Details

sample405.0ms

Algorithm

intervals

Results

186.0ms	83×	body	1280	valid
62.0ms	64×	body	640	valid
15.0ms	26×	body	320	valid
15.0ms	76×	body	80	valid
3.0ms	7×	body	160	valid

simplify1.0s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.4b

localize40.0ms

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 kx) 2.0)
0.2b	(pow (sin ky) 2.0)
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite245.0ms

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:

148.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
59.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
162.0ms	(pow (sin kx) 2.0)
154.0ms	(pow (sin ky) 2.0)
138.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.1s

Counts

113 → 113

Iterations

Useful iterations: done (1.1s)

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

prune665.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite232.0ms

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:

8.0ms	(pow (sin ky) 2.0)
73.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
103.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
37.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series836.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(pow (sin ky) 2.0)
228.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
291.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
152.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify5.4s

Counts

145 → 145

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	194	2631
1	467	2353
2	3926	2221
done	5001	2221

prune657.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite172.0ms

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:

21.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
55.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
126.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
135.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
152.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts

102 → 102

Iterations

Useful iterations: done (2.0s)

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

prune683.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`sqrt-prod`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`cbrt-prod` `unpow-prod-down` `sqrt-div` `distribute-lft-out`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 69

Calls

4 calls:

32.0ms	(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
62.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
52.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
38.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
94.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
112.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
101.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts

81 → 81

Iterations

Useful iterations: 3 (444.0ms)

Iter	Nodes	Cost
0	87	1366
1	186	1197
2	495	1151
3	1829	1148
done	5000	1148

prune927.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 9.4b

regimes1.5s

Accuracy

0% (1.6b remaining)

Error of 12.5b against oracle of 10.9b and baseline of 12.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	47
1	19	47
done	19	47

end0.0ms

sample9.5s

Algorithm

intervals

Results

4.4s	2689×	body	1280	valid
3.0s	1844×	body	640	valid
678.0ms	343×	body	160	valid
527.0ms	737×	body	320	valid
475.0ms	2387×	body	80	valid