Details

sample348.0ms

Algorithm

intervals

Results

159.0ms	86×	body	1280	valid
90.0ms	59×	body	640	valid
20.0ms	30×	body	320	valid
17.0ms	72×	body	80	valid
4.0ms	9×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2046
7	2046
6	911
5	367
4	177
3	95
2	61
1	25
0	13

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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` `insert-posit16` `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 → 76

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
13.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series801.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(hypot (sin ky) (sin kx))
365.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
278.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify1.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	2005
3	2005
2	1013
1	306
0	133

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.7b

localize39.0ms

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))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

24.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
1.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
1.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.2s

Counts

4 → 12

Calls

4 calls:

302.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
291.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
306.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
320.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.4s

Counts

168 → 168

Iterations

Iter	Nodes
done	2002
4	2002
3	1618
2	713
1	325
0	173

prune2.9s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin th) (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))))
0.2b	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
0.3b	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
0.4b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
94×	`times-frac`
67×	`*-un-lft-identity`
64×	`add-exp-log`
61×	`add-cube-cbrt`
53×	`sqrt-prod`
38×	`add-cbrt-cube`
25×	`associate-l` `prod-exp`
23×	`associate-r`
19×	`div-exp`
15×	`unswap-sqr`
13×	`pow1` `cbrt-unprod`
12×	`associate-/r*`
10×	`cbrt-undiv`
6×	`associate-/l*`
5×	`rec-exp` `1-exp` `associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip`
2×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 210

Calls

4 calls:

71.0ms	(* (sin th) (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))))
10.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
36.0ms	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
8.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series1.0s

Counts

4 → 12

Calls

4 calls:

336.0ms	(* (sin th) (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))))
205.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
227.0ms	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
235.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify1.0s

Counts

222 → 222

Iterations

Iter	Nodes
done	2003
2	2003
1	714
0	266

prune3.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.5b	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.5b	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.5b	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

100×	`cbrt-prod`
36×	`times-frac`
35×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 109

Calls

4 calls:

1.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
1.0ms	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
1.0ms	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
2.0ms	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

295.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
307.0ms	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
328.0ms	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
303.0ms	(cbrt (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))

simplify1.2s

Counts

121 → 121

Iterations

Iter	Nodes
done	2000
4	2000
3	1111
2	416
1	205
0	131

prune2.2s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.6b

regimes1.2s

Accuracy

0% (0.5b remaining)

Error of 9.3b against oracle of 8.9b and baseline of 9.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample10.7s

Algorithm

intervals

Results

5.6s	2634×	body	1280	valid
2.7s	1905×	body	640	valid
850.0ms	780×	body	320	valid
632.0ms	2313×	body	80	valid
618.0ms	368×	body	160	valid