Details

analyze1.5s (18.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample134.0ms (1.7%)

Algorithm

1×

intervals

Results

46.0ms	61×	body	1280	invalid
33.0ms	245×	body	80	valid
22.0ms	44×	body	640	invalid
5.0ms	14×	body	320	invalid
2.0ms	3×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	5×	body	160	invalid
1.0ms	6×	body	80	invalid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify468.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune28.0ms (0.4%)

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

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.re)
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms (0.3%)

Algorithm

1×	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:

9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(* (atan2 x.im x.re) y.re)

series91.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5128	689

prune176.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 19.5b

Counts

70 → 10

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b	(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 (0.5%)

Algorithm

1×	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:

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)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series73.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(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)))
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)))

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4955	688
1	4955	688

prune169.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Merged error: 19.2b

Counts

75 → 10

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms (0.3%)

Algorithm

1×	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:

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

series173.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms	(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)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5054	851

prune137.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	51	10	61

Merged error: 19.2b

Counts

61 → 10

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(* y.re (atan2 x.im x.re))
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

rewrite19.0ms (0.2%)

Algorithm

1×	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:

7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(* y.re (atan2 x.im x.re))

series73.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(* y.re (atan2 x.im x.re))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5128	689

prune112.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	68	10	78

Merged error: 19.2b

Counts

78 → 10

regimes491.0ms (6.1%)

Accuracy

Total 3.4b remaining (15.3%)

Threshold costs 0b (0%)

bsearch52.0ms (0.7%)

Steps

Iters	Range		Point
6	-4.387572817025468e-299	-1.0382332020571772e-299	-1.0480241195093906e-299

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms (0%)

sample3.9s (49.2%)

Algorithm

1×

intervals

Results

1.6s	2116×	body	1280	invalid
861.0ms	7574×	body	80	valid
609.0ms	1236×	body	640	invalid
161.0ms	459×	body	320	invalid
101.0ms	135×	body	1280	valid
66.0ms	137×	body	640	valid
53.0ms	31×	body	2560	invalid
44.0ms	195×	body	160	invalid
43.0ms	373×	body	80	invalid
36.0ms	98×	body	320	valid
14.0ms	56×	body	160	valid

Details

analyze1.5s (18.5%)

sample134.0ms (1.7%)

simplify468.0ms (5.8%)

prune28.0ms (0.4%)

localize25.0ms (0.3%)

rewrite23.0ms (0.3%)

series91.0ms (1.1%)

simplify44.0ms (0.6%)

prune176.0ms (2.2%)

localize29.0ms (0.4%)

rewrite41.0ms (0.5%)

series73.0ms (0.9%)

simplify59.0ms (0.7%)

prune169.0ms (2.1%)

localize30.0ms (0.4%)

rewrite25.0ms (0.3%)

series173.0ms (2.2%)

simplify41.0ms (0.5%)

prune137.0ms (1.7%)

localize25.0ms (0.3%)

rewrite19.0ms (0.2%)

series73.0ms (0.9%)

simplify44.0ms (0.6%)

prune112.0ms (1.4%)

regimes491.0ms (6.1%)

bsearch52.0ms (0.7%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.9s (49.2%)

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