Details

sample168.0ms

Algorithm

intervals

Results

63.0ms	77×	body	1280	valid
33.0ms	253×	body	80	valid
23.0ms	41×	body	640	valid
10.0ms	26×	body	320	valid
3.0ms	8×	body	160	valid
2.0ms	1×	body	2560	valid

simplify680.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	84	36
4	201	36
5	855	36
done	5001	36

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.5b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

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:

4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
75.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts

68 → 68

Iterations

Useful iterations: 3 (138.0ms)

Iter	Nodes	Cost
0	105	860
1	216	797
2	489	703
3	1010	686
4	2008	686
5	4632	686
done	5000	686

prune156.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 19.3b

Counts

70 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(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)))

rewrite41.0ms

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:

5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(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)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(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)))

simplify600.0ms

Counts

65 → 65

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	79	1170
1	164	1083
2	339	771
3	697	718
4	1630	718
done	5000	718

prune143.0ms

Filtered

53 candidates to 65 candidates (-22.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Merged error: 19.3b

Counts

72 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

11.1b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify897.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	102	1535
1	214	1310
2	476	1154
3	1089	1132
4	3033	1132
done	5000	1132

prune154.0ms

Filtered

54 candidates to 71 candidates (-31.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	70	8	78

Merged error: 19.3b

Counts

78 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(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)))

simplify1.1s

Counts

58 → 58

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	77	984
1	160	918
2	326	802
3	669	780
4	1397	780
5	3493	780
done	5001	780

prune151.0ms

Filtered

52 candidates to 58 candidates (-11.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	55	11	66

Merged error: 19.3b

Counts

66 → 11

regimes548.0ms

Accuracy

80.3% (2.9b remaining)

Error of 22.3b against oracle of 19.4b and baseline of 34.0b

bsearch98.0ms

Steps

Iters	Range		Point
9	-1.1320017857953323e-301	8.126837495347253e-308	7.9933606979313e-311

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	39	65
done	39	65

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	2226×	body	1280	valid
945.0ms	7968×	body	80	valid
736.0ms	1433×	body	640	valid
191.0ms	527×	body	320	valid
71.0ms	47×	body	2560	valid
63.0ms	250×	body	160	valid

Details

sample168.0ms

simplify680.0ms

prune20.0ms

localize24.0ms

rewrite33.0ms

series101.0ms

simplify1.4s

prune156.0ms

localize29.0ms

rewrite41.0ms

series84.0ms

simplify600.0ms

prune143.0ms

localize26.0ms

rewrite23.0ms

series138.0ms

simplify897.0ms

prune154.0ms

localize35.0ms

rewrite27.0ms

series142.0ms

simplify1.1s

prune151.0ms

regimes548.0ms

bsearch98.0ms

simplify3.0ms

end0.0ms

sample4.3s

Profiling