Details

sample343.0ms

Algorithm

intervals

Results

155.0ms	85×	body	1280	valid
47.0ms	62×	body	640	valid
12.0ms	75×	body	80	valid
9.0ms	19×	body	320	valid
5.0ms	15×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4952
6	1182
5	304
4	132
3	66
2	39
1	23
0	13

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize42.0ms

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)))

rewrite167.0ms

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:

112.0ms	(* (/ (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)
38.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series704.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
154.0ms	(pow (sin kx) 2.0)
174.0ms	(pow (sin ky) 2.0)
150.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.0s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
3	4224
2	1321
1	456
0	189

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.2b

localize39.0ms

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))

rewrite47.0ms

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))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
36.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series763.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(hypot (sin ky) (sin kx))
272.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
326.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify2.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5007
3	2899
2	970
1	304
0	132

prune571.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.2b

localize38.0ms

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	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
6.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
38.0ms	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

series724.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(hypot (sin ky) (sin kx))
230.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
333.0ms	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

simplify2.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5007
3	2055
2	765
1	309
0	139

prune587.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.2b

localize71.0ms

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))

rewrite5.0ms

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

series645.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (hypot (sin ky) (sin kx)))
172.0ms	(cbrt (sin ky))
126.0ms	(cbrt (sin ky))
126.0ms	(cbrt (sin ky))

simplify2.4s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	3325
3	983
2	347
1	143
0	68

prune451.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.2b

regimes1.8s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.4s	2710×	body	1280	valid
2.2s	1845×	body	640	valid
816.0ms	766×	body	320	valid
562.0ms	2312×	body	80	valid
181.0ms	367×	body	160	valid