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

sample156.0ms

Algorithm

intervals

Results

69.0ms	85×	body	1280	invalid
29.0ms	242×	body	80	valid
19.0ms	37×	body	640	invalid
4.0ms	2×	body	2560	invalid
3.0ms	8×	body	320	invalid
3.0ms	7×	body	320	valid
3.0ms	5×	body	640	valid
2.0ms	8×	body	160	invalid
2.0ms	13×	body	80	invalid
2.0ms	2×	body	1280	valid

simplify473.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4897	36
1	4897	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: 32.0b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(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)))

series90.0ms

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)))
72.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5121	685

prune154.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 20.0b

Counts

70 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sin-sum`

Counts

4 → 49

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
128.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5017	883

prune160.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	59	9	68

Merged error: 19.9b

Counts

68 → 9

localize37.0ms

Local error

Found 4 expressions with local error:

28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
33.1b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `sqrt-prod`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow1/3` `sin-sum` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 54

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
11.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)))) y.im) (* (atan2 x.im x.re) y.re)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
129.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4894	900
1	4894	900

prune180.0ms

Filtered

54 candidates to 66 candidates (-22.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 19.9b

Counts

75 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.1b	(sin (+ (* (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

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

Counts

4 → 57

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt 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)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify49.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4894	737
1	4894	737

prune106.0ms

Filtered

57 candidates to 69 candidates (-21.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	69	9	78

Merged error: 19.9b

Counts

78 → 9

regimes438.0ms

Accuracy

77.3% (3.1b remaining)

Error of 22.4b against oracle of 19.3b and baseline of 32.9b

bsearch109.0ms

Steps

Iters	Range		Point
11	-3.562227136135574e-306	1.368089651932655e-291	2.592194019921e-310

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	145	65
1	145	65

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2105×	body	1280	invalid
878.0ms	7574×	body	80	valid
632.0ms	1258×	body	640	invalid
163.0ms	459×	body	320	invalid
117.0ms	72×	body	2560	invalid
84.0ms	116×	body	1280	valid
74.0ms	151×	body	640	valid
47.0ms	382×	body	80	invalid
45.0ms	194×	body	160	invalid
35.0ms	101×	body	320	valid
14.0ms	58×	body	160	valid

Details

analyze1.5s

sample156.0ms

simplify473.0ms

prune21.0ms

localize24.0ms

rewrite22.0ms

series90.0ms

simplify60.0ms

prune154.0ms

localize28.0ms

rewrite26.0ms

series175.0ms

simplify62.0ms

prune160.0ms

localize37.0ms

rewrite25.0ms

series177.0ms

simplify45.0ms

prune180.0ms

localize26.0ms

rewrite24.0ms

series91.0ms

simplify49.0ms

prune106.0ms

regimes438.0ms

bsearch109.0ms

simplify3.0ms

end0.0ms

sample4.1s

Profiling