Details

sample210.0ms

Algorithm

intervals

Results

59.0ms	74×	body	1280	valid
37.0ms	294×	body	80	valid
35.0ms	61×	body	640	valid
24.0ms	13×	body	160	valid
11.0ms	28×	body	320	valid

simplify163.0ms

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (sqrt 2.0) (cos th))
0.6b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite51.0ms

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:

6.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(/ (sqrt 2.0) (cos th))
32.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series376.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* a1 a1) (* a2 a2))
85.0ms	(/ (sqrt 2.0) (cos th))
261.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify2.0s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	4529
1	680
0	250

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a2 a2) (* a1 a1))
0.2b	(/ (sqrt 2.0) (cos th))
0.6b	(/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2.0) (cos th)))

rewrite63.0ms

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:

11.0ms	(+ (* a2 a2) (* a1 a1))
11.0ms	(/ (sqrt 2.0) (cos th))
29.0ms	(/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2.0) (cos th)))

series367.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ (* a2 a2) (* a1 a1))
83.0ms	(/ (sqrt 2.0) (cos th))
237.0ms	(/ (+ (* a2 a2) (* a1 a1)) (/ (sqrt 2.0) (cos th)))

simplify1.8s

Counts

167 → 167

Iterations

Iter	Nodes
done	5001
2	4256
1	681
0	250

prune920.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (* a2 a2) (* a1 a1))) (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (pow a1 2) (* a2 a2)))))
0.3b	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (pow a1 2) (* a2 a2))))
5.5b	(sqrt (+ (* a2 a2) (* a1 a1)))
5.5b	(sqrt (+ (pow a1 2) (* a2 a2)))

rewrite283.0ms

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:

84.0ms	(/ (sqrt (+ (* a2 a2) (* a1 a1))) (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (pow a1 2) (* a2 a2)))))
49.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (pow a1 2) (* a2 a2))))
7.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
13.0ms	(sqrt (+ (pow a1 2) (* a2 a2)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (sqrt (+ (* a2 a2) (* a1 a1))) (/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (pow a1 2) (* a2 a2)))))
179.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (pow a1 2) (* a2 a2))))
52.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
58.0ms	(sqrt (+ (pow a1 2) (* a2 a2)))

simplify2.8s

Counts

1210 → 1210

Iterations

Iter	Nodes
done	5001
1	3515
0	1198

prune4.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (sqrt (+ (* a2 a2) (* a1 a1))) (sqrt 2.0)) (/ (/ 1 (cos th)) (sqrt (+ (pow a1 2) (* a2 a2)))))
0.4b	(/ (sqrt (+ (* a2 a2) (* a1 a1))) (sqrt 2.0))
5.5b	(sqrt (+ (* a2 a2) (* a1 a1)))
5.5b	(sqrt (+ (pow a1 2) (* a2 a2)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

11868×	`times-frac`
4990×	`add-sqr-sqrt`
4988×	`*-un-lft-identity` `add-cube-cbrt`
4707×	`sqrt-prod`
374×	`div-inv`
90×	`associate-/r*`
88×	`sqrt-div`
83×	`associate-/r/`
46×	`associate-/l*`
44×	`flip3-+` `flip-+`
41×	`add-exp-log`
28×	`div-exp`
27×	`add-cbrt-cube`
16×	`cbrt-undiv`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp`
1×	`sqrt-undiv`

Counts

4 → 3605

Calls

4 calls:

154.0ms	(/ (/ (sqrt (+ (* a2 a2) (* a1 a1))) (sqrt 2.0)) (/ (/ 1 (cos th)) (sqrt (+ (pow a1 2) (* a2 a2)))))
20.0ms	(/ (sqrt (+ (* a2 a2) (* a1 a1))) (sqrt 2.0))
13.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
11.0ms	(sqrt (+ (pow a1 2) (* a2 a2)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (/ (sqrt (+ (* a2 a2) (* a1 a1))) (sqrt 2.0)) (/ (/ 1 (cos th)) (sqrt (+ (pow a1 2) (* a2 a2)))))
175.0ms	(/ (sqrt (+ (* a2 a2) (* a1 a1))) (sqrt 2.0))
39.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))
63.0ms	(sqrt (+ (pow a1 2) (* a2 a2)))

simplify2.6s

Counts

3617 → 3617

Iterations

Iter	Nodes
done	5000
0	3245

prune20.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes537.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	17

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.0s	2437×	body	1280	valid
1.3s	1058×	body	320	valid
1.2s	8054×	body	80	valid
923.0ms	2105×	body	640	valid
120.0ms	550×	body	160	valid