Details

sample3.3s

Algorithm

intervals

Results

1.6s	62×	body	1280	valid
190.0ms	256×	body	80	valid
160.0ms	38×	body	640	valid
59.0ms	24×	body	320	valid
12.0ms	10×	body	160	valid
4.0ms	1×	body	2560	valid

simplify11.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (213.0ms)

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize65.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite374.0ms

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:

16.0ms	(* (atan2 x.im x.re) y.im)
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
274.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.3s

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (atan2 x.im x.re) y.im)
118.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
77.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0s	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify10.1s

Counts

68 → 68

Iterations

Useful iterations: 3 (2.9s)

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

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.2b

localize446.0ms

Local error

Found 4 expressions with local error:

28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite383.0ms

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:

182.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
68.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
66.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series3.0s

Counts

4 → 12

Calls

4 calls:

315.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
660.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
1.0s	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
974.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify5.6s

Counts

51 → 51

Iterations

Useful iterations: 3 (722.0ms)

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

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.2b

localize845.0ms

Local error

Found 4 expressions with local error:

33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

48.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
152.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
64.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series3.0s

Counts

4 → 12

Calls

4 calls:

1.1s	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
701.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
319.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
846.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify24.1s

Counts

44 → 44

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	42	1056
1	65	1052
2	86	908
3	141	904
4	465	904
5	4285	904
done	5000	904

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.2b

localize554.0ms

Local error

Found 4 expressions with local error:

33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

33.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series2.2s

Counts

4 → 12

Calls

4 calls:

375.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
586.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
692.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
514.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify19.5s

Counts

44 → 44

Iterations

Useful iterations: 3 (167.0ms)

Iter	Nodes	Cost
0	42	1056
1	65	1052
2	86	908
3	141	904
4	465	904
5	4285	904
done	5000	904

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 19.2b

regimes1.2s

Accuracy

79.7% (2.8b remaining)

Error of 22.6b against oracle of 19.8b and baseline of 33.5b

bsearch812.0ms

Steps

Iters	Range		Point
9	-1.2015403599485584e-302	8.17206264245515e-309	-2.4905017820195e-310

simplify14.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	30	65
1	39	65
2	41	65
3	43	65
done	43	65

end0.0ms

sample45.7s

Algorithm

intervals

Results

18.2s	2292×	body	1280	valid
13.4s	7943×	body	80	valid
9.2s	1416×	body	640	valid
2.4s	564×	body	320	valid
504.0ms	256×	body	160	valid
374.0ms	40×	body	2560	valid