Details

sample487.0ms

Algorithm

intervals

Results

172.0ms	64×	body	1280	valid
58.0ms	257×	body	80	valid
50.0ms	49×	body	640	valid
15.0ms	22×	body	320	valid
10.0ms	3×	body	2560	valid
2.0ms	5×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	85	36
4	220	36
5	1023	36
done	5000	36

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize93.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

14.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (atan2 x.im x.re) y.im)
74.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
306.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.9s

Counts

68 → 68

Iterations

Useful iterations: 3 (865.0ms)

Iter	Nodes	Cost
0	98	845
1	202	787
2	554	701
3	2840	686
done	5001	686

prune926.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.4b

localize121.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum`

Counts

4 → 53

Calls

4 calls:

14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
255.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
284.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

65 → 65

Iterations

Useful iterations: 3 (255.0ms)

Iter	Nodes	Cost
0	73	1155
1	150	1073
2	308	767
3	733	718
4	2354	718
done	5001	718

prune992.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.4b

localize118.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
46.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series971.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
300.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
303.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
301.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

51 → 51

Iterations

Useful iterations: 3 (252.0ms)

Iter	Nodes	Cost
0	71	1005
1	144	975
2	294	851
3	654	842
4	1878	842
done	5001	842

prune967.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.4b

localize168.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
312.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series970.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
301.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
292.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
304.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (292.0ms)

Iter	Nodes	Cost
0	87	1257
1	169	1227
2	328	881
3	775	842
4	2453	842
done	5002	842

prune873.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.4b

regimes931.0ms

Accuracy

73.3% (3.8b remaining)

Error of 23.2b against oracle of 19.3b and baseline of 33.7b

bsearch950.0ms

Steps

Iters	Range	Point
9	-3.3603542884328756e-305	1.1816968720805067e-306	-3.74344114573463e-310
9	-1.2618836190012003e-250	-4.5788347452376576e-256	-5.792029271889603e-251
9	-3.582918381276583e-34	-6.717343741613054e-42	-9.165303032490151e-42

Iters

Range

Point

-3.3603542884328756e-305

1.1816968720805067e-306

-3.74344114573463e-310

-1.2618836190012003e-250

-4.5788347452376576e-256

-5.792029271889603e-251

-3.582918381276583e-34

-6.717343741613054e-42

-9.165303032490151e-42

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	53	244
1	72	244
done	72	244

end0.0ms

sample11.0s

Algorithm

intervals

Results

4.6s	2210×	body	1280	valid
2.7s	7949×	body	80	valid
2.0s	1460×	body	640	valid
437.0ms	562×	body	320	valid
203.0ms	47×	body	2560	valid
93.0ms	211×	body	160	valid