Details

sample377.0ms

Algorithm

intervals

Results

132.0ms	87×	body	1280	valid
76.0ms	72×	body	80	valid
65.0ms	67×	body	640	valid
10.0ms	17×	body	320	valid
8.0ms	13×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

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))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`associate-/r*` `add-exp-log` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 117

Calls

4 calls:

54.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
6.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
38.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
165.0ms	(pow (sin kx) 2.0)
137.0ms	(pow (sin ky) 2.0)
137.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1650
1	395
0	178

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.9b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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 kx) (sin ky))
19.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
7.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

series711.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(hypot (sin kx) (sin ky))
315.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
220.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify1.4s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1324
1	304
0	132

prune747.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin kx) (sin ky))
0.2b	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
0.3b	(/ (sin th) (hypot (sin kx) (sin ky)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `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-r/` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin kx) (sin ky))
23.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
11.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))

series759.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(hypot (sin kx) (sin ky))
311.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
271.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))

simplify1.3s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1411
1	277
0	121

prune751.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.8b

localize95.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

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:

1.0ms	(cbrt (hypot (sin kx) (sin ky)))
1.0ms	(cbrt (sin ky))
1.0ms	(cbrt (sin ky))
1.0ms	(cbrt (sin ky))

series562.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (hypot (sin kx) (sin ky)))
116.0ms	(cbrt (sin ky))
124.0ms	(cbrt (sin ky))
118.0ms	(cbrt (sin ky))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	1280
2	375
1	130
0	64

prune576.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 6.8b

regimes1.8s

Accuracy

0% (0.2b remaining)

Error of 8.7b against oracle of 8.5b and baseline of 8.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample9.5s

Algorithm

intervals

Results

5.4s	2766×	body	1280	valid
1.9s	1903×	body	640	valid
979.0ms	713×	body	320	valid
586.0ms	2255×	body	80	valid
126.0ms	363×	body	160	valid