Details

sample411.0ms

Algorithm

intervals

Results

58.0ms	73×	body	1280	valid
36.0ms	49×	body	640	valid
28.0ms	257×	body	80	valid
5.0ms	16×	body	320	valid
3.0ms	2×	body	2560	valid
2.0ms	8×	body	160	valid

simplify42.0ms

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

prune18.0ms

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: 33.0b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(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)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
171.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2507	386
4	5002	386

prune353.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	58	10	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 19.6b

Counts

70 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify66.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	148	607
1	303	551
2	643	551
3	1810	551
4	5001	548

prune386.0ms

Filtered

65 candidates to 55 candidates (84.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Merged error: 19.6b

Counts

75 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.8b	(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:

7.0ms	(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)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
150.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
148.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify166.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1512	487
4	4748	486
5	5001	486

prune360.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	50	11	61

Merged error: 19.6b

Counts

61 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.5b	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`cbrt-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `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×	`cube-mult` `unpow-prod-down` `sin-sum` `pow1/3` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

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)))
2.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

series266.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
154.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

simplify81.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 4 (75.0ms)

Iter	Nodes	Cost
0	201	447
1	502	417
2	1079	417
3	2484	417
4	5001	415

prune330.0ms

Filtered

67 candidates to 55 candidates (82.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	67	11	78

Merged error: 19.6b

Counts

78 → 11

regimes418.0ms

Accuracy

74% (3.8b remaining)

Error of 22.7b against oracle of 18.9b and baseline of 33.5b

bsearch320.0ms

Steps

Iters	Range		Point
11	-1.329912432178342e-295	2.0275104442738615e-300	1.9052671912502e-308
9	-3.291493950790207e-124	-1.2824460829140723e-131	-1.7427937851165968e-131

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	69
1	54	69

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2208×	body	1280	valid
849.0ms	7934×	body	80	valid
675.0ms	1379×	body	640	valid
190.0ms	558×	body	320	valid
72.0ms	44×	body	2560	valid
59.0ms	253×	body	160	valid

Details

sample411.0ms

simplify42.0ms

prune18.0ms

localize25.0ms

rewrite23.0ms

series263.0ms

simplify79.0ms

prune353.0ms

localize39.0ms

rewrite68.0ms

series266.0ms

simplify66.0ms

prune386.0ms

localize27.0ms

rewrite27.0ms

series486.0ms

simplify166.0ms

prune360.0ms

localize26.0ms

rewrite17.0ms

series266.0ms

simplify81.0ms

prune330.0ms

regimes418.0ms

bsearch320.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling