Details

sample208.0ms

Algorithm

intervals

Results

93.0ms	88×	body	1280	valid
37.0ms	73×	body	640	valid
29.0ms	258×	body	80	valid
11.0ms	30×	body	320	valid
2.0ms	11×	body	160	valid

simplify415.0ms

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize153.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (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))

rewrite332.0ms

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

Counts

4 → 172

Calls

4 calls:

88.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
133.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
48.0ms	(/ (cos th) (sqrt 2.0))
48.0ms	(/ (cos th) (sqrt 2.0))

series578.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
161.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
99.0ms	(/ (cos th) (sqrt 2.0))
96.0ms	(/ (cos th) (sqrt 2.0))

simplify4.0s

Counts

184 → 184

Iterations

Iter	Nodes
done	5000
2	1756
1	536
0	184

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize183.0ms

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)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite410.0ms

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×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 473

Calls

4 calls:

95.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
55.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
108.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
31.0ms	(/ (cos th) (sqrt 2.0))

series626.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
197.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
88.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
111.0ms	(/ (cos th) (sqrt 2.0))

simplify6.1s

Counts

485 → 485

Iterations

Iter	Nodes
done	5001
2	2969
1	1145
0	481

prune4.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize190.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.5b	(/ (sqrt 2.0) a1)
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite575.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
40×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
23×	`div-inv`
21×	`associate-/r*`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 748

Calls

4 calls:

265.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
16.0ms	(/ (sqrt 2.0) a1)
38.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
68.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
65.0ms	(/ (sqrt 2.0) a1)
164.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
126.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify4.5s

Counts

760 → 760

Iterations

Iter	Nodes
done	5000
1	1695
0	584

prune7.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize190.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (sqrt 2.0)) a1)
0.3b	(* (sqrt (sqrt 2.0)) (/ (sqrt (sqrt 2.0)) a1))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

687×	`sqrt-prod`
639×	`times-frac`
389×	`add-sqr-sqrt`
356×	`*-un-lft-identity` `add-cube-cbrt`
43×	`associate-/l*`
31×	`associate-r`
21×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
14×	`div-inv`
12×	`unswap-sqr`
9×	`associate-l`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 506

Calls

4 calls:

17.0ms	(/ (sqrt (sqrt 2.0)) a1)
79.0ms	(* (sqrt (sqrt 2.0)) (/ (sqrt (sqrt 2.0)) a1))
39.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
96.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sqrt (sqrt 2.0)) a1)
79.0ms	(* (sqrt (sqrt 2.0)) (/ (sqrt (sqrt 2.0)) a1))
191.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
123.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify7.7s

Counts

518 → 518

Iterations

Iter	Nodes
done	5000
2	3387
1	1226
0	500

prune4.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes1.9s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.3s	2574×	body	1280	valid
2.0s	8046×	body	80	valid
1.5s	2182×	body	640	valid
501.0ms	1051×	body	320	valid
151.0ms	565×	body	160	valid