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

sample161.0ms

Algorithm

intervals

Results

66.0ms	79×	body	1280	invalid
29.0ms	246×	body	80	valid
25.0ms	48×	body	640	invalid
7.0ms	4×	body	2560	invalid
5.0ms	14×	body	320	invalid
2.0ms	4×	body	640	valid
1.0ms	6×	body	160	invalid
1.0ms	4×	body	160	valid
1.0ms	7×	body	80	invalid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid

simplify471.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune29.0ms

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: 33.6b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(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.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)))

series89.0ms

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)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
71.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5069	689

prune147.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 17.1b

Counts

70 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(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)))

rewrite25.0ms

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)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
133.0ms	(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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4881	889
1	4881	889

prune140.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	61	7	68

Merged error: 17.1b

Counts

68 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (* y.im (atan2 x.im x.re)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(sin (+ (* (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

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* y.im (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)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (* y.im (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)))
54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4698	637
1	4698	637

prune123.0ms

Filtered

50 candidates to 59 candidates (-18.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Merged error: 17.1b

Counts

66 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
35.3b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

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)))
14.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
134.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4859	889
1	4859	889

prune111.0ms

Filtered

51 candidates to 61 candidates (-19.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	61	7	68

Merged error: 17.1b

Counts

68 → 7

regimes382.0ms

Accuracy

79.3% (3.0b remaining)

Error of 22.5b against oracle of 19.5b and baseline of 33.9b

bsearch79.0ms

Steps

Iters	Range		Point
8	-1.860806577041847e-305	4.3133035984950444e-308	-2.8978419282618e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	2022×	body	1280	invalid
833.0ms	7540×	body	80	valid
666.0ms	1312×	body	640	invalid
147.0ms	415×	body	320	invalid
101.0ms	138×	body	1280	valid
81.0ms	160×	body	640	valid
76.0ms	42×	body	2560	invalid
50.0ms	394×	body	80	invalid
45.0ms	187×	body	160	invalid
35.0ms	100×	body	320	valid
15.0ms	62×	body	160	valid

Details

analyze1.5s

sample161.0ms

simplify471.0ms

prune29.0ms

localize24.0ms

rewrite23.0ms

series89.0ms

simplify45.0ms

prune147.0ms

localize33.0ms

rewrite25.0ms

series182.0ms

simplify50.0ms

prune140.0ms

localize29.0ms

rewrite18.0ms

series87.0ms

simplify76.0ms

prune123.0ms

localize34.0ms

rewrite28.0ms

series181.0ms

simplify68.0ms

prune111.0ms

regimes382.0ms

bsearch79.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling