Details

sample868.0ms

Algorithm

intervals

Results

357.0ms	98×	body	1280	valid
89.0ms	61×	body	640	valid
57.0ms	24×	body	320	valid
19.0ms	64×	body	80	valid
5.0ms	9×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.0b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite28.0ms

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))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
15.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series759.0ms

Counts

3 → 9

Calls

3 calls:

149.0ms	(hypot (sin ky) (sin kx))
249.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
361.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	2001
3	2001
2	1003
1	305
0	133

prune593.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(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))

rewrite38.0ms

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` `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-l/` `-commutative`

Counts

3 → 76

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
12.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
25.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series644.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(hypot (sin ky) (sin kx))
208.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
285.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	2005
3	2005
2	948
1	307
0	135

prune600.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin th) (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

rewrite28.0ms

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))
12.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
13.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series811.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(hypot (sin ky) (sin kx))
297.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
343.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify978.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	874
1	281
0	125

prune571.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.9b

localize29.0ms

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))))

rewrite30.0ms

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:

23.0ms	(* (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))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.7s

Counts

4 → 12

Calls

4 calls:

324.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
311.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
718.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
341.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.5s

Counts

168 → 168

Iterations

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

prune1.2s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.9b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 9.1b against oracle of 8.9b and baseline of 9.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample11.8s

Algorithm

intervals

Results

6.7s	2761×	body	1280	valid
2.7s	1858×	body	640	valid
1.1s	2289×	body	80	valid
747.0ms	762×	body	320	valid
308.0ms	330×	body	160	valid