Details

sample116.0ms

Algorithm

intervals

Results

58.0ms	82×	body	1280	valid
26.0ms	56×	body	640	valid
8.0ms	89×	body	80	valid
6.0ms	22×	body	320	valid
1.0ms	7×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	39	10
2	67	10
3	153	10
4	439	10
5	1830	10
6	5001	10
done	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize16.0ms

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))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite127.0ms

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:

81.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
34.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
102.0ms	(pow (sin kx) 2.0)
105.0ms	(pow (sin ky) 2.0)
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Counts

130 → 130

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	403	1038
1	1435	967
2	5002	965
done	5002	965

prune515.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.0b

localize12.0ms

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))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
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` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
21.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series523.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(hypot (sin ky) (sin kx))
171.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
232.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify133.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4965	644
3	5001	644
done	5001	644

prune309.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
9.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
18.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series562.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(hypot (sin ky) (sin kx))
208.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
233.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify34.0ms

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	258	719
1	1032	641
2	5002	641
done	5002	641

prune312.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

26.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series924.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
220.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
228.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
232.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify46.0ms

Counts

164 → 164

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	291	2447
1	993	2341
2	5001	2212
done	5001	2212

prune657.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 8.0b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 8.8b against oracle of 8.6b and baseline of 8.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7
done	10	7

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.0s	2756×	body	1280	valid
971.0ms	1833×	body	640	valid
212.0ms	2313×	body	80	valid
208.0ms	747×	body	320	valid
71.0ms	351×	body	160	valid