Details

sample113.0ms

Algorithm

intervals

Results

58.0ms	85×	body	1280	valid
28.0ms	71×	body	640	valid
6.0ms	70×	body	80	valid
4.0ms	16×	body	320	valid
2.0ms	14×	body	160	valid

simplify3.6s

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	325	16
6	905	16
7	3228	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize15.0ms

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)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

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:

19.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin kx) 2.0)
1.0ms	(pow (sin ky) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
106.0ms	(pow (sin kx) 2.0)
105.0ms	(pow (sin ky) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.4s

Counts

112 → 112

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	170	1738
1	330	1574
2	800	1509
3	2480	1509
done	5000	1509

prune395.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite53.0ms

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:

24.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
1.0ms	(pow (sin kx) 2.0)
1.0ms	(pow (sin ky) 2.0)
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
110.0ms	(pow (sin kx) 2.0)
106.0ms	(pow (sin ky) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.4s

Counts

199 → 199

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	288	4423
1	642	3870
2	1507	3406
3	4093	3358
done	5001	3358

prune437.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-r`
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-l`
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` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 106

Calls

4 calls:

1.0ms	(pow (sin kx) 2.0)
1.0ms	(pow (sin ky) 2.0)
50.0ms	(* (sin ky) (/ 1 (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:

104.0ms	(pow (sin kx) 2.0)
103.0ms	(pow (sin ky) 2.0)
131.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.6s

Counts

118 → 118

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	198	1690
1	448	1438
2	1166	1284
3	3520	1284
done	5001	1284

prune402.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.7b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
13.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (sin kx))
102.0ms	(cbrt (sin kx))
101.0ms	(cbrt (sin kx))
80.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify1.0s

Counts

60 → 60

Iterations

Useful iterations: 3 (205.0ms)

Iter	Nodes	Cost
0	81	818
1	187	744
2	481	620
3	1621	609
done	5001	609

prune268.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 13.3b

regimes1.0s

Accuracy

63.1% (0.6b remaining)

Error of 11.7b against oracle of 11.1b and baseline of 12.7b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	55
1	41	55
done	41	55

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.0s	2731×	body	1280	valid
783.0ms	1856×	body	640	valid
234.0ms	766×	body	320	valid
204.0ms	2329×	body	80	valid
57.0ms	318×	body	160	valid