Details

sample348.0ms

Algorithm

intervals

Results

39.0ms	62×	body	1280	valid
24.0ms	258×	body	80	valid
15.0ms	37×	body	640	valid
5.0ms	18×	body	320	valid
1.0ms	3×	body	160	valid

simplify39.0ms

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

prune33.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 35.0b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(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

4×	`sqrt-div`
2×	`flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`+-commutative` `*-commutative`

Counts

4 → 9

Calls

4 calls:

2.0ms	(* (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)))
10.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify122.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	113	131
1	231	131
2	470	131
3	1138	131
4	3555	131
5	5001	131

prune130.0ms

Filtered

21 candidates to 18 candidates (85.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	16	5	21
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	17	6	23

Merged error: 22.6b

Counts

23 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div`
2×	`flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`+-commutative` `*-commutative`

Counts

4 → 9

Calls

4 calls:

2.0ms	(* (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)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
145.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify124.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	113	131
1	231	131
2	470	131
3	1138	131
4	3555	131
5	5001	131

prune124.0ms

Filtered

21 candidates to 18 candidates (85.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 22.6b

Counts

27 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
15.8b	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

2×	`sin-sum` `sqrt-div` `*-commutative`
1×	`+-commutative` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 7

Calls

4 calls:

2.0ms	(* (atan2 x.im x.re) y.re)
2.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
126.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify126.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	121	100
1	251	98
2	499	98
3	1196	98
4	3760	98
5	5002	98

prune95.0ms

Filtered

19 candidates to 13 candidates (68.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	18	7	25

Merged error: 16.3b

Counts

25 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (* -1 x.re)) y.re)
1.3b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
15.8b	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative`
2×	`sin-sum`
1×	`+-commutative`

Counts

4 → 5

Calls

4 calls:

3.0ms	(* (log (* -1 x.re)) y.re)
2.0ms	(* (atan2 x.im x.re) y.re)
2.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (log (* -1 x.re)) y.re)
16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
134.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify88.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	85	81
1	134	77
2	212	77
3	555	77
4	1338	77
5	5001	77

prune42.0ms

Filtered

17 candidates to 9 candidates (52.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	17	7	24

Merged error: 16.3b

Counts

24 → 7

regimes252.0ms

Accuracy

76.8% (5.4b remaining)

Error of 18.5b against oracle of 13.1b and baseline of 36.3b

bsearch165.0ms

Steps

Iters	Range		Point
10	-2.6393627062331543e-300	2.6427537794451112e-306	2.4499326006478e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	33
1	49	33

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	2118×	body	1280	valid
713.0ms	7925×	body	80	valid
578.0ms	1387×	body	640	valid
152.0ms	533×	body	320	valid
67.0ms	43×	body	2560	valid
46.0ms	246×	body	160	valid