Details

sample488.0ms

Algorithm

intervals

Results

216.0ms	81×	body	1280	valid
75.0ms	56×	body	640	valid
32.0ms	34×	body	320	valid
22.0ms	76×	body	80	valid
5.0ms	9×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	3061
6	850
5	327
4	155
3	80
2	49
1	25
0	13

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
0.2b	(pow (sin kx) 2)
0.2b	(pow (sin ky) 2)
3.8b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite49.0ms

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` `insert-posit16` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 106

Calls

4 calls:

23.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
3.0ms	(pow (sin kx) 2)
3.0ms	(pow (sin ky) 2)
17.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
20.0ms	(pow (sin kx) 2)
28.0ms	(pow (sin ky) 2)
132.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify1.9s

Counts

118 → 118

Iterations

Iter	Nodes
done	5010
3	2546
2	999
1	383
0	171

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.2b	(* (sin kx) (sin kx))
0.2b	(* (sin ky) (sin ky))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `sqrt-div` `swap-sqr` `associate-r` `associate-l*` `sin-mult`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r/` `associate-/l*`
2×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `frac-add` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `sqr-sin` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 116

Calls

4 calls:

39.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
10.0ms	(* (sin kx) (sin kx))
10.0ms	(* (sin ky) (sin ky))
19.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
29.0ms	(* (sin kx) (sin kx))
21.0ms	(* (sin ky) (sin ky))
123.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.2s

Counts

128 → 128

Iterations

Iter	Nodes
done	5121
3	3903
2	1676
1	442
0	191

prune822.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
12×	`sqrt-div`
8×	`sin-mult`
7×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 86

Calls

4 calls:

22.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
22.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
29.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
80.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
99.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
130.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
3	2204
2	731
1	314
0	172

prune929.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.3b

localize98.0ms

Local error

Found 4 expressions with local error:

3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-div` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sin-mult`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

13.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
17.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
99.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
111.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
99.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
4	2181
3	874
2	363
1	150
0	68

prune663.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.3b

regimes1.2s

Accuracy

0% (1.7b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample12.0s

Algorithm

intervals

Results

5.9s	2678×	body	1280	valid
4.0s	1840×	body	640	valid
823.0ms	2358×	body	80	valid
797.0ms	779×	body	320	valid
233.0ms	345×	body	160	valid