Details

sample3.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.064087%

Guaranteed chance to sample good point: 64.723486%

Results

58.0ms	72×	body	1280	invalid
28.0ms	236×	body	80	valid
24.0ms	47×	body	640	invalid
5.0ms	7×	body	1280	valid
4.0ms	11×	body	320	invalid
3.0ms	6×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	11×	body	80	invalid
1.0ms	3×	body	160	valid
0.0ms	1×	body	160	invalid

simplify399.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune16.0ms

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: 35.2b

Counts

2 → 1

localize48.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(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)))

rewrite21.0ms

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)))

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)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify85.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune135.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	8	69

Merged error: 21.9b

Counts

69 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

30.8b	(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)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
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

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)))
8.0ms	(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)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

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)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	152	580
1	321	508
2	672	505
3	1724	505
4	5001	504

prune131.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	49	10	59

Merged error: 21.9b

Counts

59 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

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

series215.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify186.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 5 (180.0ms)

Iter	Nodes	Cost
0	75	640
1	119	548
2	183	544
3	474	544
4	1108	544
5	5001	528

prune138.0ms

Filtered

44 candidates to 44 candidates (0.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	39	5	44
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	42	12	54

Merged error: 21.9b

Counts

54 → 12

localize42.0ms

Local error

Found 4 expressions with local error:

33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

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

series218.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms	(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)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify181.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 5 (175.0ms)

Iter	Nodes	Cost
0	75	640
1	119	548
2	183	544
3	474	544
4	1108	544
5	5001	528

prune81.0ms

Filtered

44 candidates to 44 candidates (0.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	44	12	56

Merged error: 21.9b

Counts

56 → 12

regimes708.0ms

Accuracy

77.3% (3.2b remaining)

Error of 22.5b against oracle of 19.2b and baseline of 33.5b

bsearch125.0ms

Steps

Iters	Range		Point
10	-2.39638253738344e-305	2.1492374293308147e-294	-2.57901117131064e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample7.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.064087%

Guaranteed chance to sample good point: 64.723486%

Results

1.5s	2024×	body	1280	invalid
868.0ms	7531×	body	80	valid
619.0ms	1248×	body	640	invalid
164.0ms	471×	body	320	invalid
103.0ms	143×	body	1280	valid
87.0ms	172×	body	640	valid
67.0ms	38×	body	2560	invalid
47.0ms	410×	body	80	invalid
35.0ms	153×	body	160	invalid
34.0ms	99×	body	320	valid
13.0ms	55×	body	160	valid

Details

sample3.5s

simplify399.0ms

prune16.0ms

localize48.0ms

rewrite21.0ms

series88.0ms

simplify85.0ms

prune135.0ms

localize26.0ms

rewrite24.0ms

series168.0ms

simplify63.0ms

prune131.0ms

localize33.0ms

rewrite27.0ms

series215.0ms

simplify186.0ms

prune138.0ms

localize42.0ms

rewrite27.0ms

series218.0ms

simplify181.0ms

prune81.0ms

regimes708.0ms

bsearch125.0ms

simplify2.0ms

end0.0ms

sample7.3s

Profiling