Details

sample298.0ms

Algorithm

intervals

Results

126.0ms	87×	body	1280	valid
41.0ms	67×	body	640	valid
9.0ms	72×	body	80	valid
6.0ms	17×	body	320	valid
5.0ms	13×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite117.0ms

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×	`associate-/r*` `add-exp-log`
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` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

43.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
5.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
57.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series663.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
170.0ms	(pow (sin kx) 2.0)
170.0ms	(pow (sin ky) 2.0)
118.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1591
1	382
0	170

prune919.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 187

Calls

4 calls:

39.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
46.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
150.0ms	(pow (sin kx) 2.0)
173.0ms	(pow (sin ky) 2.0)
106.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.4s

Counts

199 → 199

Iterations

Iter	Nodes
done	5002
2	4094
1	767
0	288

prune1.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
0.3b	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

1005×	`times-frac`
608×	`*-un-lft-identity`
437×	`add-sqr-sqrt`
436×	`add-cube-cbrt`
215×	`sqrt-prod`
92×	`unpow-prod-down`
86×	`distribute-lft-out`
46×	`add-exp-log` `div-inv`
32×	`div-exp`
30×	`sqrt-div` `associate-/l*`
29×	`associate-/r/`
16×	`add-cbrt-cube`
15×	`flip3-+` `flip-+`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`pow1`
6×	`pow-unpow`
4×	`add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 516

Calls

4 calls:

9.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
67.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
36.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(pow (sin kx) 2.0)
147.0ms	(pow (sin ky) 2.0)
167.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
135.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.3s

Counts

528 → 528

Iterations

Iter	Nodes
done	5001
1	2415
0	686

prune1.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
0.2b	(* (sin ky) (sin ky))
0.3b	(* (sqrt (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky))
3.8b	(sqrt (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
35×	`sqrt-prod`
34×	`*-un-lft-identity`
32×	`add-cube-cbrt`
31×	`times-frac`
22×	`associate-l`
16×	`pow1`
12×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`associate-/r/`
7×	`sin-mult`
6×	`associate-r`
5×	`unswap-sqr`
4×	`add-log-exp`
3×	`rem-sqrt-square` `associate-/r` `sqrt-pow1` `flip3-+` `swap-sqr` `frac-add` `flip-+` `div-inv` `associate-/l`
2×	`sqrt-div` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `pow-flip` `inv-pow`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `pow-plus` `pow1/2` `1-exp` `associate-*l/` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 130

Calls

4 calls:

18.0ms	(/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
14.0ms	(* (sin ky) (sin ky))
77.0ms	(* (sqrt (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky))
28.0ms	(sqrt (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
35.0ms	(* (sin ky) (sin ky))
200.0ms	(* (sqrt (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky))
198.0ms	(sqrt (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))

simplify2.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	2808
1	489
0	209

prune1.4s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.7b

regimes2.1s

Accuracy

67.5% (0.5b remaining)

Error of 11.6b against oracle of 11.1b and baseline of 12.6b

bsearch3.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.4s	2766×	body	1280	valid
1.9s	1903×	body	640	valid
496.0ms	713×	body	320	valid
491.0ms	2255×	body	80	valid
241.0ms	363×	body	160	valid