Details

sample390.0ms

Algorithm

intervals

Results

139.0ms	84×	body	1280	valid
79.0ms	27×	body	320	valid
51.0ms	52×	body	640	valid
17.0ms	82×	body	80	valid
5.0ms	11×	body	160	valid

simplify969.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize42.0ms

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))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite213.0ms

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:

127.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
4.0ms	(pow (sin kx) 2.0)
5.0ms	(pow (sin ky) 2.0)
69.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
203.0ms	(pow (sin kx) 2.0)
141.0ms	(pow (sin ky) 2.0)
131.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	180	1660
1	449	1562
2	1841	1473
done	5000	1469

prune683.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

67.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms	(pow (sin ky) 2.0)
116.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
54.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
161.0ms	(pow (sin ky) 2.0)
233.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
105.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify5.2s

Counts

145 → 145

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	194	2631
1	467	2353
2	3929	2221
done	5000	2221

prune716.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.5b	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
34×	`sqrt-pow1`
30×	`pow1`
28×	`sqrt-div`
20×	`add-cube-cbrt`
19×	`swap-sqr`
18×	`pow1/2`
15×	`unpow-prod-down`
14×	`distribute-lft-out`
11×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

8.0ms	(pow (sin ky) 2.0)
249.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
62.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
39.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(pow (sin ky) 2.0)
95.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
107.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
129.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.6s

Counts

154 → 154

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	165	3639
1	383	2252
2	1581	2123
done	5002	2086

prune761.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite168.0ms

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:

32.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
56.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
32.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

308.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
483.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
120.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
112.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts

102 → 102

Iterations

Useful iterations: done (1.9s)

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

prune619.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 10.6b

regimes1.8s

Accuracy

58.5% (0.7b remaining)

Error of 12.2b against oracle of 11.5b and baseline of 13.1b

bsearch4.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	66
1	39	66
done	39	66

end0.0ms

sample8.9s

Algorithm

intervals

Results

4.4s	2683×	body	1280	valid
2.2s	1898×	body	640	valid
1.0s	725×	body	320	valid
498.0ms	2329×	body	80	valid
265.0ms	365×	body	160	valid