Details

sample198.0ms

Algorithm

intervals

Results

58.0ms	264×	body	80	valid
58.0ms	86×	body	1280	valid
36.0ms	78×	body	640	valid
12.0ms	36×	body	320	valid
5.0ms	23×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

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)))

rewrite89.0ms

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))
11.0ms	(/ (sqrt 2.0) (cos th))
52.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series391.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* a1 a1) (* a2 a2))
76.0ms	(/ (sqrt 2.0) (cos th))
278.0ms	(/ (+ (* 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 (6 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

559×	`times-frac`
244×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
168×	`cbrt-prod`
84×	`sqrt-prod`
43×	`div-inv`
35×	`associate-/r*`
32×	`add-exp-log`
22×	`add-cbrt-cube`
19×	`associate-/l*`
16×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `sum-log` `associate-/r/`

Counts

4 → 364

Calls

4 calls:

12.0ms	(+ (* a1 a1) (* a2 a2))
13.0ms	(/ (cbrt (sqrt 2.0)) (cos th))
25.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
78.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cbrt (sqrt 2.0)) (cos th)))

series1.2s

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* a1 a1) (* a2 a2))
339.0ms	(/ (cbrt (sqrt 2.0)) (cos th))
552.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
249.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cbrt (sqrt 2.0)) (cos th)))

simplify1.9s

Counts

376 → 376

Iterations

Iter	Nodes
done	5001
1	1894
0	541

prune2.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ (cbrt (cbrt (sqrt 2.0))) (cos th)))
0.3b	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ (cbrt (cbrt (sqrt 2.0))) (cos th))))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

13325×	`times-frac`
8236×	`cbrt-prod`
6099×	`add-sqr-sqrt`
5932×	`*-un-lft-identity` `add-cube-cbrt`
4739×	`sqrt-prod`
2325×	`associate-r`
201×	`div-inv`
118×	`add-exp-log`
78×	`add-cbrt-cube`
58×	`associate-/l*`
55×	`cbrt-undiv` `div-exp`
40×	`associate-/r*`
36×	`unswap-sqr`
35×	`prod-exp` `cbrt-unprod`
10×	`associate-l`
8×	`pow1`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 4891

Calls

4 calls:

128.0ms	(/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ (cbrt (cbrt (sqrt 2.0))) (cos th)))
1.2s	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ (cbrt (cbrt (sqrt 2.0))) (cos th))))
7.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
13.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

681.0ms	(/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ (cbrt (cbrt (sqrt 2.0))) (cos th)))
254.0ms	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ (cbrt (cbrt (sqrt 2.0))) (cos th))))
53.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
47.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify15.0s

Counts

4903 → 4903

Iterations

Iter	Nodes
done	5000
0	4120

prune44.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))
0.3b	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))) (/ 1 (cbrt (cbrt (sqrt 2.0))))) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ 1 (cos th))))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1984×	`times-frac`
953×	`add-exp-log`
900×	`add-sqr-sqrt`
898×	`*-un-lft-identity` `add-cube-cbrt`
759×	`associate-r`
597×	`sqrt-prod`
468×	`cbrt-prod`
455×	`div-exp`
408×	`prod-exp`
213×	`add-cbrt-cube`
125×	`cbrt-undiv`
118×	`cbrt-unprod`
73×	`div-inv`
70×	`rec-exp` `1-exp`
11×	`pow1`
6×	`frac-times` `sqrt-div` `associate-l/` `associate-/l`
4×	`add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-*r/` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `un-div-inv` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `associate-/r/` `-commutative`

Counts

4 → 1038

Calls

4 calls:

64.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))
830.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))) (/ 1 (cbrt (cbrt (sqrt 2.0))))) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ 1 (cos th))))
17.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
14.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

675.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0)))))
267.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (sqrt 2.0))))) (/ 1 (cbrt (cbrt (sqrt 2.0))))) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ 1 (cos th))))
39.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
71.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify3.5s

Counts

1050 → 1050

Iterations

Iter	Nodes
done	5001
0	1538

prune7.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes511.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.1s	2543×	body	1280	valid
1.3s	8005×	body	80	valid
1.1s	2145×	body	640	valid
839.0ms	1061×	body	320	valid
153.0ms	522×	body	160	valid