Details

analyze1.4s

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

sample123.0ms

Algorithm

intervals

Results

42.0ms	56×	body	1280	invalid
26.0ms	239×	body	80	valid
17.0ms	34×	body	640	invalid
5.0ms	13×	body	320	invalid
4.0ms	8×	body	640	valid
3.0ms	4×	body	1280	valid
2.0ms	9×	body	160	invalid
2.0ms	15×	body	80	invalid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify507.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4970	36
1	4970	36

prune19.0ms

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: 31.8b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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)))
18.0ms	(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)))

series81.0ms

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)))
62.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify56.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4737	680
1	4737	680

prune150.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 19.6b

Counts

70 → 8

localize15.0ms

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))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.1b	(* (atan2 x.im x.re) y.im)
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

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:

3.0ms	(- (* (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)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
24.0ms	(* (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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5159	896

prune139.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 4.1b

Counts

85 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(cos (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

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)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(cos (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series72.0ms

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

simplify49.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5074	679

prune151.0ms

Filtered

55 candidates to 65 candidates (-18.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	64	11	75

Merged error: 4.0b

Counts

75 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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

series70.0ms

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

simplify54.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4737	680
1	4737	680

prune112.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	68	11	79

Merged error: 4.0b

Counts

79 → 11

regimes545.0ms

Accuracy

81.5% (5.5b remaining)

Error of 8.7b against oracle of 3.2b and baseline of 33.0b

bsearch1.5s

Steps

Iters	Range		Point
10	-1.9469281993079768e-303	2.270033269815668e-298	-3.4130425136327e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	27
1	27	27

end0.0ms

analyze1.2s

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

sample3.5s

Algorithm

intervals

Results

1.3s	1869×	body	1280	invalid
812.0ms	7603×	body	80	valid
605.0ms	1299×	body	640	invalid
173.0ms	524×	body	320	invalid
72.0ms	103×	body	1280	valid
71.0ms	153×	body	640	valid
52.0ms	242×	body	160	invalid
42.0ms	386×	body	80	invalid
32.0ms	97×	body	320	valid
10.0ms	44×	body	160	valid

Details

analyze1.4s

sample123.0ms

simplify507.0ms

prune19.0ms

localize23.0ms

rewrite36.0ms

series81.0ms

simplify56.0ms

prune150.0ms

localize15.0ms

rewrite16.0ms

series72.0ms

simplify46.0ms

prune139.0ms

localize30.0ms

rewrite34.0ms

series72.0ms

simplify49.0ms

prune151.0ms

localize24.0ms

rewrite18.0ms

series70.0ms

simplify54.0ms

prune112.0ms

regimes545.0ms

bsearch1.5s

simplify2.0ms

end0.0ms

analyze1.2s

sample3.5s

Profiling