Details

sample422.0ms

Algorithm

intervals

Results

232.0ms	17×	body	320	valid
84.0ms	87×	body	1280	valid
37.0ms	67×	body	640	valid
8.0ms	72×	body	80	valid
5.0ms	13×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize60.0ms

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)))

rewrite88.0ms

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:

33.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
156.0ms	(pow (sin kx) 2.0)
189.0ms	(pow (sin ky) 2.0)
144.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify980.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1650
1	395
0	178

prune921.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

localize25.0ms

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)))

rewrite36.0ms

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))
16.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
18.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

series806.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms	(hypot (sin kx) (sin ky))
341.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
266.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify893.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1324
1	304
0	132

prune809.0ms

Pruning

19 alts after pruning (19 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))
0.1b	(* (/ (sin ky) (* 1 (hypot (sin kx) (sin ky)))) (sin th))
0.2b	(/ (sin ky) (* 1 (hypot (sin kx) (sin ky))))

rewrite70.0ms

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 kx) (sin ky))
50.0ms	(* (/ (sin ky) (* 1 (hypot (sin kx) (sin ky)))) (sin th))
19.0ms	(/ (sin ky) (* 1 (hypot (sin kx) (sin ky))))

series779.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(hypot (sin kx) (sin ky))
343.0ms	(* (/ (sin ky) (* 1 (hypot (sin kx) (sin ky)))) (sin th))
254.0ms	(/ (sin ky) (* 1 (hypot (sin kx) (sin ky))))

simplify1.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1837
1	326
0	132

prune604.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.8b

localize37.0ms

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)))

rewrite52.0ms

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))
35.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
13.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))

series851.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms	(hypot (sin kx) (sin ky))
333.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
319.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))

simplify1.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1411
1	277
0	121

prune533.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.8b

regimes1.6s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample9.3s

Algorithm

intervals

Results

5.9s	2766×	body	1280	valid
1.9s	1903×	body	640	valid
445.0ms	713×	body	320	valid
441.0ms	2255×	body	80	valid
203.0ms	363×	body	160	valid