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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample139.0ms

Algorithm

intervals

Results

46.0ms	59×	body	1280	invalid
34.0ms	245×	body	80	valid
23.0ms	42×	body	640	invalid
4.0ms	2×	body	2560	invalid
3.0ms	4×	body	1280	valid
2.0ms	6×	body	320	invalid
2.0ms	7×	body	160	invalid
2.0ms	12×	body	80	invalid
1.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify470.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune25.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 32.6b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sin (+ (* (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×	`sin-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	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series89.0ms

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)))
71.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify44.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5069	689

prune130.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 16.8b

Counts

69 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

6.1b	(cbrt (* y.im (atan2 x.im x.re)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cbrt-prod` `sin-sum` `pow1/3`

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* y.im (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)))
6.0ms	(sin (+ (* (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:

22.0ms	(cbrt (* y.im (atan2 x.im x.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4698	637
1	4698	637

prune103.0ms

Filtered

50 candidates to 59 candidates (-18.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	59	5	64

Merged error: 16.8b

Counts

64 → 5

localize36.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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×	`sin-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	(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)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify39.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5054	851

prune99.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	51	5	56

Merged error: 16.8b

Counts

56 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
16.5b	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sin (+ (* (log (neg x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5190	596

prune84.0ms

Filtered

53 candidates to 71 candidates (-34.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Merged error: 10.9b

Counts

76 → 7

regimes459.0ms

Accuracy

73.6% (5.3b remaining)

Error of 18.2b against oracle of 12.9b and baseline of 33.1b

bsearch266.0ms

Steps

Iters	Range	Point
10	-3.58090349319467e-302	2.440688741743257e-305	1.37412629624546e-310
10	-1.11381973783109e-155	-8.308437884770607e-173	-2.8270281610831167e-158
6	-1.980106304771906e-57	-1.3637009136029932e-58	-2.9034009460476134e-58

Iters

Range

Point

-3.58090349319467e-302

2.440688741743257e-305

1.37412629624546e-310

-1.11381973783109e-155

-8.308437884770607e-173

-2.8270281610831167e-158

-1.980106304771906e-57

-1.3637009136029932e-58

-2.9034009460476134e-58

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	121	144
1	121	144

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	2017×	body	1280	invalid
876.0ms	7576×	body	80	valid
667.0ms	1300×	body	640	invalid
155.0ms	440×	body	320	invalid
95.0ms	127×	body	1280	valid
78.0ms	44×	body	2560	invalid
66.0ms	135×	body	640	valid
53.0ms	430×	body	80	invalid
47.0ms	185×	body	160	invalid
38.0ms	103×	body	320	valid
14.0ms	59×	body	160	valid

Details

analyze1.5s

sample139.0ms

simplify470.0ms

prune25.0ms

localize24.0ms

rewrite22.0ms

series89.0ms

simplify44.0ms

prune130.0ms

localize29.0ms

rewrite17.0ms

series88.0ms

simplify77.0ms

prune103.0ms

localize36.0ms

rewrite25.0ms

series172.0ms

simplify39.0ms

prune99.0ms

localize23.0ms

rewrite17.0ms

series59.0ms

simplify67.0ms

prune84.0ms

regimes459.0ms

bsearch266.0ms

simplify3.0ms

end0.0ms

sample4.0s

Profiling