Details

sample341.0ms

Algorithm

intervals

Results

126.0ms	99×	body	1280	valid
89.0ms	49×	body	640	valid
12.0ms	24×	body	320	valid
11.0ms	19×	body	160	valid
9.0ms	65×	body	80	valid

simplify4.7s

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	136	16
5	311	16
6	1019	16
7	4223	16
done	5001	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize33.0ms

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)
0.3b	(pow (sin kx) 2.0)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite204.0ms

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:

144.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
5.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
45.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
187.0ms	(pow (sin ky) 2.0)
152.0ms	(pow (sin kx) 2.0)
146.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.9s

Counts

113 → 113

Iterations

Useful iterations: 2 (252.0ms)

Iter	Nodes	Cost
0	180	1660
1	391	1562
2	1016	1469
3	3466	1469
done	5000	1469

prune614.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 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)))))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite249.0ms

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:

4.0ms	(pow (sin kx) 2.0)
66.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
117.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
56.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(pow (sin kx) 2.0)
202.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
257.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
122.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.4s

Counts

145 → 145

Iterations

Useful iterations: 2 (336.0ms)

Iter	Nodes	Cost
0	196	2631
1	401	2350
2	1149	2215
3	3648	2215
done	5000	2215

prune701.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.3b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

164×	`sqrt-prod`
130×	`add-sqr-sqrt`
123×	`times-frac`
120×	`*-un-lft-identity`
72×	`add-cube-cbrt`
39×	`associate-r` `associate-l`
24×	`unpow-prod-down` `distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div` `unswap-sqr`
11×	`associate-/r*`
8×	`pow1`
6×	`associate-/r/`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 209

Calls

4 calls:

259.0ms	(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
62.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
51.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
57.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
221.0ms	(/ (sin ky) (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)))
122.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.5s

Counts

221 → 221

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	261	6529
1	654	6011
2	1912	5414
done	5001	5412

prune1.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite176.0ms

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:

38.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
55.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
35.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
42.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
95.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
108.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
120.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	160	2119
1	282	1894
2	636	1807
3	1703	1797
done	5001	1791

prune635.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.9b

regimes1.7s

Accuracy

55.1% (0.8b remaining)

Error of 12.1b against oracle of 11.3b and baseline of 13.0b

bsearch4.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	87
1	44	87
done	44	87

end1.0ms

sample9.1s

Algorithm

intervals

Results

5.3s	2718×	body	1280	valid
2.2s	1844×	body	640	valid
561.0ms	752×	body	320	valid
474.0ms	2323×	body	80	valid
128.0ms	363×	body	160	valid