Details

analyze1.5s

Algorithm

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

sample128.0ms

Algorithm

intervals

Results

41.0ms	58×	body	1280	invalid
31.0ms	241×	body	80	valid
18.0ms	37×	body	640	invalid
8.0ms	22×	body	320	invalid
4.0ms	5×	body	1280	valid
2.0ms	5×	body	640	valid
2.0ms	7×	body	160	invalid
1.0ms	4×	body	320	valid
1.0ms	10×	body	80	invalid
0.0ms	1×	body	160	valid

simplify469.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune28.0ms

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: 33.3b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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

Counts

4 → 56

Calls

4 calls:

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

series92.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5029	677

prune131.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

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: 19.4b

Counts

70 → 5

localize17.0ms

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))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

Algorithm

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:

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

series80.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
27.0ms	(* (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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4931	892
1	4931	892

prune126.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	75	7	82

Merged error: 3.6b

Counts

82 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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

Counts

4 → 56

Calls

4 calls:

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (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)))
56.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify46.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5029	677

prune136.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	68	7	75

Merged error: 3.6b

Counts

75 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm

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×	`cos-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

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

series176.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
57.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
58.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4993	815
1	4993	815

prune84.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	50	8	58

Merged error: 3.6b

Counts

58 → 8

regimes473.0ms

Accuracy

81.8% (5.4b remaining)

Error of 9.0b against oracle of 3.7b and baseline of 33.2b

bsearch76.0ms

Steps

Iters	Range		Point
9	-4.283679741380354e-306	1.2000194640375912e-303	4.1007807237685e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	27
1	59	27

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	1921×	body	1280	invalid
816.0ms	7536×	body	80	valid
631.0ms	1335×	body	640	invalid
177.0ms	539×	body	320	invalid
95.0ms	132×	body	1280	valid
78.0ms	164×	body	640	valid
47.0ms	425×	body	80	invalid
47.0ms	215×	body	160	invalid
38.0ms	116×	body	320	valid
12.0ms	52×	body	160	valid

Details

analyze1.5s

sample128.0ms

simplify469.0ms

prune28.0ms

localize25.0ms

rewrite22.0ms

series92.0ms

simplify45.0ms

prune131.0ms

localize17.0ms

rewrite19.0ms

series80.0ms

simplify50.0ms

prune126.0ms

localize30.0ms

rewrite20.0ms

series78.0ms

simplify46.0ms

prune136.0ms

localize29.0ms

rewrite26.0ms

series176.0ms

simplify41.0ms

prune84.0ms

regimes473.0ms

bsearch76.0ms

simplify2.0ms

end0.0ms

sample3.7s

Profiling