Details

analyze1.5s (19.9%)

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

sample120.0ms (1.6%)

Algorithm

1×

intervals

Results

33.0ms	47×	body	1280	invalid
26.0ms	237×	body	80	valid
14.0ms	31×	body	640	invalid
10.0ms	15×	body	320	invalid
4.0ms	6×	body	1280	valid
4.0ms	9×	body	640	valid
3.0ms	14×	body	160	invalid
1.0ms	11×	body	80	invalid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify510.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune21.0ms (0.3%)

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: 33.8b

Counts

2 → 2

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.8b	(* (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)))
31.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms (0.5%)

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:

16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(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)

series83.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.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)))

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5029	677

prune151.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 20.0b

Counts

70 → 5

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (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)
1.8b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(* (atan2 x.im x.re) y.im)

series77.0ms (1%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
25.0ms	(* (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)))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4925	844
1	4925	844

prune162.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 4.6b

Counts

85 → 7

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow (exp (atan2 x.im x.re)) y.im)
0.5b	(exp (atan2 x.im x.re))
5.8b	(log (pow (exp (atan2 x.im x.re)) y.im))
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(pow (exp (atan2 x.im x.re)) y.im)
2.0ms	(log (pow (exp (atan2 x.im x.re)) y.im))
2.0ms	(exp (atan2 x.im x.re))

series36.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(log (pow (exp (atan2 x.im x.re)) y.im))
13.0ms	(pow (exp (atan2 x.im x.re)) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(exp (atan2 x.im x.re))

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4985	573
1	4985	573

prune150.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	76	7	83

Merged error: 4.6b

Counts

83 → 7

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.8b	(* (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)))
31.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms (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:

7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(* (atan2 x.im x.re) y.im)

series71.0ms (1%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.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)))

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5029	677

prune120.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	69	6	75

Merged error: 4.6b

Counts

75 → 6

regimes395.0ms (5.3%)

Accuracy

Total 5.2b remaining (57.8%)

Threshold costs 0b (0%)

bsearch84.0ms (1.1%)

Steps

Iters	Range		Point
10	-9.460081165269269e-306	2.8864059499213444e-298	-4.4389537412967e-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%)

sample3.6s (48.5%)

Algorithm

1×

intervals

Results

1.3s	1934×	body	1280	invalid
812.0ms	7569×	body	80	valid
583.0ms	1261×	body	640	invalid
173.0ms	519×	body	320	invalid
90.0ms	129×	body	1280	valid
76.0ms	165×	body	640	valid
53.0ms	245×	body	160	invalid
44.0ms	404×	body	80	invalid
28.0ms	87×	body	320	valid
11.0ms	50×	body	160	valid

Details

analyze1.5s (19.9%)

sample120.0ms (1.6%)

simplify510.0ms (6.9%)

prune21.0ms (0.3%)

localize25.0ms (0.3%)

rewrite35.0ms (0.5%)

series83.0ms (1.1%)

simplify45.0ms (0.6%)

prune151.0ms (2%)

localize17.0ms (0.2%)

rewrite19.0ms (0.3%)

series77.0ms (1%)

simplify40.0ms (0.5%)

prune162.0ms (2.2%)

localize21.0ms (0.3%)

rewrite13.0ms (0.2%)

series36.0ms (0.5%)

simplify52.0ms (0.7%)

prune150.0ms (2%)

localize27.0ms (0.4%)

rewrite21.0ms (0.3%)

series71.0ms (1%)

simplify43.0ms (0.6%)

prune120.0ms (1.6%)

regimes395.0ms (5.3%)

bsearch84.0ms (1.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.6s (48.5%)

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