Details

sample394.0ms

Algorithm

intervals

Results

184.0ms	78×	body	1280	valid
64.0ms	68×	body	640	valid
19.0ms	31×	body	320	valid
16.0ms	68×	body	80	valid
5.0ms	11×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	35	16
3	64	16
4	140	16
5	632	16
done	5000	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

155.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(pow (sin ky) 2.0)
7.0ms	(pow (sin kx) 2.0)
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
195.0ms	(pow (sin ky) 2.0)
198.0ms	(pow (sin kx) 2.0)
147.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.4s

Counts

113 → 113

Iterations

Useful iterations: 2 (447.0ms)

Iter	Nodes	Cost
0	180	1660
1	449	1562
2	1848	1469
done	5000	1469

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

164.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(pow (sin ky) 2.0)
7.0ms	(pow (sin kx) 2.0)
59.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series792.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
192.0ms	(pow (sin ky) 2.0)
175.0ms	(pow (sin kx) 2.0)
134.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.6s

Counts

113 → 113

Iterations

Useful iterations: 2 (451.0ms)

Iter	Nodes	Cost
0	180	1660
1	449	1562
2	1848	1469
done	5000	1469

prune1.4s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.7b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-r`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

8.0ms	(pow (sin ky) 2.0)
9.0ms	(pow (sin kx) 2.0)
197.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
62.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series899.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(pow (sin ky) 2.0)
226.0ms	(pow (sin kx) 2.0)
303.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
164.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify7.6s

Counts

113 → 113

Iterations

Useful iterations: 2 (1.9s)

Iter	Nodes	Cost
0	195	1650
1	505	1473
2	3773	1375
done	5000	1375

prune1.2s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 11.7b

localize86.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

36.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
61.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
58.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
66.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series771.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
151.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
152.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
141.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.9s

Counts

102 → 102

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	160	2119
1	289	1894
2	826	1807
3	3516	1797
done	5001	1791

prune1.1s

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 11.7b

regimes3.4s

Accuracy

0% (1.2b remaining)

Error of 12.4b against oracle of 11.2b and baseline of 12.4b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: done (6.0ms)

Iter	Nodes	Cost
0	18	23
1	23	21
done	23	20

end0.0ms

sample11.8s

Algorithm

intervals

Results

6.7s	2747×	body	1280	valid
2.5s	1826×	body	640	valid
748.0ms	346×	body	160	valid
650.0ms	760×	body	320	valid
514.0ms	2321×	body	80	valid