Details

analyze1.6s

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

sample144.0ms

Algorithm

intervals

Results

50.0ms	66×	body	1280	invalid
29.0ms	240×	body	80	valid
20.0ms	39×	body	640	invalid
7.0ms	18×	body	320	invalid
6.0ms	7×	body	1280	valid
5.0ms	8×	body	80	invalid
3.0ms	5×	body	640	valid
2.0ms	7×	body	160	invalid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify461.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune21.0ms

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: 32.8b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (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)))
34.4b	(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)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

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)))
70.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify43.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5029	677

prune140.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 18.9b

Counts

70 → 6

localize20.0ms

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)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

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	(exp (- (* (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)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4925	844
1	4925	844

prune138.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Merged error: 4.2b

Counts

86 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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

series166.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify40.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4993	815
1	4993	815

prune130.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	49	10	59

Merged error: 4.2b

Counts

59 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(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

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 46

Calls

4 calls:

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

series117.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify40.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4993	762
1	4993	762

prune106.0ms

Filtered

52 candidates to 58 candidates (-11.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	58	10	68

Merged error: 4.2b

Counts

68 → 10

regimes461.0ms

Accuracy

50.2% (7.9b remaining)

Error of 11.9b against oracle of 4.0b and baseline of 19.9b

bsearch125.0ms

Steps

Iters	Range		Point
6	3.3760851120800503e+140	2.765816723024936e+141	3.7837062290455336e+140
7	-2.3953943659807407e+70	-4.3068679606691235e+68	-4.396837502534833e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	48
1	73	48

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1923×	body	1280	invalid
898.0ms	7562×	body	80	valid
643.0ms	1282×	body	640	invalid
200.0ms	553×	body	320	invalid
90.0ms	116×	body	1280	valid
77.0ms	152×	body	640	valid
61.0ms	247×	body	160	invalid
48.0ms	397×	body	80	invalid
41.0ms	114×	body	320	valid
14.0ms	56×	body	160	valid

Details

analyze1.6s

sample144.0ms

simplify461.0ms

prune21.0ms

localize26.0ms

rewrite22.0ms

series88.0ms

simplify43.0ms

prune140.0ms

localize20.0ms

rewrite18.0ms

series76.0ms

simplify38.0ms

prune138.0ms

localize30.0ms

rewrite24.0ms

series166.0ms

simplify40.0ms

prune130.0ms

localize32.0ms

rewrite22.0ms

series117.0ms

simplify40.0ms

prune106.0ms

regimes461.0ms

bsearch125.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling