Details

sample413.0ms

Algorithm

intervals

Results

127.0ms	85×	body	1280	valid
66.0ms	19×	body	320	valid
55.0ms	62×	body	640	valid
15.0ms	75×	body	80	valid
6.0ms	15×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	654
4	156
3	68
2	39
1	23
0	13

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
20×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `hypot-def`
8×	`distribute-lft-out` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 118

Calls

4 calls:

138.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
37.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
140.0ms	(pow (sin kx) 2.0)
180.0ms	(pow (sin ky) 2.0)
107.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1918
1	465
0	189

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-l`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
10.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
20.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series833.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(hypot (sin ky) (sin kx))
268.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
371.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify1.3s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1355
1	304
0	132

prune784.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.2b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
0.2b	(* (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))) (sin th))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
7×	`associate-l`
6×	`times-frac` `div-exp`
5×	`pow1` `cbrt-unprod`
4×	`cbrt-undiv`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`1-exp` `div-inv`
1×	`hypot-udef` `clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `associate-l/` `*-commutative` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
18.0ms	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
50.0ms	(* (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))) (sin th))

series748.0ms

Counts

3 → 9

Calls

3 calls:

180.0ms	(hypot (sin ky) (sin kx))
253.0ms	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
315.0ms	(* (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))) (sin th))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1956
1	329
0	132

prune635.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot (sin ky) (sin kx)))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

7.0ms	(cbrt (hypot (sin ky) (sin kx)))
2.0ms	(cbrt (sin ky))
2.0ms	(cbrt (sin ky))
2.0ms	(cbrt (sin ky))

series669.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(cbrt (hypot (sin ky) (sin kx)))
131.0ms	(cbrt (sin ky))
166.0ms	(cbrt (sin ky))
124.0ms	(cbrt (sin ky))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
3	1428
2	416
1	143
0	68

prune532.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.2b

regimes1.7s

Accuracy

0% (0.1b remaining)

Error of 8.9b against oracle of 8.8b and baseline of 8.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	16
2	16
1	15
0	11

end0.0ms

sample9.6s

Algorithm

intervals

Results

5.6s	2710×	body	1280	valid
2.3s	1845×	body	640	valid
685.0ms	2312×	body	80	valid
567.0ms	766×	body	320	valid
134.0ms	367×	body	160	valid