Details

sample375.0ms

Algorithm

intervals

Results

143.0ms	88×	body	1280	valid
76.0ms	68×	body	80	valid
57.0ms	59×	body	640	valid
22.0ms	33×	body	320	valid
4.0ms	8×	body	160	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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite130.0ms

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:

48.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
61.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
172.0ms	(pow (sin kx) 2.0)
168.0ms	(pow (sin ky) 2.0)
105.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: 2 (212.0ms)

Iter	Nodes	Cost
0	170	1738
1	328	1556
2	794	1503
3	2419	1503
done	5000	1503

prune553.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.3b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.3b	(pow (sin ky) 2.0)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite146.0ms

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` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

8.0ms	(pow (sin kx) 2.0)
71.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
8.0ms	(pow (sin ky) 2.0)
38.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series660.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (sin kx) 2.0)
186.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
190.0ms	(pow (sin ky) 2.0)
134.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.0s

Counts

199 → 199

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	288	4423
1	601	3676
2	1239	3406
3	3581	3358
done	5000	3358

prune746.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite277.0ms

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` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 516

Calls

4 calls:

111.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
8.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
57.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
174.0ms	(pow (sin kx) 2.0)
169.0ms	(pow (sin ky) 2.0)
102.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.7s

Counts

528 → 528

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	686	17925
1	1770	13716
2	2836	12634
done	5001	12466

prune1.0s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.4b	(/ (/ 1 (sin ky)) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

1071×	`times-frac`
646×	`*-un-lft-identity`
640×	`sqrt-prod`
472×	`add-sqr-sqrt`
470×	`add-cube-cbrt`
91×	`unpow-prod-down`
88×	`distribute-lft-out`
49×	`div-inv`
33×	`sqrt-div` `associate-/r*`
29×	`associate-/r/`
16×	`flip3-+` `flip-+`
14×	`add-exp-log`
13×	`associate-/l*`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`div-exp`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-unpow`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `1-exp` `pow-exp` `clear-num` `associate-/l/` `sqr-pow`

Counts

4 → 544

Calls

4 calls:

4.0ms	(pow (sin ky) 2.0)
84.0ms	(/ (/ 1 (sin ky)) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
37.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
47.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(pow (sin ky) 2.0)
229.0ms	(/ (/ 1 (sin ky)) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
101.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
134.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify4.4s

Counts

556 → 556

Iterations

Useful iterations: 3 (2.5s)

Iter	Nodes	Cost
0	731	20287
1	1472	16467
2	2225	15839
3	4853	15837
done	5001	15837

prune1.2s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.1b

regimes1.9s

Accuracy

0% (1.6b remaining)

Error of 12.4b against oracle of 10.9b and baseline of 12.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	49
1	22	49
done	22	49

end0.0ms

sample8.9s

Algorithm

intervals

Results

4.7s	2737×	body	1280	valid
2.3s	1809×	body	640	valid
564.0ms	776×	body	320	valid
545.0ms	2326×	body	80	valid
331.0ms	352×	body	160	valid