Details

analyze1.5s (20%)

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
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample151.0ms (2%)

Algorithm

1×

intervals

Results

53.0ms	73×	body	1280	invalid
32.0ms	239×	body	80	valid
25.0ms	49×	body	640	invalid
7.0ms	19×	body	320	invalid
4.0ms	5×	body	1280	valid
4.0ms	7×	body	640	valid
2.0ms	9×	body	160	invalid
1.0ms	3×	body	320	valid
1.0ms	7×	body	80	invalid
0.0ms	2×	body	160	valid

simplify481.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune30.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 36.8b

Counts

2 → 1

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
31.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (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)))
3.0ms	(* (atan2 x.im x.re) y.im)

series90.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(* (atan2 x.im x.re) y.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	5029	677

prune134.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 24.2b

Counts

69 → 4

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.0b	(* (atan2 x.im x.re) y.im)
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 65

Calls

4 calls:

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

series74.0ms (1%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
24.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4931	892
1	4931	892

prune147.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	75	6	81

Merged error: 4.0b

Counts

81 → 6

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log x.im) y.re)
1.0b	(* (atan2 x.im x.re) y.im)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

4.0ms	(* (log x.im) y.re)
4.0ms	(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
3.0ms	(* (atan2 x.im x.re) y.im)

series40.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
10.0ms	(* (log x.im) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5146	450

prune100.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 4.0b

Counts

63 → 6

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log (neg x.re)) y.re)
1.0b	(* (atan2 x.im x.re) y.im)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

4.0ms	(* (log (neg x.re)) y.re)
4.0ms	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
3.0ms	(* (atan2 x.im x.re) y.im)

series45.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

27.0ms	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
11.0ms	(* (log (neg x.re)) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	6389	492

prune74.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	57	6	63

Merged error: 4.0b

Counts

63 → 6

regimes442.0ms (5.8%)

Accuracy

Total 5.5b remaining (60.3%)

Threshold costs 0b (0%)

bsearch107.0ms (1.4%)

Steps

Iters	Range		Point
11	-2.742474779525847e-286	2.77114183577462e-295	-3.89342332684725e-310

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms (0%)

sample3.8s (50.1%)

Algorithm

1×

intervals

Results

1.4s	1948×	body	1280	invalid
865.0ms	7549×	body	80	valid
644.0ms	1314×	body	640	invalid
189.0ms	549×	body	320	invalid
102.0ms	138×	body	1280	valid
79.0ms	160×	body	640	valid
53.0ms	228×	body	160	invalid
48.0ms	396×	body	80	invalid
32.0ms	94×	body	320	valid
14.0ms	59×	body	160	valid

Details

analyze1.5s (20%)

sample151.0ms (2%)

simplify481.0ms (6.3%)

prune30.0ms (0.4%)

localize24.0ms (0.3%)

rewrite23.0ms (0.3%)

series90.0ms (1.2%)

simplify46.0ms (0.6%)

prune134.0ms (1.8%)

localize16.0ms (0.2%)

rewrite20.0ms (0.3%)

series74.0ms (1%)

simplify52.0ms (0.7%)

prune147.0ms (1.9%)

localize11.0ms (0.1%)

rewrite12.0ms (0.2%)

series40.0ms (0.5%)

simplify64.0ms (0.8%)

prune100.0ms (1.3%)

localize12.0ms (0.2%)

rewrite12.0ms (0.2%)

series45.0ms (0.6%)

simplify78.0ms (1%)

prune74.0ms (1%)

regimes442.0ms (5.8%)

bsearch107.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.8s (50.1%)

Profiling