Details

sample163.0ms

Algorithm

intervals

Results

50.0ms	77×	body	1280	valid
48.0ms	227×	body	80	valid
24.0ms	56×	body	640	valid
8.0ms	25×	body	320	valid
3.0ms	14×	body	160	valid

simplify198.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	49	13
3	76	13
4	95	13
5	111	13
6	125	13
7	139	13
done	139	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative`

Counts

3 → 98

Calls

3 calls:

8.0ms	(+ (* a1 a1) (* a2 a2))
64.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
11.0ms	(/ (cos th) (sqrt 2.0))

series492.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* a1 a1) (* a2 a2))
348.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
96.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

107 → 107

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	158	1536
1	480	1469
2	1599	1325
done	5000	1322

prune447.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
34×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `prod-exp` `cbrt-unprod` `flip-+`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `associate-/l/`

Counts

4 → 717

Calls

4 calls:

19.0ms	(+ (* a1 a1) (* a2 a2))
209.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
12.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
49.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* a1 a1) (* a2 a2))
342.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
162.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.5s

Counts

729 → 729

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	553	15882
1	1946	14258
done	5000	13265

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.3b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0)))
0.3b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))))

rewrite640.0ms

Algorithm

rewrite-expression-head

Rules

1497×	`sqrt-prod`
998×	`times-frac`
606×	`add-sqr-sqrt`
493×	`*-un-lft-identity`
487×	`associate-l`
477×	`add-cube-cbrt`
71×	`add-exp-log`
47×	`add-cbrt-cube`
39×	`unswap-sqr`
30×	`div-exp`
22×	`prod-exp`
17×	`cbrt-undiv`
16×	`associate-r` `div-inv`
14×	`cbrt-unprod`
9×	`associate-/r*`
8×	`pow1`
6×	`add-log-exp`
5×	`associate-*r/`
3×	`rec-exp` `flip3-+` `1-exp` `flip-+`
2×	`pow-prod-down` `*-commutative` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `frac-times` `frac-2neg` `distribute-lft-in` `associate-l/` `clear-num` `sum-log` `associate-/l`

Counts

4 → 639

Calls

4 calls:

17.0ms	(+ (* a1 a1) (* a2 a2))
52.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
39.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0)))
435.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* a1 a1) (* a2 a2))
175.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
490.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0)))
326.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))))

simplify2.6s

Counts

651 → 651

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	479	18833
1	1478	17580
2	4506	14075
done	5000	13971

prune3.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

rewrite577.0ms

Algorithm

rewrite-expression-head

Rules

867×	`sqrt-prod`
750×	`times-frac`
403×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
102×	`cbrt-prod`
34×	`associate-/l*`
21×	`associate-/r*`
17×	`add-exp-log`
15×	`div-inv`
11×	`sqrt-pow1` `add-cbrt-cube`
8×	`pow1` `div-exp`
7×	`pow-flip`
4×	`cbrt-undiv` `pow1/3` `add-log-exp`
3×	`pow1/2`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `pow-div`
1×	`associate-/l/` `inv-pow`

Counts

4 → 515

Calls

4 calls:

2.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)
18.0ms	(/ 1 (sqrt (sqrt 2.0)))
81.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

simplify2.9s

Counts

519 → 519

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	503	11427
1	1082	9065
2	1554	8908
3	2964	8902
done	5000	8902

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes250.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	26
1	22	26
done	22	26

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.2s	2525×	body	1280	valid
1.5s	7986×	body	80	valid
1.1s	2049×	body	640	valid
418.0ms	1057×	body	320	valid
151.0ms	503×	body	160	valid