Details

sample180.0ms

Algorithm

intervals

Results

59.0ms	65×	body	1280	valid
31.0ms	254×	body	80	valid
30.0ms	58×	body	640	valid
12.0ms	33×	body	320	valid
4.0ms	18×	body	160	valid

simplify183.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

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)))

rewrite75.0ms

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:

13.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(/ (sqrt 2.0) (cos th))
39.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series354.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (* a1 a1) (* a2 a2))
65.0ms	(/ (sqrt 2.0) (cos th))
248.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify2.1s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	4529
1	680
0	250

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2)))))
0.3b	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 1198

Calls

4 calls:

99.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2)))))
20.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
12.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
7.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2)))))
195.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (* a2 a2))))
66.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
63.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify4.0s

Counts

1210 → 1210

Iterations

Iter	Nodes
done	5001
1	3459
0	1170

prune6.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0)))))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

3516×	`times-frac`
2682×	`sqrt-prod`
1657×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
324×	`associate-/r*`
53×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
15×	`associate-/l*`
10×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log`

Counts

4 → 1554

Calls

4 calls:

10.0ms	(+ (* a1 a1) (* a2 a2))
28.0ms	(/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))
87.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0)))))
20.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* a1 a1) (* a2 a2))
62.0ms	(/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))
201.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0)))))
123.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify3.8s

Counts

1566 → 1566

Iterations

Iter	Nodes
done	5002
1	4490
0	1460

prune7.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(/ (sqrt (sqrt 2.0)) (cos th))
0.2b	(/ (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
0.3b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (cos th)))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

2850×	`times-frac`
1845×	`sqrt-prod`
1321×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
110×	`associate-/l*`
47×	`div-inv`
43×	`associate-/r*`
20×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r/`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg` `associate-/l/`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `sum-log`

Counts

4 → 1212

Calls

4 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
7.0ms	(/ (sqrt (sqrt 2.0)) (cos th))
89.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
47.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (cos th)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* a1 a1) (* a2 a2))
87.0ms	(/ (sqrt (sqrt 2.0)) (cos th))
231.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
358.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt (sqrt 2.0)) (cos th)))

simplify2.6s

Counts

1224 → 1224

Iterations

Iter	Nodes
done	5000
1	3555
0	1228

prune5.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes495.0ms

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	21
1	21
0	17

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.8s	2548×	body	1280	valid
1.6s	2177×	body	640	valid
1.5s	7942×	body	80	valid
415.0ms	997×	body	320	valid
148.0ms	534×	body	160	valid