Details

sample5.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 49.816805%

Results

55.0ms	67×	body	1280	invalid
28.0ms	239×	body	80	valid
19.0ms	38×	body	640	invalid
8.0ms	22×	body	320	invalid
4.0ms	8×	body	640	valid
4.0ms	5×	body	1280	valid
2.0ms	16×	body	80	invalid
1.0ms	5×	body	160	invalid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify407.0ms

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

prune15.0ms

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: 32.8b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (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)))
34.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite32.0ms

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)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(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)))

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)))
64.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

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

prune141.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 18.4b

Counts

69 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

4.6b	(cbrt (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)))
34.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (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)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cbrt (atan2 x.im x.re))
5.0ms	(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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	170	414
1	367	380
2	792	377
3	2193	377
4	5002	375

prune119.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 18.4b

Counts

69 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

4.6b	(cbrt (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)))
34.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(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)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (atan2 x.im x.re))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
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)))

simplify69.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (63.0ms)

Iter	Nodes	Cost
0	170	414
1	367	380
2	792	377
3	2193	377
4	5002	375

prune118.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

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

Merged error: 18.4b

Counts

69 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.6b	(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)))
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)))

series167.0ms

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)))
54.0ms	(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)))

simplify60.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

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

prune85.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	48	11	59

Merged error: 18.4b

Counts

59 → 11

regimes504.0ms

Accuracy

76.4% (3.3b remaining)

Error of 22.4b against oracle of 19.1b and baseline of 33.1b

bsearch113.0ms

Steps

Iters	Range		Point
10	-2.39638253738344e-305	4.459492553828564e-299	-1.7419962621888e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample8.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 49.816805%

Results

1.5s	2016×	body	1280	invalid
878.0ms	7560×	body	80	valid
642.0ms	1260×	body	640	invalid
159.0ms	454×	body	320	invalid
98.0ms	136×	body	1280	valid
83.0ms	171×	body	640	valid
66.0ms	36×	body	2560	invalid
47.0ms	407×	body	80	invalid
41.0ms	178×	body	160	invalid
33.0ms	85×	body	320	valid
11.0ms	48×	body	160	valid

Details

sample5.1s

simplify407.0ms

prune15.0ms

localize23.0ms

rewrite32.0ms

series81.0ms

simplify81.0ms

prune141.0ms

localize26.0ms

rewrite15.0ms

series76.0ms

simplify70.0ms

prune119.0ms

localize35.0ms

rewrite15.0ms

series76.0ms

simplify69.0ms

prune118.0ms

localize26.0ms

rewrite24.0ms

series167.0ms

simplify60.0ms

prune85.0ms

regimes504.0ms

bsearch113.0ms

simplify2.0ms

end0.0ms

sample8.8s

Profiling