Details

sample644.0ms

Algorithm

intervals

Results

210.0ms	88×	body	1280	valid
51.0ms	59×	body	640	valid
21.0ms	33×	body	320	valid
16.0ms	68×	body	80	valid
3.0ms	8×	body	160	valid

simplify5.0s

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

localize27.0ms

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)))

rewrite154.0ms

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:

85.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(pow (sin kx) 2.0)
7.0ms	(pow (sin ky) 2.0)
49.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
174.0ms	(pow (sin kx) 2.0)
149.0ms	(pow (sin ky) 2.0)
151.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: 2 (249.0ms)

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

prune561.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.1b

localize43.0ms

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)))

rewrite157.0ms

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)
93.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
7.0ms	(pow (sin ky) 2.0)
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(pow (sin kx) 2.0)
190.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
166.0ms	(pow (sin ky) 2.0)
124.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.8s

Counts

199 → 199

Iterations

Useful iterations: 3 (1.3s)

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

prune613.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.1b

localize28.0ms

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)))

rewrite209.0ms

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)))
4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
178.0ms	(pow (sin kx) 2.0)
127.0ms	(pow (sin ky) 2.0)
100.0ms	(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

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.1b

localize37.0ms

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)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-l`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`sqrt-prod`
15×	`add-exp-log`
14×	`unpow-prod-down`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 105

Calls

4 calls:

4.0ms	(pow (sin kx) 2.0)
129.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
4.0ms	(pow (sin ky) 2.0)
56.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (sin kx) 2.0)
181.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
147.0ms	(pow (sin ky) 2.0)
134.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.2s

Counts

117 → 117

Iterations

Useful iterations: 2 (286.0ms)

Iter	Nodes	Cost
0	181	1705
1	387	1495
2	1000	1397
3	2770	1397
done	5001	1397

prune538.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.1b

regimes1.4s

Accuracy

0% (1.3b remaining)

Error of 12.2b against oracle of 10.9b and baseline of 12.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	20	20
done	20	20

end0.0ms

sample9.3s

Algorithm

intervals

Results

5.3s	2737×	body	1280	valid
2.3s	1809×	body	640	valid
579.0ms	2326×	body	80	valid
423.0ms	776×	body	320	valid
124.0ms	352×	body	160	valid