes
done	5001
1	1987
0	661

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
0.3b	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a2 a2))
1.0b	(/ 1 (sqrt (sqrt 2)))
1.0b	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

1556×	`times-frac`
1537×	`sqrt-prod`
849×	`add-sqr-sqrt`
792×	`*-un-lft-identity`
780×	`add-cube-cbrt`
392×	`cbrt-prod`
376×	`associate-l`
64×	`add-exp-log`
44×	`add-cbrt-cube`
43×	`associate-/r*`
35×	`associate-/l*`
31×	`div-inv`
29×	`unswap-sqr`
26×	`div-exp`
17×	`prod-exp`
16×	`cbrt-undiv`
13×	`pow1`
11×	`cbrt-unprod`
7×	`sqrt-pow1` `pow-flip`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow1/2` `pow-prod-down`
2×	`pow1/3` `pow-div`
1×	`associate-r` `associate-l/` `associate-/r/` `-commutative` `inv-pow` `associate-/l/`

Counts

4 → 1002

Calls

4 calls:

16.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
58.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a2 a2))
8.0ms	(/ 1 (sqrt (sqrt 2)))
34.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

series689.0ms

Counts

4 → 8

Calls

4 calls:

148.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
541.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a2 a2))
0.0ms	(/ 1 (sqrt (sqrt 2)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

simplify2.3s

Counts

1010 → 1010

Iterations

Iter	Nodes
done	5001
1	2246
0	781

prune5.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes516.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample8.3s

Algorithm

intervals

Results

2.8s	2449×	body	1280	valid
2.3s	2010×	body	640	valid
1.5s	7946×	body	80	valid
1.1s	980×	body	320	valid
219.0ms	521×	body	160	valid