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

sample133.0ms

Algorithm

intervals

Results

43.0ms	58×	body	1280	invalid
28.0ms	239×	body	80	valid
22.0ms	36×	body	640	invalid
4.0ms	11×	body	320	invalid
4.0ms	7×	body	640	valid
4.0ms	2×	body	2560	invalid
3.0ms	8×	body	320	valid
2.0ms	8×	body	160	invalid
2.0ms	14×	body	80	invalid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify479.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune20.0ms

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: 30.6b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.re)
26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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.re)
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:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sin (+ (* (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	5128	689

prune182.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	12	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Merged error: 16.7b

Counts

70 → 13

localize35.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.1b	(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)))

rewrite24.0ms

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)))
11.0ms	(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)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
129.0ms	(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)))

simplify51.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4881	889
1	4881	889

prune190.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	60	14	74

Merged error: 16.6b

Counts

74 → 14

localize37.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
35.1b	(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)))
20.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
130.0ms	(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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4863	882
1	4863	882

prune220.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	65	15	80

Merged error: 16.6b

Counts

80 → 15

localize46.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
35.1b	(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)))

rewrite27.0ms

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)
12.0ms	(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)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)
130.0ms	(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)))

simplify53.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4863	882
1	4863	882

prune167.0ms

Filtered

53 candidates to 66 candidates (-24.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	66	15	81

Merged error: 16.6b

Counts

81 → 15

regimes663.0ms

Accuracy

77% (3.1b remaining)

Error of 22.7b against oracle of 19.6b and baseline of 33.1b

bsearch85.0ms

Steps

Iters	Range		Point
10	-2.4211875433973154e-301	3.030138394093397e-303	-1.6968397933695e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	2010×	body	1280	invalid
868.0ms	7558×	body	80	valid
602.0ms	1206×	body	640	invalid
159.0ms	456×	body	320	invalid
90.0ms	124×	body	1280	valid
84.0ms	167×	body	640	valid
70.0ms	40×	body	2560	invalid
43.0ms	370×	body	80	invalid
41.0ms	176×	body	160	invalid
34.0ms	91×	body	320	valid
14.0ms	60×	body	160	valid

Details

analyze1.5s

sample133.0ms

simplify479.0ms

prune20.0ms

localize25.0ms

rewrite23.0ms

series91.0ms

simplify43.0ms

prune182.0ms

localize35.0ms

rewrite24.0ms

series178.0ms

simplify51.0ms

prune190.0ms

localize37.0ms

rewrite25.0ms

series177.0ms

simplify54.0ms

prune220.0ms

localize46.0ms

rewrite27.0ms

series179.0ms

simplify53.0ms

prune167.0ms

regimes663.0ms

bsearch85.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling