Details

sample177.0ms

Algorithm

intervals

Results

76.0ms	86×	body	1280	valid
30.0ms	62×	body	640	valid
27.0ms	247×	body	80	valid
10.0ms	30×	body	320	valid
3.0ms	12×	body	160	valid

simplify141.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	126
5	111
4	95
3	76
2	49
1	25
0	12

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (sqrt 2.0) (cos th))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
93×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `associate-/r/`

Counts

3 → 158

Calls

3 calls:

12.0ms	(+ (* a1 a1) (* a2 a2))
11.0ms	(/ (sqrt 2.0) (cos th))
26.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series360.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* a1 a1) (* a2 a2))
52.0ms	(/ (sqrt 2.0) (cos th))
266.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify2.3s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	4529
1	680
0	250

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (sqrt 2.0) (cos th))
0.2b	(/ 1 (/ (/ (sqrt 2.0) (cos th)) (+ (* a1 a1) (* a2 a2))))
0.4b	(/ (/ (sqrt 2.0) (cos th)) (+ (* a1 a1) (* a2 a2)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

852×	`times-frac`
415×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
78×	`associate-/r*`
32×	`add-exp-log`
31×	`associate-/l*`
23×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp`
11×	`associate-/r/`
10×	`cbrt-undiv`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`+-commutative` `sum-log` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 474

Calls

4 calls:

13.0ms	(+ (* a1 a1) (* a2 a2))
9.0ms	(/ (sqrt 2.0) (cos th))
33.0ms	(/ 1 (/ (/ (sqrt 2.0) (cos th)) (+ (* a1 a1) (* a2 a2))))
44.0ms	(/ (/ (sqrt 2.0) (cos th)) (+ (* a1 a1) (* a2 a2)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* a1 a1) (* a2 a2))
57.0ms	(/ (sqrt 2.0) (cos th))
311.0ms	(/ 1 (/ (/ (sqrt 2.0) (cos th)) (+ (* a1 a1) (* a2 a2))))
167.0ms	(/ (/ (sqrt 2.0) (cos th)) (+ (* a1 a1) (* a2 a2)))

simplify2.3s

Counts

486 → 486

Iterations

Iter	Nodes
done	5000
1	1816
0	608

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2))))
0.3b	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.7b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.7b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

2766×	`times-frac`
1395×	`sqrt-prod`
1284×	`add-sqr-sqrt`
1282×	`*-un-lft-identity` `add-cube-cbrt`
160×	`associate-/l*`
58×	`div-inv`
22×	`sqrt-div`
18×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
12×	`associate-/r*`
11×	`flip3-+` `flip-+`
9×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 1198

Calls

4 calls:

122.0ms	(/ (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2))))
39.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
10.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2))))
132.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
70.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
50.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify3.2s

Counts

1210 → 1210

Iterations

Iter	Nodes
done	5000
1	2872
0	1114

prune5.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize45.0ms

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

rewrite128.0ms

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:

40.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
35.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
17.0ms	(/ (cos th) (sqrt 2.0))
24.0ms	(/ (cos th) (sqrt 2.0))

series454.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
124.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
63.0ms	(/ (cos th) (sqrt 2.0))
71.0ms	(/ (cos th) (sqrt 2.0))

simplify1.9s

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
2	2868
1	541
0	181

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes717.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.2s	2444×	body	1280	valid
1.5s	2058×	body	640	valid
1.1s	8058×	body	80	valid
594.0ms	1112×	body	320	valid
120.0ms	565×	body	160	valid