Details

analyze1.6s

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

sample258.0ms

Algorithm

intervals

Results

27.0ms	240×	body	80	valid
3.0ms	4×	body	1280	valid
3.0ms	5×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	3×	body	320	valid

simplify494.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

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: 32.5b

Counts

2 → 2

localize48.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.re)
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b	(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.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)))

series93.0ms

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)))
75.0ms	(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

prune172.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	10	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	11	70

Merged error: 18.6b

Counts

70 → 11

localize53.0ms

Local error

Found 4 expressions with local error:

4.3b	(cbrt (atan2 x.im x.re))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* y.re (cbrt (atan2 x.im x.re))))))

rewrite18.0ms

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)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* y.re (cbrt (atan2 x.im x.re))))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cbrt (atan2 x.im x.re))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* y.re (cbrt (atan2 x.im x.re))))))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4998	635
1	4998	635

prune133.0ms

Filtered

46 candidates to 61 candidates (-32.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	61	11	72

Merged error: 18.6b

Counts

72 → 11

localize51.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b	(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

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)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
57.0ms	(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)))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5054	851

prune139.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	51	11	62

Merged error: 18.6b

Counts

62 → 11

localize73.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (exp (atan2 x.im x.re)) y.im)
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

3.0ms	(pow (exp (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	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (exp (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)))
57.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* y.re (atan2 x.im x.re))))

simplify73.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4898	746
1	4898	746

prune96.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	70	11	81

Merged error: 18.6b

Counts

81 → 11

regimes480.0ms

Accuracy

77.1% (3.3b remaining)

Error of 22.1b against oracle of 18.9b and baseline of 33.1b

bsearch98.0ms

Steps

Iters	Range		Point
7	-1.7445426909345827e-308	5.808735514183314e-307	-1.58933453831505e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample7.8s

Algorithm

intervals

Results

818.0ms	7566×	body	80	valid
87.0ms	115×	body	1280	valid
79.0ms	157×	body	640	valid
36.0ms	104×	body	320	valid
13.0ms	58×	body	160	valid

Details

analyze1.6s

sample258.0ms

simplify494.0ms

prune20.0ms

localize48.0ms

rewrite22.0ms

series93.0ms

simplify43.0ms

prune172.0ms

localize53.0ms

rewrite18.0ms

series82.0ms

simplify42.0ms

prune133.0ms

localize51.0ms

rewrite27.0ms

series174.0ms

simplify41.0ms

prune139.0ms

localize73.0ms

rewrite19.0ms

series82.0ms

simplify73.0ms

prune96.0ms

regimes480.0ms

bsearch98.0ms

simplify2.0ms

end0.0ms

sample7.8s

Profiling