Details

sample122.0ms

Algorithm

intervals

Results

66.0ms	92×	body	1280	valid
25.0ms	61×	body	640	valid
8.0ms	17×	body	160	valid
6.0ms	67×	body	80	valid
5.0ms	19×	body	320	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)))

rewrite43.0ms

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:

21.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin kx) 2.0)
114.0ms	(pow (sin ky) 2.0)
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: 2 (107.0ms)

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

prune379.0ms

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)))

rewrite60.0ms

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:

1.0ms	(pow (sin ky) 2.0)
21.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms	(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)
149.0ms	(/ (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)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts

124 → 124

Iterations

Useful iterations: done (1.2s)

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

prune512.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.9b

localize25.0ms

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)))

rewrite61.0ms

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:

11.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(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)))
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)))

simplify854.0ms

Counts

102 → 102

Iterations

Useful iterations: 3 (265.0ms)

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

prune521.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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) (pow (sin ky) 2)))

rewrite65.0ms

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:

11.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

368.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: 3 (397.0ms)

Iter	Nodes	Cost
0	187	2119
1	342	1882
2	892	1795
3	2649	1777
done	5000	1777

prune402.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 8.9b

regimes1.1s

Accuracy

60.3% (0.6b remaining)

Error of 11.9b against oracle of 11.2b and baseline of 12.8b

bsearch4.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.0s	2743×	body	1280	valid
782.0ms	1863×	body	640	valid
221.0ms	2314×	body	80	valid
205.0ms	739×	body	320	valid
67.0ms	341×	body	160	valid