Details

sample124.0ms

Algorithm

intervals

Results

71.0ms	92×	body	1280	valid
25.0ms	61×	body	640	valid
6.0ms	67×	body	80	valid
5.0ms	19×	body	320	valid
3.0ms	17×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	34	16
3	63	16
4	126	16
5	297	16
6	884	16
7	3183	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

23.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
104.0ms	(pow (sin kx) 2.0)
109.0ms	(pow (sin ky) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	170	1738
1	330	1550
2	815	1503
3	2679	1503
done	5000	1503

prune390.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

62×	`sqrt-prod`
56×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`times-frac`
32×	`add-cube-cbrt`
15×	`unpow-prod-down`
12×	`distribute-lft-out`
11×	`associate-/r*`
8×	`sqrt-div`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `div-inv` `sqr-pow`

Counts

4 → 112

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
22.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow (sin ky) 2.0)
148.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

124 → 124

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	180	2341
1	342	2048
2	858	1988
3	2779	1986
done	5000	1985

prune517.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite71.0ms

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:

15.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify874.0ms

Counts

102 → 102

Iterations

Useful iterations: 3 (271.0ms)

Iter	Nodes	Cost
0	160	2119
1	284	1894
2	664	1807
3	1863	1797
done	5001	1797

prune492.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
57×	`sqrt-prod`
33×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
14×	`unpow-prod-down` `distribute-lft-out`
11×	`associate-/r*`
10×	`cbrt-prod`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

23.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
108.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
101.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

120 → 120

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	179	2528
1	340	2247
2	798	2155
3	2098	2147
done	5000	2146

prune515.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.9b

regimes1.0s

Accuracy

61.9% (0.6b remaining)

Error of 11.9b against oracle of 11.2b and baseline of 12.9b

bsearch4.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	55
1	47	55
done	47	55

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	2743×	body	1280	valid
785.0ms	1863×	body	640	valid
210.0ms	739×	body	320	valid
204.0ms	2314×	body	80	valid
70.0ms	341×	body	160	valid