Details

sample122.0ms

Algorithm

intervals

Results

68.0ms	90×	body	1280	valid
26.0ms	68×	body	640	valid
6.0ms	23×	body	320	valid
6.0ms	68×	body	80	valid
1.0ms	7×	body	160	valid

simplify50.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize15.0ms

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)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite126.0ms

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)
7.0ms	(pow (sin ky) 2.0)
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
101.0ms	(pow (sin kx) 2.0)
102.0ms	(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

prune463.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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))
8.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
19.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series534.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(hypot (sin ky) (sin kx))
169.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
239.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify136.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

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

prune280.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.3b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
8.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
31.0ms	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

series537.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(hypot (sin ky) (sin kx))
169.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
243.0ms	(* (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))) (sin th))

simplify36.0ms

Counts

73 → 73

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	312	659
1	1144	556
2	5001	556
done	5001	556

prune251.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.3b

localize15.0ms

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))))

rewrite43.0ms

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:

29.0ms	(* (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))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series944.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
236.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
231.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
227.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify48.0ms

Counts

164 → 164

Iterations

Useful iterations: 2 (31.0ms)

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

prune601.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.3b

regimes810.0ms

Accuracy

0% (0.6b remaining)

Error of 9.2b against oracle of 8.7b and baseline of 9.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	41
1	25	41
done	25	41

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	2719×	body	1280	valid
760.0ms	1892×	body	640	valid
216.0ms	760×	body	320	valid
202.0ms	2287×	body	80	valid
65.0ms	342×	body	160	valid