Details

sample369.0ms

Algorithm

intervals

Results

144.0ms	84×	body	1280	valid
49.0ms	61×	body	640	valid
14.0ms	27×	body	320	valid
11.0ms	70×	body	80	valid
5.0ms	14×	body	160	valid

simplify4.9s

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: 12.8b

localize34.0ms

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)
1.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite149.0ms

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:

90.0ms	(* (/ (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)
35.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series674.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
147.0ms	(pow (sin kx) 2.0)
159.0ms	(pow (sin ky) 2.0)
170.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.2s

Counts

130 → 130

Iterations

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

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize27.0ms

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))

rewrite34.0ms

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:

1.0ms	(hypot (sin ky) (sin kx))
14.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
16.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series792.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(hypot (sin ky) (sin kx))
265.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
368.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify2.1s

Counts

82 → 82

Iterations

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

prune767.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.9b

localize86.0ms

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))))

rewrite64.0ms

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` `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 → 152

Calls

4 calls:

44.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.4s

Counts

4 → 12

Calls

4 calls:

361.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
365.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
318.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
308.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify3.6s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
4	4759
3	1695
2	754
1	322
0	171

prune1.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.9b

localize72.0ms

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))))

rewrite52.0ms

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` `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 → 152

Calls

4 calls:

34.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.3s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
325.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
302.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
327.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify3.3s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
4	4759
3	1695
2	754
1	322
0	171

prune1.5s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 10.9b

regimes2.0s

Accuracy

0% (0.5b remaining)

Error of 9.3b against oracle of 8.7b and baseline of 9.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	14

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.3s	2685×	body	1280	valid
2.4s	1872×	body	640	valid
652.0ms	2332×	body	80	valid
461.0ms	755×	body	320	valid
125.0ms	356×	body	160	valid