Details

analyze1.5s (18.6%)

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

sample168.0ms (2.1%)

Algorithm

1×

intervals

Results

79.0ms	95×	body	1280	invalid
29.0ms	241×	body	80	valid
19.0ms	37×	body	640	invalid
7.0ms	18×	body	320	invalid
4.0ms	8×	body	640	valid
3.0ms	4×	body	1280	valid
3.0ms	11×	body	160	invalid
1.0ms	10×	body	80	invalid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify495.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune20.0ms (0.2%)

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

localize40.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
28.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms (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:

8.0ms	(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.im)

series87.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
10.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5069	689

prune153.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 21.1b

Counts

70 → 7

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

28.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms (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:

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

series171.0ms (2.1%)

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)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(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)))

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5054	851

prune127.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	50	8	58

Merged error: 21.1b

Counts

58 → 8

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
28.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

rewrite18.0ms (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:

6.0ms	(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	(* (atan2 x.im x.re) y.im)

series73.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5069	689

prune136.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Merged error: 21.1b

Counts

76 → 8

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

12.1b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
28.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms (0.2%)

Algorithm

1×	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:

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

series122.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5144	1134

prune136.0ms (1.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 21.1b

Counts

79 → 9

regimes452.0ms (5.5%)

Accuracy

Total 3.1b remaining (13.5%)

Threshold costs 0b (0%)

bsearch86.0ms (1.1%)

Steps

Iters	Range		Point
8	-2.750531836398237e-307	1.4213517346234429e-306	-3.1791748587786e-310

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%)

sample4.0s (49.3%)

Algorithm

1×

intervals

Results

1.6s	2082×	body	1280	invalid
862.0ms	7554×	body	80	valid
636.0ms	1240×	body	640	invalid
172.0ms	483×	body	320	invalid
107.0ms	144×	body	1280	valid
83.0ms	168×	body	640	valid
57.0ms	35×	body	2560	invalid
48.0ms	390×	body	80	invalid
39.0ms	169×	body	160	invalid
30.0ms	85×	body	320	valid
12.0ms	49×	body	160	valid

Details

analyze1.5s (18.6%)

sample168.0ms (2.1%)

simplify495.0ms (6.1%)

prune20.0ms (0.2%)

localize40.0ms (0.5%)

rewrite22.0ms (0.3%)

series87.0ms (1.1%)

simplify46.0ms (0.6%)

prune153.0ms (1.9%)

localize30.0ms (0.4%)

rewrite24.0ms (0.3%)

series171.0ms (2.1%)

simplify43.0ms (0.5%)

prune127.0ms (1.6%)

localize24.0ms (0.3%)

rewrite18.0ms (0.2%)

series73.0ms (0.9%)

simplify46.0ms (0.6%)

prune136.0ms (1.7%)

localize27.0ms (0.3%)

rewrite20.0ms (0.2%)

series122.0ms (1.5%)

simplify48.0ms (0.6%)

prune136.0ms (1.7%)

regimes452.0ms (5.5%)

bsearch86.0ms (1.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.0s (49.3%)

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